BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 3.1, Problem 63E

(A)

To determine

To find:

The coordinate line , its position at time t

Expert Solution

Answer to Problem 63E

  x33+c

Explanation of Solution

Given:

The function

  f(x)=x2

  F'(x)=f(x)

Concept used:

Antiderivative :- A function F(x) is antiderivative of on an interval I if F'(x)=f(x) for all x in interval I

The entire family of antiderivative of a function by adding a constant to a known antiderivative

So, if F(x) is the antiderivative of f(x) , then the family of the antiderivatives would be F(x)+c

Calculation:

The function f(x)=x2.............(1)

if F'(x)=f(x)

Integrating the equation (1) by given the limit of t

  x2dx=x33+c

(B)

To determine

To find:

The coordinate line , its position at time t

Expert Solution

Answer to Problem 63E

  x44+c,x55+c

Explanation of Solution

Given:

The function

  f(x)=x3,x4

  F'(x)=f(x)

Concept used:

Antiderivative :- A function F(x) is antiderivative of on an interval I if F'(x)=f(x) for all x in interval I

The entire family of antiderivative of a function by adding a constant to a known antiderivative

So, if F(x) is the antiderivative of f(x) , then the family of the antiderivatives would be F(x)+c

Calculation:

The function f(x)=x3,x4.............(1)

if F'(x)=f(x)

Integrating the equation (1) by given the limit of t

  x3dx=x44+cx4dx=x55+c

(C)

To determine

To find:

The coordinate line , its position at time t

Expert Solution

Answer to Problem 63E

  xn+1n+1+c

Explanation of Solution

Given:

The function

  f(x)=xn

  F'(x)=f(x)

Concept used:

Antiderivative :- A function F(x) is antiderivative of on an interval I if F'(x)=f(x) for all x in interval I

The entire family of antiderivative of a function by adding a constant to a known antiderivative

So, if F(x) is the antiderivative of f(x) , then the family of the antiderivatives would be F(x)+c

Calculation:

The function f(x)=xn.............(1)

if F'(x)=f(x)

Integrating the equation (1) by given the limit of t

  xndx=xn+1n+1+c

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