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# math mid 2.pdf

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School
University of British Columbia
Department
Mathematics
Course
MATH 100
Professor
Steven Barnes
Semester
Fall

Description
Full Name: Signature: Student Number: 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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