#24 due Monday and "quiz" link for after class
Read 6.5 but replace p. 352 with the following: The linear approximation of f(x) for x near a is
f(x) ≈ f(a) + f '(a)(x-a). This should approximate any f with a line, as in the point slope form f(x) ≈ y1 + m (x-x1).
6.4; 30, 36.
6.5; 1, 25, 29, 32, 35: do all these problems using differentials.
Exercises: For each of the following, write down the linear approximation f(x) ≈ f(a) + f '(a)(x-a) for x near a; then, if requested, test it by using it to approximate the specific value(s). (An example answer looks like: x^5 ≈ 1+5(x-1) for x near 1; test (1.003)^5 ≈ 1+5(.003)=1.015 (actual 1.01509...).)
A. f(x) = sin(x) for x near 0; test sin(.03); test sin(-.12)
B. f(x) = x^(1/2) for x near 25.
C. f(x) = ln(x) for x near 1; test ln(.996).
D. f(x) = (1+x)^n for x near 0; test 1.001^37.
The "Quiz" is a way to record your grade out of 10 from in-class corrections.
For Monday: You may bring past assignment and problem numbers that you want to go over.
Grading method: Last attempt