Prelim 1

# Prelim 1 - PRELIM 1 Math 112 Write your name your...

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Problem 4 (8 points each) Are the following equalities true or false? Justify your answer. 1. R 1 - 1 1 x dx = 0 2. R 1 ( 1 x 2 + 1 ) dx = 3. R 1 - 1 dx ( x - 5)( x +10)( x +12) = Problem 5 (6 points) Suppose that f and g are continuous functions and that f ( x ) > g ( x ) + 3 > 0 on the interval [1,3]. If Z 3 1 g ( x ) dx = 5 , is it possible that R 3 1 f ( x ) dx = 9? Explain your answer . Check before you hand in the exam booklet, if you wrote your name, your
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Unformatted text preview: instructor’s name and the time of your class on the exam booklet. 2 TRIGONOMETRIC IDENTITIES sin2 x = 2 sin x cos x cos2 x = cos 2 x-sin 2 x sin 2 x = 1-cos2 x 2 cos 2 x = 1+cos2 x 2 cos 2 x + sin 2 x = 1 1 + tan 2 x = sec 2 x cot 2 x + 1 = csc 2 x DERIVATIVE FORMULAS d dx sin x = cos x d dx tan x = sec 2 x d dx sec x = sec x tan x d dx cos x =-sin x d dx cot x = csc 2 x d dx csc x =-csc x cot x d dx sin-1 x = 1 √ 1-x 2 d dx tan-1 x = 1 1+ x 2 d dx sec-1 x = 1 x √ x 2-1 d dx cos-1 x =-1 √ 1-x 2 d dx cot-1 x =-1 1+ x 2 d dx csc-1 x =-1 x √ x 2-1 INTEGRAL FORMULAS R x n dx = x n +1 n +1 + C for n 6 =-1 R e x dx = e x + C R 1 x dx = ln | x | + C R sin x dx =-cos x + C R cos x dx = sin x + C R sec x dx = ln | sec x + tan x | + C R csc x dx =-ln | csc x + cot x | + C R sec 2 x dx = tan x + C R 1 √ 1-x 2 dx = sin-1 x + C R 1 1+ x 2 dx = tan-1 x + C 3...
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