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

Want to see more full solutions like this?

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 .

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Students have asked these similar questions

Solve the following initial value problem the initial conditions aw +3. = 12z+18 +9, Əz2 მი w(x, 0)=2x3+3x²+8x ду From (38) auction we obtain follow (x, 0) =i (6x²-6x+2).

Question 1 20 pts Test data on the bending strength of construction wood poles of various diameter are presented below assuming the same length. Kip- 1000 lbf. Using the following data with 2nd order Newton polynomial interpolation, we want to determine the strength of the material for x=4.9 in. Which data point will be used as x? After you found x0, enter the value of x-xo in the solution. Answer shall be in one decimal place. Distance (in) Strength (kips) 100 3.6 1.1 5.6 3.6 5.6 200 300 400 500

Test data on the bending strength of construction wood poles of various diameter are presented below assuming the same length. Kip- 1000 lbf. Using the following data with 2nd order Newton polynomial interpolation, we want to determine the strength of the material for x=4.3 in. Which data point will be used as x0? After you found x0, enter the value of x-xo in the solution. Answer shall be in one decimal place. Distance (in) Strength (kips) 100 2.7 1 6.8 0.6 5.7 200 300 400 500

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 .

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

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 .

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

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 .

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

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

Want to see more full solutions like this?

Chapter 2 Solutions