The function ƒ ( x ) = x 3 is defined on the interval [ 1 , 5 ] , a. Graph f , indicating the area A under f from 1 to 5.

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Answer 1

Question

Chapter 14.5, Problem 16AYU

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

a. Graph $f$ ,
indicating the area $A$ under $f$ from 1 to 5.

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

b. Approximate the area $A$ by Partition $[1, 5]$ into four subintervals of equal length and choose $u$ as the left endpoint of each subinterval.

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

c. Approximate the area $A$ by Partition $[1, 5]$ into eight subintervals of equal length and choose $u$ as the left endpoint of each subinterval.

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

d. Express the area $A$ as an integral.

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

e. Use a graphing utility to approximate the integral.

Expert Solution & Answer

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Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a. f(x) = (x + 4x4) 5, a = -1 lim f(x) X--1 = lim x+4x X--1 lim X-1 4 x+4x 5 ))" 5 )) by the power law by the sum law lim (x) + lim X--1 4 4x X-1 -(0,00+( Find f(-1). f(-1)=243 lim (x) + -1 +4 35 4 ([ ) lim (x4) 5 x-1 Thus, by the definition of continuity, f is continuous at a = -1. by the multiple constant law by the direct substitution property

1. Compute Lo F⚫dr, where and C is defined by F(x, y) = (x² + y)i + (y − x)j r(t) = (12t)i + (1 − 4t + 4t²)j from the point (1, 1) to the origin.

2. Consider the vector force: F(x, y, z) = 2xye²i + (x²e² + y)j + (x²ye² — z)k. (A) [80%] Show that F satisfies the conditions for a conservative vector field, and find a potential function (x, y, z) for F. Remark: To find o, you must use the method explained in the lecture. (B) [20%] Use the Fundamental Theorem for Line Integrals to compute the work done by F on an object moves along any path from (0,1,2) to (2, 1, -8).

Answer 2

Question

Chapter 14.5, Problem 16AYU

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

a. Graph $f$ ,
indicating the area $A$ under $f$ from 1 to 5.

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

b. Approximate the area $A$ by Partition $[1, 5]$ into four subintervals of equal length and choose $u$ as the left endpoint of each subinterval.

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

c. Approximate the area $A$ by Partition $[1, 5]$ into eight subintervals of equal length and choose $u$ as the left endpoint of each subinterval.

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

d. Express the area $A$ as an integral.

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

e. Use a graphing utility to approximate the integral.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 14.5, Problem 16AYU

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

a. Graph $f$ ,
indicating the area $A$ under $f$ from 1 to 5.

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

b. Approximate the area $A$ by Partition $[1, 5]$ into four subintervals of equal length and choose $u$ as the left endpoint of each subinterval.

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

c. Approximate the area $A$ by Partition $[1, 5]$ into eight subintervals of equal length and choose $u$ as the left endpoint of each subinterval.

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

d. Express the area $A$ as an integral.

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

e. Use a graphing utility to approximate the integral.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 14.5, Problem 16AYU

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

a. Graph $f$ ,
indicating the area $A$ under $f$ from 1 to 5.

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

b. Approximate the area $A$ by Partition $[1, 5]$ into four subintervals of equal length and choose $u$ as the left endpoint of each subinterval.

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

c. Approximate the area $A$ by Partition $[1, 5]$ into eight subintervals of equal length and choose $u$ as the left endpoint of each subinterval.

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

d. Express the area $A$ as an integral.

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

e. Use a graphing utility to approximate the integral.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 5

Chapter 14.5, Problem 16AYU

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

a. Graph $f$ ,
indicating the area $A$ under $f$ from 1 to 5.

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

b. Approximate the area $A$ by Partition $[1, 5]$ into four subintervals of equal length and choose $u$ as the left endpoint of each subinterval.

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

c. Approximate the area $A$ by Partition $[1, 5]$ into eight subintervals of equal length and choose $u$ as the left endpoint of each subinterval.

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

d. Express the area $A$ as an integral.

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

e. Use a graphing utility to approximate the integral.

Answer 6

Chapter 14.5, Problem 16AYU

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

a. Graph $f$ ,
indicating the area $A$ under $f$ from 1 to 5.

Answer 7

Chapter 14.5, Problem 16AYU

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

a. Graph $f$ ,
indicating the area $A$ under $f$ from 1 to 5.

Answer 8

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

b. Approximate the area $A$ by Partition $[1, 5]$ into four subintervals of equal length and choose $u$ as the left endpoint of each subinterval.

Answer 9

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

b. Approximate the area $A$ by Partition $[1, 5]$ into four subintervals of equal length and choose $u$ as the left endpoint of each subinterval.

Answer 10

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

c. Approximate the area $A$ by Partition $[1, 5]$ into eight subintervals of equal length and choose $u$ as the left endpoint of each subinterval.

Answer 11

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

c. Approximate the area $A$ by Partition $[1, 5]$ into eight subintervals of equal length and choose $u$ as the left endpoint of each subinterval.

Answer 12

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

d. Express the area $A$ as an integral.

Answer 13

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

d. Express the area $A$ as an integral.

Answer 14

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

e. Use a graphing utility to approximate the integral.

Answer 15

To determine

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

e. Use a graphing utility to approximate the integral.

Answer 16

Expert Solution & Answer

Answer 17

Expert Solution & Answer

Answer 18

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Answer 19

Ch. 14.1 - Graph f( x )={ 3x2ifx2 3ifx=2 (pp.100-102)Ch. 14.1 - Prob. 2AYU Ch. 14.1 - Prob. 3AYU Ch. 14.1 - Prob. 4AYU Ch. 14.1 - True or False lim xc f( x )=N may be described by...Ch. 14.1 - Prob. 6AYU Ch. 14.1 - lim x2 ( 4 x 3 )Ch. 14.1 - lim x3 ( 2 x 2 +1 )Ch. 14.1 - lim x0 x+1 x 2 +1 Ch. 14.1 - Prob. 10AYU

The function ƒ ( x ) = x 3 is defined on the interval [ 1 , 5 ] , a. Graph f , indicating the area A under f from 1 to 5.

Solution Summary: The author illustrates how the function (x ) = x 3 is defined on the interval.

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

a. Graph $f$ ,
indicating the area $A$ under $f$ from 1 to 5.

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

b. Approximate the area $A$ by Partition $[1, 5]$ into four subintervals of equal length and choose $u$ as the left endpoint of each subinterval.

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

c. Approximate the area $A$ by Partition $[1, 5]$ into eight subintervals of equal length and choose $u$ as the left endpoint of each subinterval.

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

d. Express the area $A$ as an integral.

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

e. Use a graphing utility to approximate the integral.

Want to see the full answer?

Chapter 14 Solutions

Additional Math Textbook Solutions

The function ƒ ( x ) = x 3 is defined on the interval [ 1 , 5 ] , a. Graph f , indicating the area A under f from 1 to 5.

Solution Summary: The author illustrates how the function (x ) = x 3 is defined on the interval.

To solve: The function ƒ( x ) = x 3 is defined on the interval [ 1, 5 ] , a. Graph f , indicating the area A under f from 1 to 5.

To solve: The function ƒ( x ) = x 3 is defined on the interval [ 1, 5 ] , b. Approximate the area A by Partition [ 1, 5 ] into four subintervals of equal length and choose u as the left endpoint of each subinterval.

To solve: The function ƒ( x ) = x 3 is defined on the interval [ 1, 5 ] , c. Approximate the area A by Partition [ 1, 5 ] into eight subintervals of equal length and choose u as the left endpoint of each subinterval.

To solve: The function ƒ( x ) = x 3 is defined on the interval [ 1, 5 ] , d. Express the area A as an integral.

To solve: The function ƒ( x ) = x 3 is defined on the interval [ 1, 5 ] , e. Use a graphing utility to approximate the integral.

Want to see the full answer?

Chapter 14 Solutions

Additional Math Textbook Solutions

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

a. Graph $f$ ,
indicating the area $A$ under $f$ from 1 to 5.

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

b. Approximate the area $A$ by Partition $[1, 5]$ into four subintervals of equal length and choose $u$ as the left endpoint of each subinterval.

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

c. Approximate the area $A$ by Partition $[1, 5]$ into eight subintervals of equal length and choose $u$ as the left endpoint of each subinterval.

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

d. Express the area $A$ as an integral.

To solve: The function $ƒ (x) = x^{3}$ is defined on the interval $[1, 5]$ ,

e. Use a graphing utility to approximate the integral.