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Differential Calculus
Mid-Year Exam Review
The sides of a triangle have length of 10, 20, &
20. Find the measures of the angles.
Find the area of the shape below:
30
7
120o
24
Find the angle measures of the triangle:
a = 60
b = 20
c = 75
A ship proceeds on a course of 300o for 2 hours
at a speed of 15 knots. Then it changes course to
200o for 3 hours at the same speed. At that time
how far is the ship from its starting point?
If

15
is obtuse and tan    , find
8
cos 2
Solve:
cos 2 x  cos x  0
0  x  2
Solve:
sin 2 x  cos x
0  x  2
Find all roots in rectangular form.
3
8i
Find the limit:
lim f (x) 
x 2
3x 3  2x, x  2
f (x)  
x  2
13x,
Find the limit:
lim f (x) 
x 2
Find the limit:
lim f (x) 
x 4
Find the limit:
 x 2  2x  4 2  24
lim 
x 4
x

4


 




Find the slope of the line
tangent to the curve at x = 4
3
x  4x 5
f (x) 
x
Find the derivative
2x  5
f (x)  2
x 1
3
Find the velocity of the particle
when the acceleration first
becomes positive
s(t)  2x  x  5x  6
3
2