Math 131 Form 222 Test 2 With Answers - La Sierra University Page 3
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1
2
3
46
10
5. (5 pts) Let ( ) = [3
+ csc(5 )]
. Find
( ). Do not simplify your answer.
10
6
Solution: First, ( ) =
where
= 3
+ csc(5 ), then
9
( ) = 10
5
and where
= 18
5 csc(5 ) cot(5 ) and so
6
9
5
( ) = 10[3
+ csc(5 )]
18
5 csc(5 ) cot(5 )
6. (10 pts) Use implicit differentiation to find
for the curve
2
3
4
+ 2
+ 3
=
3
and then find the slope of the tangent line to the curve at the point (0
1).
2
3
Solution: Differentiating 4
+ 2
+ 3
=
3 with respect to
yields
2
8 + 2 + 2
+ 9
= 0
Solving for
yields
8 + 2
=
2
2 + 9
At the point (0
1) we have
8(0) + 2( 1)
2
=
=
at (0
1)
2
2(0) + 9( 1
)
9
2
The slope of the tangent line to the curve at the point (0
1) is
=
.
9
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