#39 ## Linear Approximation and Estimation### Functions and Linear ApproximationsBelow are various functions where linear approximation techniques are applied to estimate certain values. For each function, choose an appropriate value of \( a \) to ensure a small error in estimation.#### Functions1. \( f(x) = \frac{12 - x^2}{x} \); \( a = 2 \); evaluate \( f(2.1) \).2. \( f(x) = \sin x \); \( a = \pi/4 \); evaluate \( f(0.75) \).3. \( f(x) = \ln(1 + x) \); \( a = 0 \); evaluate \( f(0.09) \).4. \( f(x) = x/(x + 1) \); \( a = 1 \); evaluate \( f(1.1) \).5. \( f(x) = \cos x \); \( a = 0 \); evaluate \( f(-0.01) \).6. \( f(x) = e^x \); \( a = 0 \); evaluate \( f(0.05) \).7. \( f(x) = (8 + x)^{-1/3} \); \( a = 0 \); evaluate \( f(-0.1) \).8. \( f(x) = \sqrt[3]{x} \); \( a = 81 \); evaluate \( f(85) \).9. \( f(x) = 1/(x + 1) \); \( a = 0 \); evaluate \( f(1.1) \).10. \( f(x) = \cos x \); \( a = \pi/4 \); evaluate \( \cos 0.8 \).11. \( f(x) = e^{-x} \); \( a = 0 \); evaluate \( e^{-0.03} \).12. \( f(x) = \tan x \); \( a = 0 \); evaluate \( \tan 3^\circ \).### Estimations with Linear ApproximationFor each of the following, use linear approximation to estimate the values:1. \( 1/203 \)2. \( \tan(-2^\circ) \)3. \( \sqrt{146} \)4. \( \sqrt[3]{

Name: #39 ## Linear Approximation and Estimation### Functions and Linear App
Uploaded: 2024-03-05T11:52:21.000Z
Channel: Bartleby
Description: #39 ## Linear Approximation and Estimation### Functions and Linear ApproximationsBelow are various functions where linear approximation techniques are applied to estimate certain values. For each function, choose an appropriate value of \( a \) to en