Solution Found!
Answer: Explain why or why not Determine whether the
Chapter 4, Problem 39E(choose chapter or problem)
Determine whether the following statements are true and give an explanation or counterexample.
a. The linear approximation to \(f(x)=x^{2}\) at the point (0, 0) is L(x) = 0.
b. Linear approximation provides a good approximation to f(x) = |x| at (0, 0).
c. If f(x) = mx + b, then at any point x = a, the linear approximation to f is L(x) = f(x).
Questions & Answers
QUESTION:
Determine whether the following statements are true and give an explanation or counterexample.
a. The linear approximation to \(f(x)=x^{2}\) at the point (0, 0) is L(x) = 0.
b. Linear approximation provides a good approximation to f(x) = |x| at (0, 0).
c. If f(x) = mx + b, then at any point x = a, the linear approximation to f is L(x) = f(x).
ANSWER:Solution 39E STEP 1 2 (a). The linear approximation to f(x) = x at the point (0, 0) is ) = 0. Let f be a function differentiable at an interval containing a point a.The linear approximation to f at a is given by L(x) = f(a)+f (a)(xa) Given f(x) = x and (a,f(a)) = (0,0) f(a) = 0. f(x) = 2x f (a) = 0 Therefore L(x) = 0