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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![### Problem Statement:
Given the function \( f(x, y) \) defined as:
\[ f(x, y) = \sqrt{150 - 4x^2 - 2y^2} \]
You are required to evaluate the function at the point \((5, 0)\).
### Instructions:
1. Substitute the values \( x = 5 \) and \( y = 0 \) into the function.
2. Simplify the expression inside the square root.
3. Provide the resulting value in the input box.
4. Click the "Preview" button to check your answer.
### Example Calculation:
#### Step-by-Step Solution:
1. Substitute \( x = 5 \) and \( y = 0 \) into the function:
\[ f(5, 0) = \sqrt{150 - 4(5)^2 - 2(0)^2} \]
2. Simplify the expression inside the square root:
\[ f(5, 0) = \sqrt{150 - 4(25) - 2(0)} \]
\[ f(5, 0) = \sqrt{150 - 100} \]
\[ f(5, 0) = \sqrt{50} \]
3. Thus, the value of \( f(5, 0) \) is \( \sqrt{50} \), which can be further simplified if needed.
### Input:
- Enter your answer in the provided text box.
- Click on "Preview" to verify your answer.
*Note*: Make sure to simplify the answer appropriately. For this example, \( \sqrt{50} \) can also be expressed as \( 5\sqrt{2} \).
### Interactive Component:
- Text Box: Type your computed value of \( f(5, 0) \).
- Preview Button: Click to preview and verify your input.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04c9c296-9553-456f-a4d0-60a8cdfce441%2F346a7d06-6c50-42a5-a5d3-b167855701f4%2Fcntyj24.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement:
Given the function \( f(x, y) \) defined as:
\[ f(x, y) = \sqrt{150 - 4x^2 - 2y^2} \]
You are required to evaluate the function at the point \((5, 0)\).
### Instructions:
1. Substitute the values \( x = 5 \) and \( y = 0 \) into the function.
2. Simplify the expression inside the square root.
3. Provide the resulting value in the input box.
4. Click the "Preview" button to check your answer.
### Example Calculation:
#### Step-by-Step Solution:
1. Substitute \( x = 5 \) and \( y = 0 \) into the function:
\[ f(5, 0) = \sqrt{150 - 4(5)^2 - 2(0)^2} \]
2. Simplify the expression inside the square root:
\[ f(5, 0) = \sqrt{150 - 4(25) - 2(0)} \]
\[ f(5, 0) = \sqrt{150 - 100} \]
\[ f(5, 0) = \sqrt{50} \]
3. Thus, the value of \( f(5, 0) \) is \( \sqrt{50} \), which can be further simplified if needed.
### Input:
- Enter your answer in the provided text box.
- Click on "Preview" to verify your answer.
*Note*: Make sure to simplify the answer appropriately. For this example, \( \sqrt{50} \) can also be expressed as \( 5\sqrt{2} \).
### Interactive Component:
- Text Box: Type your computed value of \( f(5, 0) \).
- Preview Button: Click to preview and verify your input.
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