Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Directions:** Find the function \( f(t) \) given the following information:
\( f''(t) = e^t + \sin(t) \)
\( f(0) = 5 \)
\( f(\pi/2) = -9 \)
---
\( f(t) = \) [input box]
**Explanation:**
To find the function \( f(t) \), you need to integrate the second derivative \( f''(t) = e^t + \sin(t) \) twice. After finding the integration constants using the initial conditions \( f(0) = 5 \) and \( f(\pi/2) = -9 \), you'll determine the exact form of \( f(t) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7d728491-ca3a-470b-9076-be2816d1a071%2F6766541b-f828-4e89-b94b-d329c32143e1%2F8eq3g2s_processed.png&w=3840&q=75)
Transcribed Image Text:**Directions:** Find the function \( f(t) \) given the following information:
\( f''(t) = e^t + \sin(t) \)
\( f(0) = 5 \)
\( f(\pi/2) = -9 \)
---
\( f(t) = \) [input box]
**Explanation:**
To find the function \( f(t) \), you need to integrate the second derivative \( f''(t) = e^t + \sin(t) \) twice. After finding the integration constants using the initial conditions \( f(0) = 5 \) and \( f(\pi/2) = -9 \), you'll determine the exact form of \( f(t) \).
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