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MATH151 Quiz 2
Department of Mathematics, Spring 2014
March 31, 2014
Questions:
1. Find the derivative of the following function
f (x)
=
f " (x)
=
=
=
x5
3x + 7
;
4
5x4 3 x3
x3
3x2 x5
4
5x7
4)
20x4 + 12 3x7 + 9x3
3x3
(x3
2x
7
3x + 7
2
(x3
4
3
(x3
4)
20x + 6x
21x2
2
4)
21x2 + 12
2
2. Find the limit
lim
x!0
tan 5x
7x cos (2x)
5 sin 5x
=
7 (5x) cos (2x) cos (5x)
5
sin 5x
5
= lim
lim
= :
x!0 7 cos (2x) cos (5x) x!0 5x
7
=
lim
x!0
3. Find the derivative of the following function
f (x)
=
f 0 (x)
=
sin x2 + 5x
125
125 sin x2 + 5x
;
124
cos x2 2x + 5
4. Find the derivative of the following function. Reduce your answer to a
ratio
p
3
f (x) =
x2 (1 x) = x2=3 (1 x) ;
2 =1=3
2 (1 x) 3x
p
f 0 (x) =
x
(1 x) x2=3 =
3
33x
2 5x
p
=
33x
5. Find the the equation of the tangent line to the graph of the function
given implicitly
x4 x2 y + y 4 = 1
1
at ( 1; 1):
4x3
2xy
x2 y 0 + 4y 3 y 0
=
0;
x2 y 0 4y 3 y 0 ;
4x3 2xy
;
y0 =
x2 4y 3
4+2
2
y 0 (( 1; 1)) =
= ;
1 4
3
2
(x + 1) :
y 1 =
3
4x3
2xy
2
=
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