The value of the expression lim w → 1 r ( w ) , where r ( w ) = ( 1 − w ) − 4 . Also estimate the value of function 0.1 and 0.01 above and below the limiting argument.

Question

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Answer 1

Question

Chapter 2.3, Problem 19E

To determine

To calculate: The value of the expression limw→1r(w) , where r(w)=(1−w)−4 . Also estimate the value of function 0.1 and 0.01 above and below the limiting argument.

Expert Solution & Answer

Answer to Problem 19E

The value of the expression limw→1r(w)cannot be estimated, value of function 0.1 and 0.01 above and below the limiting argument are r(0.9)=10000 , r(1.1)=−10000 , r(0.99)=1.0×108 and r(1.01)=−1.0×108 .

Explanation of Solution

Given information:

The function r(w)=(1−w)−4 .

Formula used:

If a function f is continuous at a point say a then limx→af(x) is the value of the function at that point that is limx→af(x)=f(a) , plug the limit in the function to evaluate the value.

Calculation:

Consider the provided function, r(w)=(1−w)−4 .

The value of the expression limw→1r(w) is evaluated when w is substitute as 1 in the expression r(w)=(1−w)−4 ,

limw→1r(w)=limw→1(1−w)−4=(1−1)−4=0−4

The limit cannot be estimated.

The value of the function r(w)=(1−w)−4 , 0.1 below the limiting argument that is w=0.9 ,

r(0.9)=(1−0.9)−4=10000

The value of the function r(w)=(1−w)−4 , 0.1 above the limiting argument that is w=1.1 ,

r(1.1)=(1−1.1)−4=−10000

The value of the function r(w)=(1−w)−4 , 0.01 below the limiting argument that is w=0.99 ,

r(0.99)=(1−0.99)−4=1.0×108

The value of the function r(w)=(1−w)−4 , 0.01 above the limiting argument that is w=1.01 ,

r(1.01)=(1−1.01)−4=−1.0×108

Thus, the value of the expression limw→1r(w) cannot be estimated, value of function 0.1 and 0.01 above and below the limiting argument are r(0.9)=10000 , r(1.1)=−10000 , r(0.99)=1.0×108 and r(1.01)=−1.0×108 .

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Answer 2

Question

Chapter 2.3, Problem 19E

To determine

To calculate: The value of the expression limw→1r(w) , where r(w)=(1−w)−4 . Also estimate the value of function 0.1 and 0.01 above and below the limiting argument.

Expert Solution & Answer

Answer to Problem 19E

The value of the expression limw→1r(w)cannot be estimated, value of function 0.1 and 0.01 above and below the limiting argument are r(0.9)=10000 , r(1.1)=−10000 , r(0.99)=1.0×108 and r(1.01)=−1.0×108 .

Explanation of Solution

Given information:

The function r(w)=(1−w)−4 .

Formula used:

If a function f is continuous at a point say a then limx→af(x) is the value of the function at that point that is limx→af(x)=f(a) , plug the limit in the function to evaluate the value.

Calculation:

Consider the provided function, r(w)=(1−w)−4 .

The value of the expression limw→1r(w) is evaluated when w is substitute as 1 in the expression r(w)=(1−w)−4 ,

limw→1r(w)=limw→1(1−w)−4=(1−1)−4=0−4

The limit cannot be estimated.

The value of the function r(w)=(1−w)−4 , 0.1 below the limiting argument that is w=0.9 ,

r(0.9)=(1−0.9)−4=10000

The value of the function r(w)=(1−w)−4 , 0.1 above the limiting argument that is w=1.1 ,

r(1.1)=(1−1.1)−4=−10000

The value of the function r(w)=(1−w)−4 , 0.01 below the limiting argument that is w=0.99 ,

r(0.99)=(1−0.99)−4=1.0×108

The value of the function r(w)=(1−w)−4 , 0.01 above the limiting argument that is w=1.01 ,

r(1.01)=(1−1.01)−4=−1.0×108

Thus, the value of the expression limw→1r(w) cannot be estimated, value of function 0.1 and 0.01 above and below the limiting argument are r(0.9)=10000 , r(1.1)=−10000 , r(0.99)=1.0×108 and r(1.01)=−1.0×108 .

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Answer 3

Question

Chapter 2.3, Problem 19E

To determine

To calculate: The value of the expression limw→1r(w) , where r(w)=(1−w)−4 . Also estimate the value of function 0.1 and 0.01 above and below the limiting argument.

Expert Solution & Answer

Answer to Problem 19E

The value of the expression limw→1r(w)cannot be estimated, value of function 0.1 and 0.01 above and below the limiting argument are r(0.9)=10000 , r(1.1)=−10000 , r(0.99)=1.0×108 and r(1.01)=−1.0×108 .

Explanation of Solution

Given information:

The function r(w)=(1−w)−4 .

Formula used:

If a function f is continuous at a point say a then limx→af(x) is the value of the function at that point that is limx→af(x)=f(a) , plug the limit in the function to evaluate the value.

Calculation:

Consider the provided function, r(w)=(1−w)−4 .

The value of the expression limw→1r(w) is evaluated when w is substitute as 1 in the expression r(w)=(1−w)−4 ,

limw→1r(w)=limw→1(1−w)−4=(1−1)−4=0−4

The limit cannot be estimated.

The value of the function r(w)=(1−w)−4 , 0.1 below the limiting argument that is w=0.9 ,

r(0.9)=(1−0.9)−4=10000

The value of the function r(w)=(1−w)−4 , 0.1 above the limiting argument that is w=1.1 ,

r(1.1)=(1−1.1)−4=−10000

The value of the function r(w)=(1−w)−4 , 0.01 below the limiting argument that is w=0.99 ,

r(0.99)=(1−0.99)−4=1.0×108

The value of the function r(w)=(1−w)−4 , 0.01 above the limiting argument that is w=1.01 ,

r(1.01)=(1−1.01)−4=−1.0×108

Thus, the value of the expression limw→1r(w) cannot be estimated, value of function 0.1 and 0.01 above and below the limiting argument are r(0.9)=10000 , r(1.1)=−10000 , r(0.99)=1.0×108 and r(1.01)=−1.0×108 .

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Answer 4

Question

Chapter 2.3, Problem 19E

To determine

To calculate: The value of the expression limw→1r(w) , where r(w)=(1−w)−4 . Also estimate the value of function 0.1 and 0.01 above and below the limiting argument.

Expert Solution & Answer

Answer to Problem 19E

The value of the expression limw→1r(w)cannot be estimated, value of function 0.1 and 0.01 above and below the limiting argument are r(0.9)=10000 , r(1.1)=−10000 , r(0.99)=1.0×108 and r(1.01)=−1.0×108 .

Explanation of Solution

Given information:

The function r(w)=(1−w)−4 .

Formula used:

If a function f is continuous at a point say a then limx→af(x) is the value of the function at that point that is limx→af(x)=f(a) , plug the limit in the function to evaluate the value.

Calculation:

Consider the provided function, r(w)=(1−w)−4 .

The value of the expression limw→1r(w) is evaluated when w is substitute as 1 in the expression r(w)=(1−w)−4 ,

limw→1r(w)=limw→1(1−w)−4=(1−1)−4=0−4

The limit cannot be estimated.

The value of the function r(w)=(1−w)−4 , 0.1 below the limiting argument that is w=0.9 ,

r(0.9)=(1−0.9)−4=10000

The value of the function r(w)=(1−w)−4 , 0.1 above the limiting argument that is w=1.1 ,

r(1.1)=(1−1.1)−4=−10000

The value of the function r(w)=(1−w)−4 , 0.01 below the limiting argument that is w=0.99 ,

r(0.99)=(1−0.99)−4=1.0×108

The value of the function r(w)=(1−w)−4 , 0.01 above the limiting argument that is w=1.01 ,

r(1.01)=(1−1.01)−4=−1.0×108

Thus, the value of the expression limw→1r(w) cannot be estimated, value of function 0.1 and 0.01 above and below the limiting argument are r(0.9)=10000 , r(1.1)=−10000 , r(0.99)=1.0×108 and r(1.01)=−1.0×108 .

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Answer 5

Chapter 2.3, Problem 19E

To determine

To calculate: The value of the expression limw→1r(w) , where r(w)=(1−w)−4 . Also estimate the value of function 0.1 and 0.01 above and below the limiting argument.

Expert Solution & Answer

Answer to Problem 19E

The value of the expression limw→1r(w)cannot be estimated, value of function 0.1 and 0.01 above and below the limiting argument are r(0.9)=10000 , r(1.1)=−10000 , r(0.99)=1.0×108 and r(1.01)=−1.0×108 .

Explanation of Solution

Given information:

The function r(w)=(1−w)−4 .

Formula used:

If a function f is continuous at a point say a then limx→af(x) is the value of the function at that point that is limx→af(x)=f(a) , plug the limit in the function to evaluate the value.

Calculation:

Consider the provided function, r(w)=(1−w)−4 .

The value of the expression limw→1r(w) is evaluated when w is substitute as 1 in the expression r(w)=(1−w)−4 ,

limw→1r(w)=limw→1(1−w)−4=(1−1)−4=0−4

The limit cannot be estimated.

The value of the function r(w)=(1−w)−4 , 0.1 below the limiting argument that is w=0.9 ,

r(0.9)=(1−0.9)−4=10000

The value of the function r(w)=(1−w)−4 , 0.1 above the limiting argument that is w=1.1 ,

r(1.1)=(1−1.1)−4=−10000

The value of the function r(w)=(1−w)−4 , 0.01 below the limiting argument that is w=0.99 ,

r(0.99)=(1−0.99)−4=1.0×108

The value of the function r(w)=(1−w)−4 , 0.01 above the limiting argument that is w=1.01 ,

r(1.01)=(1−1.01)−4=−1.0×108

Thus, the value of the expression limw→1r(w) cannot be estimated, value of function 0.1 and 0.01 above and below the limiting argument are r(0.9)=10000 , r(1.1)=−10000 , r(0.99)=1.0×108 and r(1.01)=−1.0×108 .

Answer 6

Chapter 2.3, Problem 19E

To determine

To calculate: The value of the expression limw→1r(w) , where r(w)=(1−w)−4 . Also estimate the value of function 0.1 and 0.01 above and below the limiting argument.

Expert Solution & Answer

Answer to Problem 19E

The value of the expression limw→1r(w)cannot be estimated, value of function 0.1 and 0.01 above and below the limiting argument are r(0.9)=10000 , r(1.1)=−10000 , r(0.99)=1.0×108 and r(1.01)=−1.0×108 .

Explanation of Solution

Given information:

The function r(w)=(1−w)−4 .

Formula used:

If a function f is continuous at a point say a then limx→af(x) is the value of the function at that point that is limx→af(x)=f(a) , plug the limit in the function to evaluate the value.

Calculation:

Consider the provided function, r(w)=(1−w)−4 .

The value of the expression limw→1r(w) is evaluated when w is substitute as 1 in the expression r(w)=(1−w)−4 ,

limw→1r(w)=limw→1(1−w)−4=(1−1)−4=0−4

The limit cannot be estimated.

The value of the function r(w)=(1−w)−4 , 0.1 below the limiting argument that is w=0.9 ,

r(0.9)=(1−0.9)−4=10000

The value of the function r(w)=(1−w)−4 , 0.1 above the limiting argument that is w=1.1 ,

r(1.1)=(1−1.1)−4=−10000

The value of the function r(w)=(1−w)−4 , 0.01 below the limiting argument that is w=0.99 ,

r(0.99)=(1−0.99)−4=1.0×108

The value of the function r(w)=(1−w)−4 , 0.01 above the limiting argument that is w=1.01 ,

r(1.01)=(1−1.01)−4=−1.0×108

Thus, the value of the expression limw→1r(w) cannot be estimated, value of function 0.1 and 0.01 above and below the limiting argument are r(0.9)=10000 , r(1.1)=−10000 , r(0.99)=1.0×108 and r(1.01)=−1.0×108 .

Answer 7

Chapter 2.3, Problem 19E

To determine

To calculate: The value of the expression limw→1r(w) , where r(w)=(1−w)−4 . Also estimate the value of function 0.1 and 0.01 above and below the limiting argument.

Answer 8

Expert Solution & Answer

Answer to Problem 19E

The value of the expression limw→1r(w)cannot be estimated, value of function 0.1 and 0.01 above and below the limiting argument are r(0.9)=10000 , r(1.1)=−10000 , r(0.99)=1.0×108 and r(1.01)=−1.0×108 .

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

Given information:

The function r(w)=(1−w)−4 .

Formula used:

If a function f is continuous at a point say a then limx→af(x) is the value of the function at that point that is limx→af(x)=f(a) , plug the limit in the function to evaluate the value.

Calculation:

Consider the provided function, r(w)=(1−w)−4 .

The value of the expression limw→1r(w) is evaluated when w is substitute as 1 in the expression r(w)=(1−w)−4 ,

limw→1r(w)=limw→1(1−w)−4=(1−1)−4=0−4

The limit cannot be estimated.

The value of the function r(w)=(1−w)−4 , 0.1 below the limiting argument that is w=0.9 ,

r(0.9)=(1−0.9)−4=10000

The value of the function r(w)=(1−w)−4 , 0.1 above the limiting argument that is w=1.1 ,

r(1.1)=(1−1.1)−4=−10000

The value of the function r(w)=(1−w)−4 , 0.01 below the limiting argument that is w=0.99 ,

r(0.99)=(1−0.99)−4=1.0×108

The value of the function r(w)=(1−w)−4 , 0.01 above the limiting argument that is w=1.01 ,

r(1.01)=(1−1.01)−4=−1.0×108

Thus, the value of the expression limw→1r(w) cannot be estimated, value of function 0.1 and 0.01 above and below the limiting argument are r(0.9)=10000 , r(1.1)=−10000 , r(0.99)=1.0×108 and r(1.01)=−1.0×108 .

Answer 12

Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E Ch. 2.1 - Prob. 7E Ch. 2.1 - Prob. 8E Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E

The value of the expression lim w → 1 r ( w ) , where r ( w ) = ( 1 − w ) − 4 . Also estimate the value of function 0.1 and 0.01 above and below the limiting argument.

Concept explainers

To calculate: The value of the expression limw→1r(w) , where r(w)=(1−w)−4 . Also estimate the value of function 0.1 and 0.01 above and below the limiting argument.

Answer to Problem 19E

Explanation of Solution

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Chapter 2 Solutions