MATH 1131Q Lecture Notes - Lecture 5: Squeeze Theorem, Implicit Function

• School: UConn
• Department: Mathematics
• Course: MATH 1131Q
• Professor: Amit Savkar

Document Summary

Math 1131q , lecture 5 , sections 3. 3 - 3. 5. 0 cos( ) < sin( ) / < 1 for. We have lim cos( ) = 1 and lim 1 = 1. Squeeze theorem on the functions above to see lim sin( ) / = 1 sin / is an even function, so the left and right hand limits are equal. Therefore , lim sin( ) / = 1. 0 d / dx sin(x) = cos(x) d / dx cos(x) = -sin(x) d / dx tan(x) = sec^2(x) d / dx cot(x) = -csc^2(x) d / dx sec(x) = sec(x)tan(x) d / dx csc(x) = -csc(x)cot(x) If y = f(u) and u = g(x) are both differentiable functions, then dy = dy du dx du dx. If n is any real number and u = g(x) is differentiable, then. D (u^n) = nu^(n-1) du dx dx (b > 0) e^x*lnb.