Answer
(a) When we view the graph in the viewing window $[-2\pi, 2\pi]$ by $[-4,4]$, the slope of the graph at the origin appears to be 1
(b) When we view the graph in the viewing window $[-0.4, 0.4]$ by $[-0.25,0.25]$, the slope of the graph at the origin appears to be 1
(c) When we view the graph in the viewing window $[-0.008, 0.008]$ by $[-0.005,0.005]$, the slope of the graph at the origin appears to be 0
Work Step by Step
(a) $f(x) = sin~x-\frac{1}{1000}sin(1000x)$
When we view the graph in the viewing window $[-2\pi, 2\pi]$ by $[-4,4]$, the slope of the graph at the origin appears to be 1
(b) When we view the graph in the viewing window $[-0.4, 0.4]$ by $[-0.25,0.25]$, the slope of the graph at the origin appears to be 1
This agrees with the answer from part (a)
(c) When we view the graph in the viewing window $[-0.008, 0.008]$ by $[-0.005,0.005]$, the slope of the graph at the origin appears to be 0
