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MATH 1210-004 MIDTERM2 REVIEW(2.5-3.5)
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Problem 1. Given that f(3)
5, f’(3)
=
1, g(3)
—2 find the value of ((2f + 3g)4) (3).
2, g’(3)
((4i)()
) I3
4
cz)
x
=
()
4(
13
)
Io*)(t
Problem 2. Given that f(e)
))
e arid f’(e)
Find the derivative off
=
Le
)
ece
()
-
U
=
z)
at x
e.
)
(x + 1)2 at x
2 + i) 4
(x
c
=
4(—1)
)4
(‘e
Problem 3. Find the equation of the tangent line to y
(f (f (f(x))))
=
1.
l)((41)
()
()()4)) 24
MATH 1210-004 MIDTERM2 REVIEW(2.5-3.5)
7
Problem 4. (cosx)
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5
c
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fl;4
i(
1-44+t
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Problem 5. From the top of a building l6Oft high. a ball is thrown upward with an initial
velocity of 64 ft/sec.
(a) When does it reach its maximum height?
(b) What is its maximum height?
(c) When does it hit the ground?
(d) With what speed does it hit the ground?
(e) What is its acceleration at t
)1
(6O
0
=
2?
v
6
0
4/s
S=
0
(ct)
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() V(t)
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MATH 12i0-004 MIDTERIvI2 REVIEW(2.5-3.5)
Problem 6. For the implicitly defined curve sin (rcL)
=
xy
8
find the equation of the perpenclic
ular line to the curve at the point (1, 1).
di
(J
3
Problem 7. Oil spilling from a ruptured tanker spreads in a circle on the surface of the ocean.
The area of the spifi increases at a rate of 9r m
/rnin. How fast is the radius of the spill increasing
2
when the radius is lOm?
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Problem 8. A conical paper cup is 15 cm tall with a radius of 10 cm. The cup is being filled with
water so that the water level rises at a rate of 2cm/scc. At what rate is water being poured into
the cup when the water level is 9cm?
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(4)
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MATH 1210-004 MIDTERM2 REVIEW[25-3.5)
9
Problem 9. A spherical balloon is inflated so that its radius(r) increases at a rate of
cm/sec.
How fast is the volume of the balloon increasing when the radius is 4 cm?
(3)
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(4)
cV
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dr=O.l
=
for
‘x)dX
I,’
(1) y
=
-
JT
(-Jo.i
(2) y
=
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(sin(2x) + cos(2x))
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MATH 12 10-004 MIDTERM2 REVIEW(2.5-2.9,3.1-3.3,3.5)
Problem 17. Find (if any exist) the maximum and minimum values of f(x)
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(fr
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