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 45E

(A)

To determine

To show:

The differentiation of the given function

Expert Solution

Answer to Problem 45E

  d2ydx2=3t

Explanation of Solution

Given:

The equation of motion of a particle is

  s=t33t

Where f and g have derivatives of all orders

Concept used:

Definition of the differentiation:-Differentiation is the action of computing a derivative

The derivative of a function y=f(x) of a variable x is a measure of the rate at which the value y of the function changes with respect to x

Calculation:

The function

  s=t33t...................(1)

The derivative of a function

  y=f(x)y=f(x)=dydx

Differentiating the equation (1) with respect to x

  s=dydx=ddx(t33t)s=3t23

Again Differentiating the above equation with respect to x

  d2ydx2=ddx(3t23)d2ydx2=3t

(B)

To determine

To show:

The differentiation of the given function

Expert Solution

Answer to Problem 45E

  d2ydx2=6

Explanation of Solution

Given:

The equation of motion of a particle is

  s=t33t

Where f and g have derivatives of all orders

Concept used:

Definition of the differentiation:-Differentiation is the action of computing a derivative

The derivative of a function y=f(x) of a variable x is a measure of the rate at which the value y of the function changes with respect to x

Calculation:

The function

  s=t33t...................(1)

The derivative of a function

  y=f(x)y=f(x)=dydx

Differentiating the equation (1) with respect to x

  s=dydx=ddx(t33t)s=3t23

Again Differentiating the above equation with respect to x

  d2ydx2=ddx(3t23)d2ydx2=3t

Putting the t=2

  d2ydx2=3td2ydx2=3×2d2ydx2=6

(C)

To determine

To show:

The differentiation of the given function

Expert Solution

Answer to Problem 45E

  dydx=3

Explanation of Solution

Given:

The equation of motion of a particle is

  s=t33t

Where f and g have derivatives of all orders

Concept used:

Definition of the differentiation:-Differentiation is the action of computing a derivative

The derivative of a function y=f(x) of a variable x is a measure of the rate at which the value y of the function changes with respect to x

Calculation:

The function

  s=t33t...................(1)

The derivative of a function

  y=f(x)y=f(x)=dydx

Differentiating the equation (1) with respect to x

  s=dydx=ddx(t33t)s=3t23

Putting the s=0

  s=3t23s=3

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