MAT-000 Section X Practice Test 1 Z
Name:
Give yourself thirty minutes. Do not use your book or notes. You may use a
calculator.
1. Find the x-coordinate of the center of the circle x2+ 3x+y2+ 6y= 15.
2. Find the value of the limit
lim
x→−21
x+ 2 +4
x2−4
3. At what value or values of xis the function
f(x) =
|x+ 1| − 1 if x < 0
x2+xif 0 ≤x < 1
3−xif 1 ≤x
discontinuous?
4. Let f(x) = √sin x+ cos2x+ 1. Find f0(0).
5. Find dy
dx.
(a) xcos y+ycos x= 1
(b) y=3
√3x3−x2−1
6. Find the value of the limit
lim
n→∞
n
X
i=1
1
n"i
n3
+ 1#.
7. Let f(x) = x2on the interval [0,2]. Let the interval be partitioned as follows:
P={0,1,2}. Find the value of the Riemann sum
n
X
i=1
f(x∗
i)∆xi
if each xiis the midpoint of its subinterval.
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