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Estimate the slope of the curve y = cosx at x=π\2
Comment on the slope as x gets closer to π\2
Comment on the slope as x gets closer to π\2
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GPT 3.5
To estimate the slope of the curve y = cos(x) at x = π/2, we can use the concept of the derivative.
The derivative of y = cos(x) is given by dy/dx = -sin(x).
Substituting x = π/2 into -sin(x), we have dy/dx = -sin(π/2).
The sine of π/2 is equal to 1, so the slope at x = π/2 is -1.
As x gets closer to π/2, the slope becomes steeper and approaches -1.
The derivative of y = cos(x) is given by dy/dx = -sin(x).
Substituting x = π/2 into -sin(x), we have dy/dx = -sin(π/2).
The sine of π/2 is equal to 1, so the slope at x = π/2 is -1.
As x gets closer to π/2, the slope becomes steeper and approaches -1.