Is there a way to solve this without l'hopital's rule?

Answers

Answer 1

The conclusion is that the expression [tex]\lim_{x \to \infty} \frac{6 (2^x) - 1}{5x^2+ 10}[/tex] cannot be solved without the l'hopital's rule,

How to solve the limit expression?

The limit expression is given as:

[tex]\lim_{x \to \infty} \frac{6 (2^x) - 1}{5x^2+ 10}[/tex]

The limit of the expression cannot be solved without l'hopital's rule, because a direct substitution of ∞ for x would result in the following expression ∞/∞

i.e.

[tex]\lim_{x \to \infty} \frac{6 (2^{\infty}) - 1}{5(\infty)^2+ 10} = \frac{\infty}{\infty}[/tex]

So, the best way is to apply the l'hopital's rule.

This is done as follows:

[tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} = \lim_{x \to \infty} \frac{f'(x)}{g'(x)}[/tex]

When the numerator and the denominator are differentiated, we have:

[tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} = \frac{3\ln(2)\cdot 2^{x + 1}}{10x}[/tex]

Further, differentiate

[tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} = \frac{3\ln^2(2)\cdot 2^{x + 1}}{10}[/tex]

Now, we can substitute [tex]\infty[/tex] for x

[tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} = \frac{3\ln^2(2)\cdot 2^{\infty + 1}}{10}[/tex]

Evaluate the numerator

[tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} = \frac{\infty}{10}[/tex]

Evaluate the quotient

[tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} = \infty[/tex]

Hence, the conclusion is that the expression [tex]\lim_{x \to \infty} \frac{6 (2^x) - 1}{5x^2+ 10}[/tex] cannot be solved without the l'hopital's rule

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Related Questions

100 POINTS!!!
Fill in the missing work and justification for step 3 when solving 2(x + 1) = 10.

Step Work Justification
1 2(x + 1) = 10 Given
2 2x + 2 = 10 Distributive Property
3
4 2x = 8 Simplify
5 two times x over two equals eight over two Division Property of Equality
6 x = 4 Simplify

a. 2x + 2 + 2 = 10 + 2; Addition Property of Equality
b. 2x + 2 − 2 = 10 − 2; Subtraction Property of Equality
c. (2x + 2)(2) = 10(2); Multiplication Property of Equality
d. the quantity two times x plus two all over two equals ten over two; Division Property of Equality

Answers

Answer: x = 4

Step-by-step explanation:

2(x+1)=10

Distributive properties

a*(b+c)=(a*b)+(a*c)

Using distributive properties

Then

2*(x+1)=(2*x)+(2*1)

2*(x+1)=2x+2

Now, commutative properties

a*b=b*a

Addition is cumulative

a+(-b)=(-b)+a

Therefore applying to 2x+2

2x+2+(-2)=2x+(-2)+2

Then, applying to the equation

2x+2+(-2)=10+(-2), +×-=-

2x+2 -2=10-2

2x=8

Using division properties

ax=b

If a is none zero

Then ax/a=b/a

Therefore x=b/a

Applying that to 2x=8

2x=8. Divide both side by 2 which is none zero

2x/2= 8/2

x=4

Option B

Subtraction Property of equality

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Answer:

2x + 2 − 2 = 10 − 2; Subtraction Property of Equality

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Can anyone describe the errors with the problems? For example the first answer is they did not distribute the negative

Answers

Yes they put that over they’re

Answer:

see image

Step-by-step explanation:

The output of a relation is the difference of three times the input and five. Select the correct answer from each drop-down menu. The equation that represents this relation is . The relation a function. If the domain of the relation is x > 2, the range of the relation is y > .

Answers

Answer:

The equation that represents this relation is [tex]y = 3x - 5[/tex].

The relation is a function.

If the domain of the relation is x > 2, the range of the relation is [tex]y >1[/tex]

Step-by-step explanation:

Given

Output = 3 * Input - 5

Required

Complete the gap

Solving (a):The equation for the relation.

Let

[tex]x \to[/tex] input

[tex]y \to[/tex] output

The relation is:

[tex]y = 3 * x - 5[/tex]

[tex]y = 3x - 5[/tex]

Solving (b): Is the relation, a function?

Yes; Because every value of x has a distinct value in 7

Solving (c): The range:

Domain: [tex]x > 2[/tex]

Substitute 2 for x in [tex]y = 3x - 5[/tex]

[tex]y =3 * 2 - 5[/tex]

[tex]y =6 - 5[/tex]

[tex]y =1[/tex]

The range is:

[tex]y >1[/tex]

Answer:

The equation that represents this relation is [ y= 3x - 5 ]

The relation [ is ] a function.

If the domain of the relation is x > 2, the range of the relation is y > [ 1 ].

Step-by-step explanation:

The output, y, of a relation, is the difference of three times the input, or 3x, and 5. So, y = 3x − 5.

Substituting any x-value from the domain into the equation will result in exactly one value of y, so the relation is a function.

To find the range of the relation, given the domain, substitute the boundary point of the domain into the function equation:

When x = 2, y = 3(2) − 5 = 6 − 5 = 1.

Because substituting values of x that are greater than 2 will result in values of y that are greater than 1, the range of the relation is y > 1.

Hope this helps !!

I need help ASAP!!! Please explain your answer

Answers

Answer:

804.2 km³

Step-by-step explanation:

Volume of a cylinder: πr²h

r = radius, h = height

[tex]\pi r^2h\\\pi(8)^2(4)\\\pi(64)(4)\\\pi(256)\\804.2[/tex]

Find the length of the third side. If necessary, round to the nearest tenth. 16 12

Answers

Answer:

Step-by-step explanation:

Use the Pythagorean theorem. a^2+b^2=c^2

12^2+16^2=c^2

144+256=c^2

400=c^2

20=c

Suppose Cab Company A charges a flat fee of $4.50 plus an additional $0.25/mile. Cab Company B charges a flat fee of $1 plus an additional $0.75/mile.

First, define variables. Then write two equations: one equation will represent the cost of choosing Cab Company A, and the other equation will represent the cost of choosing Cab Company B.

Answers

Hope this helps!

Could you go to my profile and go to the social studies questions, should be for 7 points, please help with all questions! Giving brainliest!

The graph of a linear relation passes through the point (-2,7) and has a slope of 1/6.
Determine an equation for this linear relation in slope intercept form.

Answers

Answer:

Step-by-step explanation:

eq. of any line withslope 1/6 is

y=1/6x+c

∵ it passes through (-2,7)

so 7=1/6(-2)+c

c=7+1/3=22/3

eq. of line is

y=1/6x+22/3

Answer:

y = 1/6x + 7 1/3

Step-by-step explanation:

Slope intercept form is y=mx+b where m is the slope and b is the y intercept

y = 1/6x+b

Substitute the point into the equation

7 = 1/6(-2)+b

7 = -1/3+b

Add 1/3 to each side

7 1/3 = b

y = 1/6x + 7 1/3

Triangles ABC and XYZ are similar. Find side x.

Answers

Answer:

x=6

Step-by-step explanation:

side AB is proportional to side XY

side AC is proportional to side XZ

Since we know side AB and side XY are proportional to each other, if we divide side AB by side XY, we can find the size difference...

12 / 4 = 3

The smaller triangle is 3 times smaller than the bigger triangle so we can find side XZ by dividing side AC by 3...

18 / 3 = 6

x = 6

The measure of the length of x is 9 units.

What are similar triangles?

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is indicated here by the symbol "≈".

Given triangles ABC ≈ XYZ

for similar triangles, corresponding sides are proportionately equal and corresponding angles are congruent,

so AB/XY = AC/XZ = BC/YZ

substitute the values

12/4 = 18/x = 9/YZ

12/4 = 18/x

x= 9 units

Hence the value of x is 9 units.

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Can someone help me with 1-5 and create problems for 6-10

Answers

The problem is that you need to subtract 15÷42 would get you 74 cherry pie will be a cantaloupe into a torch a computer is a wiring device that could help you in life the answer is 82

Given that E=MC find E when M=20 and C =2.5

Answers

Answer:

50 or 125

Step-by-step explanation:

if u want E=MC then it would be 20 ×2.5=50

if u what to find E=MC² then it would be 20×2.5×2.5 =125

ACCORDING TO ME THIS SHOULD BE THE ANSWER, BUT NOT QUITE SURE ABOUT THIS.

Answer:

E = 50

Step-by-step explanation:

If M=20 and C=2.5, replace the letters in the equation with their numerical values so E=20*2.5

20*2.5 = 50

thus E=50

What is the value of the expression 3y−z
y+5z
when y = 6 and z = 2?

Answers

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\text{Question \#1}[/tex]

[tex]\huge\textsf{3y - z}[/tex]

[tex]\huge\textsf{= 3(6) - 2}[/tex]

[tex]\huge\textsf{= 18 - 2}[/tex]

[tex]\huge\textsf{= 16}[/tex]

[tex]\boxed{\boxed{\huge\textsf{Answer: 16}}}\huge\checkmark[/tex]

[tex]\huge\text{Question \#2}[/tex]

[tex]\huge\textsf{y + 5z}[/tex]

[tex]\huge\textsf{= 6 + 5(2)}[/tex]

[tex]\huge\textsf{= 6 + 10}[/tex]

[tex]\huge\textsf{= 16}[/tex]

[tex]\boxed{\boxed{\huge\textsf{Answer: 16}}}\huge\checkmark[/tex]

[tex]\huge\textsf{\boxed{\star\underline{\underline{16 = 16}}\star}\star}[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Is -626 an integer ? If yes, why.

Answers

Answer:

Step-by-step explanation:

Because intergerss are there positive opposite and its negative

Answer and Step-by-step explanation:

-626 is an integer because it is a whole number, not a fraction.

Integers can be both positive and negative numbers. What can't be an integer are fractions and decimals.

#teamtrees #PAW (Plant And Water)

I hope this helps!

A car of 1000 kg starts to move from rest and travels a distance of 150 m in 10 second. How much force is needed?

Answers

Initial velocity=u=0m/sDistance=s=150mTime=t=10sAcceleration=a

Using second equation of kinematics

[tex]\\ \sf\longmapsto s=ut+\dfrac{1}{2}at^2[/tex]

[tex]\\ \sf\longmapsto 150=0(10)+\dfrac{1}{2}a(10)^2[/tex]

[tex]\\ \sf\longmapsto 150=\dfrac{1}{2}\times 100a[/tex]

[tex]\\ \sf\longmapsto 50a=150[/tex]

[tex]\\ \sf\longmapsto a=\dfrac{150}{50}[/tex]

[tex]\\ \sf\longmapsto a=3m/s^2[/tex]

Mass=m=1000kgForce=F

Using newtons second law

[tex]\\ \sf\longmapsto F=ma[/tex]

[tex]\\ \sf\longmapsto F=1000(3)[/tex]

[tex]\\ \sf\longmapsto F=3000N[/tex]

Use the parabola tool to graph the quadratic function
f(x)= -1/2x^2 + 7
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.

Answers

Answer:

That's the graph for the function f(x)= -1/2 x^2 + 7

The vertex is f(0) = 7

PLEASE ANSWER ASAP

Select the correct answer.
Solve the rational equation.

A.
x = 15
B.
x = 10
C.
x = 3
D.
x = -18

Answers

Answer:

D: x = -18

Step-by-step explanation:

A good way to solve this it to input all options until you find the one that fits for both options.

Option A :

15 + 6 / 15 - 3 = 21 / 12 or 7/4

So this one doesn't work.

Option B :

10 + 6 / 10 - 3 = 16 / 7

So this one also doesn't work.

Option C:

3 + 6 / 3 - 3 = 9 / 0 which is 0 by the laws of dividing by zero.

This one also doesn't work leaving only one option.

Option D:

-18 + 6 / -18 - 3 = -12 / -21 or 4 / 7

And by solving we can find out we did our work correctly and get our answer.

Can i please get this answered

Answers

Answer:

0 is the answer . The explanation is in the attachment .

Need help with this pls help

Answers

Answer:

Step-by-step explanation:

Find an equation of the line through the given points right the answer and slope intercept form

Answers

Answer:

equation is y = 2-x

Step-by-step explanation:

x1 = -3

y1 = 5

x2 = 4

y2 = -2

now

m(slope) = rise/run =(y2-y1)/(x2-x1) =(-2-5)/(4+3) = -7/7 = -1

so m = -1

now

y =mx + b

-2 = -1×4 + b

or, -2 = -4 +b

so, b = 2

now

y = mx+b

y = -1x + 2

or, y = 2-x

Determine the slope for the equation.

[tex]y = \frac{6}{5} x - 4[/tex]
Steps would help tremendously because I wanna remember how to do these :)

Answers

Answer:

slope = [tex]\frac{6}{5}[/tex]

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{6}{5}[/tex] x - 4 ← is in slope- intercept form

with slope m = [tex]\frac{6}{5}[/tex]

Answer:

6/5

Step-by-step explanation:

this equation is already in the slope intercept form, meaning the slope (gradient)is the coefficient of x( the number before x). in this case it's 6/5.

I hope this helps

help me with it please with steps

class 9 trigonometry

Answers

secA=√2

secA=sec45

A=45°

3cos²45+5tan²45/ 4tan²A-sin²45

= 3(1/√3)²+5(1)² / 4(1)²-(1/√2)²

=3/2+5/4-1/2

=13/7

Answer:

[tex]\frac{13}{7}[/tex]

Step-by-step explanation:

Using the identities

cos x =[tex]\frac{1}{secx}[/tex] , sin²x = 1 - cos²x

tan²x = sec²x - 1

Given

[tex]\frac{3cos^2A+5tan^2A}{4tan^2A-sin^2A}[/tex]

= [tex]\frac{3(\frac{1}{sec^2A}+5(sec^2A-1) }{4(sec^2A -(1-cos^2A)}[/tex]

= [tex]\frac{3.(\frac{1}{\sqrt{2})^2 } +5((\sqrt{2})^2-1) }{4((\sqrt{2})^2-1)-(1-(\frac{1}{\sqrt{2} })^2 }[/tex]

= [tex]\frac{\frac{3}{2}+5(2-1) }{4(2-1)-(1-\frac{1}{2} )}[/tex]

= [tex]\frac{\frac{3}{2} +5}{4-\frac{1}{2} }[/tex]

= [tex]\frac{\frac{13}{2} }{\frac{7}{2} }[/tex]

= [tex]\frac{13}{2}[/tex] × [tex]\frac{2}{7}[/tex]

= [tex]\frac{13}{7}[/tex]

the length of a rectangular box is 8cm. If its diagonal is 10cm. Find its width

Answers

Answer:

Step-by-step explanation:

The diagonal of this rectangular box serves as the hypotenuse of the 2 right triangles that exist within this rectangle. The length is one leg, the hypotenuse is...well, the hypotenuse, so we need to use Pythagorean's Theorem to find the missing leg.

[tex]10^2=8^2+x^2[/tex] and

[tex]100-64=x^2[/tex] and

[tex]x^2=36[/tex] so

x = 6. The width is 6.

What is the height of an iscocles trapizoid, if the lengths of its bases are 5m and 11m and the length of a leg is 4m?

Answers

Answer:

x=√5

Step-by-step explanation:

Use the pythagorean theorem

What is the result of rounding 8,888,888 to the nearest ten?

Answers

Answer:

8,888,890

Step-by-step explanation:

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Select All the correct answers

Select all the statements that are true for the following systems of equations.

System A
2x-3y=4
4x.y = 18

System B
3x - 4y 5
y = 5x + 3

System C
2x-3y - 4
12x-3y 54

1. All three systems have different solutions.

2. Systems A and B have different solutions

3. Systems A and C have the same solution

4. Systems B and C have the same solution

5. System C simplifies to
2x - 3y = 4 and 4x - y = 18 by dividing the second equation by three

Answers

Answer:

Step-by-step explanation:

kjddhllkfewtuikkbccjg

128 is the product of hectors score and 8

Fastest answer will be the brainliest

Answers

Answer:

The equation would be 8h= 128

Step-by-step explanation:

Answer:

Step-by-step explanation:

128=8h

When you divide both sides by 8, you end up with:

3.What mathematical property is used to get the resulting
expression for each line? Complete the table below.
Line 1: (7 + 10x) + 3
Line 2:
(10x + 7) + 3
Line 3:
10x + (7 + 3)
Line 4:
10x + 10

Answers

Answer:

what is the condition of loss ?1)sp>mp 2)CP>sp 3) sp>CP 4)mp>spThe UN has 4 main purposesTo keep peace throughout the world;To develop friendly relations among nations;To help nations work together to improve the lives of poor people, to conquer hunger, disease and illiteracy, and to encourage respect for each other’s rights and freedoms;To be a centre for harmonizing the actions of nations to achieve these goals

Principles of United Nations

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These principles include the equality and self-determination of nations, respect of human rights and fundamental freedoms and the obligation of member countries to obey the Charter, to cooperate with the UN Security Council and to use peaceful means to resolve conflicts.

https://en.m.wikipedia.org › wiki

Chapter I of the United Nations Charter - Wikipedia

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About featured snippets

Answers

a:2 and b:5
an:2*5:10

ab=5×2ab=10answer is option c

please mark this answer as brainlist

PLEASE HURRY

A. 70.8 ft^2
B. 69.1 ft^2
C. 65.8 ft^2
D. 73.6 ft^2

Answers

Answer:

D. 73.6 ft^2

Step-by-step explanation:

Using trigonometry to get our answer: (we can use SAS to find the area)

A = 0.5 * side a (10ft) * side b (16ft) * sin(67)

A = 80 ft * sin(67)

A = 73.64 ft

Simplify

Help me please

Answers

Answer:

[tex]\frac{-27b^{6}}{c^{18}}[/tex]

Step-by-step explanation:

first distribute the ^3, -3^3=-27, for the variables, (x^y)^3=x^(3y) so (b^2)^3=b^6 and (c^-6)^3=c^-18. now we have [tex]-27b^{6}c^{-18}[/tex]. Next we have to get rid of the negative in c^-18. x^-y=1/x^y so c^-18=[tex]\frac{1}{c^{18}}[/tex], plug it in and you get [tex]\frac{-27b^{6}}{c^{18}}[/tex]

Valeria purchases a can of chicken noodle soup and a can of tomato soup. The can of chicken noodle soup has a height of 4 inches and a radius of 2 inches. What is the volume of the can of chicken noodle soup?
Use ≈3.14 and round your answer to the nearest whole number.
The can of tomato soup has the same volume, but a radius of 2.5 inches. What is the height of the can of tomato soup?
Use ≈3.14 and round your answer to the nearest tenth.

Questions

Answers

Answer:

The height of the tomato soup can is 2.6 in.

Step-by-step explanation:

"The can of chicken noodle soup has a height of 4 inches and a radius of 2 inches."

We can find the volume of this can.

V = pi r² h

V = 3.14 * (2 in.)² * (4 in.)

V = 50.24 in.³

"The can of tomato soup has the same volume, but a radius of 2.5 inches."

Now we know the volume of the can, so we can find the height, h.

V = pi r² h

50.24 in.³ = 3.14 * (2.5 in.)² * h

50.24 in.³ = 19.625 in.² * h

h = (50.24 in.³)/(19.625 in.²)

h = 2.56 in.

Answer: The height of the tomato soup can is 2.6 in.

Answer:

:Volume of can of chicken noodle soup=50.24inch^3

:Height of can of tomato soup=2.56inches

Step-by-step explanation:

CHICKEN NOODLE SOUP :height=4inches

:radius=2inches

[ V=πr2h]

V=(3.14×2×2×4)=50.14

Now, Volume is same of both the can.

Volume of can of tomato soup=50.24;radius=2.5inches;

Height of can of tomato soup,

50.24=(3.14×2.5×2.5×h)

50.24=19.625h

h=50.24/19.625

=2.56inches

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