MAT 131 Test 2
Fall 1997
Show all work for credit. Do all your work neatly on the paper provided.
Write your name on each sheet you turn in. I will not grade any work done
on the test sheet. When you are finished turn in all sheets including the test.
Good Luck.
- 1.
-
Find the derivative of each of the given functions.
- a.
-
h(z) = 1+z2/1-z2 b. f(x) = (1-2x2+3x4)5
- c.
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g(t) = sin(t)tan(t2) d. f(x) = sin(tan(x2))
- e.
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s(t) = (t-1/1+t)3 f. P(z) = (13)4
- g.
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f(x) = xp
- 2.
-
Find dy/dx by implicit differentiation.
- a.
-
x3+y3 = 3
- b.
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(3x2y3)1/2 = 1
- c.
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x+y/x-y = 7
- d.
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sinx tany = y
- 3.
-
Find the points where the curve 1/x+1/y = 1 has horizontal
tangent line.
-
4.
-
Find second and third derivatives of the following functions.
- a.
-
f(x) = sec2 x
-
b.
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f(x) = a0+a1x+a2x2+a3x3+a4x4
- 5.
-
Find the equation for the normal line to the curve
y = x1/2+x3/2 at the point (1,2).
-
6.
-
Assume L is a differentiable function with
L¢(x) = 1/x find d/dx L(cotx) .
-
7.
-
Assume f and g are differentiable functions. Find an
expression for d/dx( f(sinx)/cos(g(x)) ).
-
8.
-
Find two functions f and g with the property that
f¢ = g¢ yet f ¹ g.
File translated from TEX by TTH, version 1.58.