Math 125 Test 2 Study Guide
Math 125 Test 2 Study Guide MATH 125
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This 2 page Study Guide was uploaded by Delaney Adams on Monday February 15, 2016. The Study Guide belongs to MATH 125 at University of Alabama - Tuscaloosa taught by a professor in Fall 2015. Since its upload, it has received 31 views. For similar materials see Calculus I in Mathematics (M) at University of Alabama - Tuscaloosa.
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Date Created: 02/15/16
Sections 1.5-1.6, 2.1-2.5 Study Guide Calculus 1 Bruce Trace Section 1.5 Continuity Intermediate value theorem: suppose f(x) is cont on the closed interval [a,b] and c is a number which lies between f(a) and f(b). Then there is some c (a,b) F(x)= x if x<1 x if x>1 29, 47, 33 Section 1.6 Limits involving infinity Lim f(x) = infinity x>c Lim f(x) = - infinity x>c Lim f(x) = L x> infinity Given any >0 Lim f(x) = L x> -infinity # 15,13,19,21,25,29 Section 2.1-2.2 #3,25,27 (2.1) #19,23,27 (2.2) f’(c)= lim [f(x)-f(c)] / x-c x>c f’(c)= derivative of f(x) lim [f(x+h) – f(x)] / h h>0 dy/dx= f’x f’(x)=derivative of f(x) d/dx (f(x))= f’(x) Section 2.3-2.4 2.3 #1,3,5,7,9,11,37,43,61,69 2.4 #3,7,9,11,15,23,29,47 d/dx (f(x) + g(x)) = f’(x) + g’(x) d/dx (f(x) – g(x)) = f’(x) – g’(x) d/dx (f(x)g(x)) = f’(x)g(x) + f(x)g’(x) d/dx (f(x)/g(x)) = (f’(x)g(x)-f(x)g’(x)) / (g(x))2 n n-1 if N is a positive integer then d/dx (x )= nx d/dx (sinx) = cos x d/dx (cosx) = sin x d/dx (secx) = sec x tan x d/dx (cscx) = csc x cot x d/dx (tanx) = sec x 2 d/dx (cotx) = -csc x2 Section 2.5 chain rule: d/dx f(g(x))= f’(g(x)) o dy/dx= dy/du (du/dx) #3,7,13,15,23,29,35
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