MA 141 Study Guide - Final Guide: Quotient Rule
Document Summary
Using two limit computations, which we will state but not prove, we can nd the derivatives of sine and cosine. Note that these two limits evaluate to about later in the semester. Theorem: the trig functions sine and cosine are di erentiable at all points r and d d sin = cos and d d cos = sin . Proof: d d sin = lim h 0. + lim h 0 h 0 cos sin h sin h h. = (sin )(0) + (cos )(1) = cos h 0 h. Evidence that of the tangent line to the original function at a given input x. d (sin ) = cos . Recall that a derivative is a function that gives the slope. First, look at the graph of sin . Let"s note where the slope is 0 or 1: slope at = 0 is m = 1.
