Ise the information in the table to find h'(a) at the giver h(x) = f(g(sin(x))); a = 0 x f(x) f'(x) g(x) g'(x) 2 7 2 -2 3 -1 3 -3 2 3 "(a) = 1. 6. 1. 6. 3. 1. 2.
Ise the information in the table to find h'(a) at the giver h(x) = f(g(sin(x))); a = 0 x f(x) f'(x) g(x) g'(x) 2 7 2 -2 3 -1 3 -3 2 3 "(a) = 1. 6. 1. 6. 3. 1. 2.
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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![Use the information in the table to find \( h'(a) \) at the given value of \( a \).
\[ h(x) = f(g(\sin(x))); \quad a = 0 \]
\[
\begin{array}{|c|c|c|c|c|}
\hline
x & f(x) & f'(x) & g(x) & g'(x) \\
\hline
0 & 2 & 7 & 0 & 2 \\
\hline
1 & 1 & -2 & 3 & 0 \\
\hline
2 & 6 & 6 & 1 & -1 \\
\hline
3 & 3 & -3 & 2 & 3 \\
\hline
\end{array}
\]
\[ h'(a) = \]
**Explanation of the table:**
The table presents values for functions \( f(x) \), \( f'(x) \), \( g(x) \), and \( g'(x) \) at specific values of \( x \). The task is to compute \( h'(a) \) using these function values for the compound function \( h(x) = f(g(\sin(x))) \), where \( a = 0 \).
- **Column 1 (x):** Represents the x-values at which the function values are evaluated.
- **Column 2 (f(x)):** Lists the function values of \( f \) at each x-value.
- **Column 3 (f'(x)):** Lists the derivative values of \( f \) at each x-value.
- **Column 4 (g(x)):** Lists the function values of \( g \) at each x-value.
- **Column 5 (g'(x)):** Lists the derivative values of \( g \) at each x-value.
The goal is to determine \( h'(0) \) based on this information.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8184eabc-db64-4ff4-8675-5dfdbf4594d7%2Ffdc29c99-1ef7-45ac-84cc-6246ef82f826%2F9wy8jq_processed.png&w=3840&q=75)
Transcribed Image Text:Use the information in the table to find \( h'(a) \) at the given value of \( a \).
\[ h(x) = f(g(\sin(x))); \quad a = 0 \]
\[
\begin{array}{|c|c|c|c|c|}
\hline
x & f(x) & f'(x) & g(x) & g'(x) \\
\hline
0 & 2 & 7 & 0 & 2 \\
\hline
1 & 1 & -2 & 3 & 0 \\
\hline
2 & 6 & 6 & 1 & -1 \\
\hline
3 & 3 & -3 & 2 & 3 \\
\hline
\end{array}
\]
\[ h'(a) = \]
**Explanation of the table:**
The table presents values for functions \( f(x) \), \( f'(x) \), \( g(x) \), and \( g'(x) \) at specific values of \( x \). The task is to compute \( h'(a) \) using these function values for the compound function \( h(x) = f(g(\sin(x))) \), where \( a = 0 \).
- **Column 1 (x):** Represents the x-values at which the function values are evaluated.
- **Column 2 (f(x)):** Lists the function values of \( f \) at each x-value.
- **Column 3 (f'(x)):** Lists the derivative values of \( f \) at each x-value.
- **Column 4 (g(x)):** Lists the function values of \( g \) at each x-value.
- **Column 5 (g'(x)):** Lists the derivative values of \( g \) at each x-value.
The goal is to determine \( h'(0) \) based on this information.
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