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Mock Test 1-1

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11 views7 pages

Mock Test 1-1

Uploaded by

tandat31052016
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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MATH 1010 – Calculus 1, Fall 2023

Mock Midterm
Time: 75 minutes. Total points: 30.

Student Name

Student ID

1. (4 points) Find f ′ (0) for ( 2


e−1/x , x ̸= 0
f (x) =
0, x=0
2. Find the points on the curve y = 2x3 − 3x2 − 12x + 20 where the tangent is

(a) perpendicular to the line y = 1 − ( x/24).


(b) parallel to the line y = 22 − 12x.
3. (4 points) The figure here shows two right circular cones, one upside down inside the
other. The two bases are parallel, and the vertex of the smaller cone lies at the center
of the larger cone’s base. What values of r and h will give the smaller cone the largest
possible volume?
4. (4 points) Find the average value of the function graphed in the accompanying figure.
5. (4 points) A bacteria population starts with 400 bacteria and grows at a rate of r (t) =
450et bacteria per hour. How many bacteria will there be after three hours?
6. Let (
− x − 1, −3 ≤ x < 0
f (x) = √
− 1 − x2 , 0 ≤ x ≤ 1.

(a) (3 points) Show that f ( x ) is continuous and sketch the graph of f ( x ).


Z 1
(b) (3 points) Find f ( x )dx.
−3
7. (4 points) Find  
1 π 2π nπ
lim sin( ) + sin( ) + . . . + sin( )
n→∞ n n n n

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