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Limits of Trig Functions

** Please see the attached file for the complete solution response **

2) The limit of f(x) = (sin x)/x as X approaches 0 is 1

a) Let (x, sin x) be a point on the graph of g near (0,0), and write a formula for the slope of the secant line joining (x, sin x) and (0,0). Evaluate this formula at x = 0.1 and x = 0.01. Then find the exact slope of the tangent line to g at the point (0,0).

b) Sketch the graph of the cosine function h(x) = cos x. What is the slope of the tangent line at the point (0,1)? Use limits to find this slope analytically.

c) Find the slope of the tangent line to k(x) = tan x at (0,0).

Solution Preview

2)  The limit of f(x) = (sin x)/x as X approaches 0 is 1 

a)  Let (x, sin x) be a point on the graph of g near (0,0), and write a formula for the slope of the secant line joining (x, sin x) and (0,0).  Evaluate this formula at x = 0.1 and x = 0.01.  Then find the exact slope of the tangent line to g at the point (0,0). 
The formula for the slope of the line joining the points (x, sin x) and (0,0) is: (please see the attached file).

At the value x=0.1, we have: (please see the attached file)
At the value x=0.01, we have: (please ...

Solution Summary

This solution provides all the steps and the graphs to complete the given trigonometry problems.

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