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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![### Calculus Problems
#### Problem 1
**Function:**
\[ g(x) = \int_1^x \sqrt{19 - t} \, dt \]
**Derivative:**
Evaluate the derivative \( g'(3) \).
---
#### Problem 2
##### Question 4
**Function:**
\[ F(x) = \int_0^{x^4} \cos t \, dt \]
**Derivative:**
Find \( F'(x) \).
- \( 4x^3 \cos x^4 \)
- \( 4x^3 \sin x^4 \)
- \( \cos x^4 \)
- \( -\sin x^4 \)
---
*Note: The above problems involve differentiating an integral function using the Fundamental Theorem of Calculus. Make sure to apply the chain rule where necessary.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F08f6f3ae-62d0-4ecf-a7d1-a70a7054db3c%2Fdd820284-c4f8-4a9c-a714-79ebe058f46d%2F3abw0u7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculus Problems
#### Problem 1
**Function:**
\[ g(x) = \int_1^x \sqrt{19 - t} \, dt \]
**Derivative:**
Evaluate the derivative \( g'(3) \).
---
#### Problem 2
##### Question 4
**Function:**
\[ F(x) = \int_0^{x^4} \cos t \, dt \]
**Derivative:**
Find \( F'(x) \).
- \( 4x^3 \cos x^4 \)
- \( 4x^3 \sin x^4 \)
- \( \cos x^4 \)
- \( -\sin x^4 \)
---
*Note: The above problems involve differentiating an integral function using the Fundamental Theorem of Calculus. Make sure to apply the chain rule where necessary.*
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