ive tried multiple times and never got the answer 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]

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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

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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