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# math mid 2.pdf

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University of British Columbia

Mathematics

MATH 100

Steven Barnes

Fall

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Math 100 (104) Practice Midterm Test 2 50 min.
No calculators.
1. Each of these short-answer questions is worth 3 marks. If a correct answer is written in the
box provided, you get 3, otherwise you can earn at most 1.
3
(a) How fast is the side length of a cube increasing if its volume is 8 m , and the volume is
increasing at a rate 1 m /s?
(b) Find the slope of the curve siny) + 2cos (x) = 1 at the point (π/4,π/4).
√
(c) Use a suitable linear approximation to ﬁnd an estimate for 5 (given as a fraction).
1 d −1
(d) Compute dx tan−1(sin (x)).
2 (9)
(e) If f(x) = xcos(x ), compute f (0). Hint: use Maclaurin polynomials.
d x2
(f)

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