MATH 2A Lecture Notes - Lecture 10: Intermediate Value Theorem

• School: UC-Irvine
• Department: Mathematics
• Course: MATH 2A
• Professor: Liu, W

Document Summary

: if f(x) lim h 0 f(x+h) f(x) h h(2+(x+h)(2+x) = (3)/((2+x) 2 ) exists, we say that f is differentiable at x=a. : find f (x) where f(x) = (((1 (x+h))/(2+(x+h))) ((1 x)/(2+x)) (1 (x+h))(2+x) (1 x)(2+(x+h)) (1 x h)(2+x) (1 x)(2+x+h) (1 x)(2+x) h(2+x) (1 x)(2+x) (1 x)h. Math 2a lecture 10: derivatives and differential equations. Ex 1 lim h 0 lim h 0 lim h 0 lim h 0 lim h 0. : if x>0, lim h lim lim h 0 h h 0 x<0 f(x+h) f(x) lim h 0. H lim h 0 h x=0 f(x+h) f(x) lim h 0 f(h) f(0) lim h 0. If f(x) is differentiable at x=a, then f(c) is continuous at x=a. = -1, so f(x) is also differentiable for x<0. h 0. =1, so f(x) is differentiable for x>0. h f is not differentiable at x=0 f(x+h) f(x) h h h.