MATH 221 Midterm: MATH 221 KSU Test 1f05
15 Feb 2019
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Department
Course
Professor
NAME Rec. Instructor:
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CALCULUS II - EXAM I
September 20, 2005
Show all work for full credit. No books, notes or calculators are permitted. The point value of each
problem is given in the left-hand margin.
logb(x) = ln x
ln bbx=exln b
Zaxdx =1
ln aax+CZsin x dx =−cos x+C
Zcos x dx = sin x+CZtan x dx =−ln |cos x|+C
Zcot x dx = ln |sin x|+CZsec x dx = ln |sec x+tan x|+C
Zcsc x dx =−ln |csc x+ cot x|+CZsec2x dx = tan x+C
Zcsc2x dx =−cot x+CZsec xtan x dx = sec x+C
Zcsc xcot x dx =−csc x+CZdx
√a2−x2= arcsin(x
a) + C
Zdx
a2+x2=1
aarctan(x
a) + CZdx
x√x2−a2=1
aarcsec(|x|
a) + C
page 2 of 5
(20) 1. Calculate the following derivatives. Do not simplify.
a) d
dt arcsin(π−2x)
b) d
dx
xln x
x2−3
(10) 2. Use logarithmic differentiation to find y′.
y=e−x√x+ 1
(x3−5)7
Document Summary
The point value of each problem is given in the left-hand margin. logb(x) = ln x ln b. Z cos x dx = sin x + c bx = ex ln b. Z sin x dx = cos x + c. Z tan x dx = ln| cos x| + c. Z cot x dx = ln| sin x|+c. Z sec x dx = ln| sec x+tan x|+c. Z csc x dx = ln| csc x + cot x| + c. Z sec2 x dx = tan x + c. Z csc2 x dx = cot x + c. Z csc x cot x dx = csc x + c. Z sec x tan x dx = sec x + c. Do not simplify: d dt arcsin( 2x) page 2 of 5 b) d dx x ln x x2 3 (10) 2.
