York University, Department of Mathematics and Statistics
Math 1013 “Applied Calculus I”, Fall 2014
Test 2 (Sections A and D)
2014-11-03
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1. (10 pts) Compute the first derivative of the following functions:
√
t(1 + 3t)5
(1a) h(t) =
sin(t)
(1b) f (x) = ln(1 + x2 ) tan(x)
2
Extra space for question 1
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2. (15 pts)
(2a) Find
dy
if exy = x + y + xy.
dx
(2b) Find the equation of the tangent line at the point where x = 0 to
the curve described by the equation exy = x + y + xy.
4
Extra space for question 2
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3. (10 pts) The area of the cube is increasing at a rate 4 cm2 /s. How
fast is the volume of the cube increasing when the edge length is 10
cm?
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Extra space for question 3
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4. (20 pts) Sketch the graph of the function f (x) = 3x4 − 8x3 + 6x2 − 2.
Make sure to follow the seven-step procedure presented in class: find
the domain, intercepts (if possible), check for symmetries and asymptotes, find intervals of increase/decrease, local maxima and minima,
intervals of up/down concavity and inflection points.
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Extra space for question 4
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Extra space for question 4
10
Extra space (mark clearly which question you are solving here)
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Extra space (mark clearly which question you are solving here)
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