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 4, Problem 53RE
To determine

Tofind:the function using its first derivative.

Expert Solution

Answer to Problem 53RE

Thefunction using its first derivative f(t)=t2+3Cost+2 .

Explanation of Solution

Given:

  f(t)=2t-3sint,f(0)=5 .

Concept used:

Antiderivative=integration

  f(t)dt=f(t) . Or dydtdt=y .

Since, the multiplication of two operators ×ddt=1 .

Integration formula:

  xndx=xn+1n+1 .

Calculation:

  f(t)=2t-3sint,f(0)=5 .

  f(t)dt=2tdt-3sintdt .

  f(t)dt=t2+3Cost+C

  f(t)=t2+3Cost+C .

  f(0)=(0)2+3Cos0+C

  5=(0)2+3Cos0+C

  C=2 .

  f(t)=t2+3Cost+2 .

Hence the function using its first derivative f(t)=t2+3Cost+2 .

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