Problem 61E

61. (a) Graph the function $f(x)=\sin x-\frac{1}{1000} \sin (1000 x)$ in the

viewing rectangle $[-2 \pi, 2 \pi]$ by $[-4,4] .$ What slope does the graph appear to have at the origin?

(b) Zoom in to the viewing window $[-0.4,0.4]$ by $[-0.25,0.25]$ and estimate the value of $f^{\prime}(0)$. Does this agree with your answer from part (a)?

(c) Now zoom in to the viewing window $[-0.008,0.008]$ by $[-0.005,0.005] .$ Do you wish to revise your estimate for $f^{\prime}(0) ?$

Step-by-Step Solution