The resistance R of a copper wire at temperature T = 30°C is R = 152. Estimate the resistance at T = 32 °C, assuming t dR T-30 = 0.0692/°C. (Use decimal notation. Give your answer to two decimal places.) R(32) ≈
The resistance R of a copper wire at temperature T = 30°C is R = 152. Estimate the resistance at T = 32 °C, assuming t dR T-30 = 0.0692/°C. (Use decimal notation. Give your answer to two decimal places.) R(32) ≈
Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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![The resistance \( R \) of a copper wire at temperature \( T = 30^\circ \text{C} \) is \( R = 15 \, \Omega \). Estimate the resistance at \( T = 32^\circ \text{C} \), assuming that
\[
\frac{dR}{dT}\bigg|_{T=30} = 0.06 \, \Omega/\text{°C}.
\]
(Use decimal notation. Give your answer to two decimal places.)
\[
R(32) \approx \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \Omega
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbe70156d-6630-4fa1-bd10-160edc6ae6ae%2F5c8a64e3-2a79-4f9f-bfc1-dfb6b768fbb4%2Fgfooahf_processed.png&w=3840&q=75)
Transcribed Image Text:The resistance \( R \) of a copper wire at temperature \( T = 30^\circ \text{C} \) is \( R = 15 \, \Omega \). Estimate the resistance at \( T = 32^\circ \text{C} \), assuming that
\[
\frac{dR}{dT}\bigg|_{T=30} = 0.06 \, \Omega/\text{°C}.
\]
(Use decimal notation. Give your answer to two decimal places.)
\[
R(32) \approx \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \Omega
\]
![**Task: Use Linearization to Estimate \(\frac{1}{\sqrt{15}}\) and Calculate Percentage Error**
To estimate \(\frac{1}{\sqrt{15}}\) using linearization, we consider the function \(f(x) = \frac{1}{\sqrt{x}}\) and its linear approximation \(L(x)\) at \(a = 16\).
**1. Estimate \(\frac{1}{\sqrt{15}}\) using the linearization \(L(x)\) of \(f(x)\):**
- **Formula:** \(L(x) = f(a) + f'(a)(x - a)\)
- **Given:** \(a = 16\)
- **Instructions:** Use decimal notation. Provide your answer to five decimal places.
**\[L(15) \approx \]**
[Fill in the value after calculation]
---
**2. Find the actual value of \(\frac{1}{\sqrt{15}}\):**
- **Instructions:** Use decimal notation. Provide your answer to five decimal places.
**\[\frac{1}{\sqrt{15}} \approx \]**
[Fill in the actual value]
---
**3. Calculate the percentage error of Linear Approximation:**
- **Formula:** \(\text{Percentage Error} = \left|\frac{\text{Approximate Value} - \text{Actual Value}}{\text{Actual Value}}\right| \times 100%\)
- **Instructions:** Use decimal notation. Provide your answer to two decimal places.
**\[\text{Percentage error} \approx \]**
[Fill in the percentage error]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbe70156d-6630-4fa1-bd10-160edc6ae6ae%2F5c8a64e3-2a79-4f9f-bfc1-dfb6b768fbb4%2F3j5smo2p_processed.png&w=3840&q=75)
Transcribed Image Text:**Task: Use Linearization to Estimate \(\frac{1}{\sqrt{15}}\) and Calculate Percentage Error**
To estimate \(\frac{1}{\sqrt{15}}\) using linearization, we consider the function \(f(x) = \frac{1}{\sqrt{x}}\) and its linear approximation \(L(x)\) at \(a = 16\).
**1. Estimate \(\frac{1}{\sqrt{15}}\) using the linearization \(L(x)\) of \(f(x)\):**
- **Formula:** \(L(x) = f(a) + f'(a)(x - a)\)
- **Given:** \(a = 16\)
- **Instructions:** Use decimal notation. Provide your answer to five decimal places.
**\[L(15) \approx \]**
[Fill in the value after calculation]
---
**2. Find the actual value of \(\frac{1}{\sqrt{15}}\):**
- **Instructions:** Use decimal notation. Provide your answer to five decimal places.
**\[\frac{1}{\sqrt{15}} \approx \]**
[Fill in the actual value]
---
**3. Calculate the percentage error of Linear Approximation:**
- **Formula:** \(\text{Percentage Error} = \left|\frac{\text{Approximate Value} - \text{Actual Value}}{\text{Actual Value}}\right| \times 100%\)
- **Instructions:** Use decimal notation. Provide your answer to two decimal places.
**\[\text{Percentage error} \approx \]**
[Fill in the percentage error]
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