Assignment:
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).
Provide complete and step by step solution for the question and show calculations and use formulas.