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How do you find the slope of the tangent line to the graph of the given function # y=sinx+3#; #x=pi#?

Answer 1

You can take the derivative, and plug in #x = pi#.

#[(df(pi))/(dx)] = [cosx + 0]|_(x=pi) = cospi = -1#

The slope of a tangent line at #x = a# is always just the derivative of the function evaluated at #x = a#, while #d/(dx)[sinu] = cosu((du)/(dx))# (Chain Rule).

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Answer 2

Adam Adkins

To find the slope of the tangent line to the graph of the function y = sin(x) + 3 at x = π, we need to take the derivative of the function and evaluate it at x = π. The derivative of y = sin(x) + 3 is dy/dx = cos(x). Evaluating this at x = π, we get dy/dx = cos(π) = -1. Therefore, the slope of the tangent line to the graph of y = sin(x) + 3 at x = π is -1.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.