Solution Found!
Linear approximation a. Write The equation of the line
Chapter 4, Problem 7E(choose chapter or problem)
a. Write the equation of the line that represents the linear approximation to the following functions at the given point a.
b. Graph the function and the linear approximation near x = a.
c. Use the linear approximation to estimate the given function value.
d. Compute the percent error in your approximation: \(100 \cdot \mid \text { approx-exact }|/| \text { exact } \mid\)
\(f(x)=12-x^{2} ; \quad a=2 ; f(2.1)\)
Questions & Answers
QUESTION:
a. Write the equation of the line that represents the linear approximation to the following functions at the given point a.
b. Graph the function and the linear approximation near x = a.
c. Use the linear approximation to estimate the given function value.
d. Compute the percent error in your approximation: \(100 \cdot \mid \text { approx-exact }|/| \text { exact } \mid\)
\(f(x)=12-x^{2} ; \quad a=2 ; f(2.1)\)
ANSWER:SOLUTION STEP 1 Given f(x) = 12 x ;a = 2;f(2.1) f(x) = 2x (a). Equation of the line of linear approximation y = L(x) = f(a) + f(a)(x a) 2 Thus f(a) = 12 2 = 12 4 = 8 f(a) = 2 × 2 = 4 Therefore y = L(x) = f(a) + f(a)(x a) y = 8 + 4(x a) =