A3_Winter2016.pdf - DISTANCE EDUCATION MATH 1500 WINTER...

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DISTANCE EDUCATION MATH 1500 WINTER TERM 2016: D01/D02 Assignment 3 Sections 3.3, 3.4, 3.5, 3.6, 3.9. Total Marks: 60 Due Date: Feb 20, 2016 . SHOW ALL WORK to get full marks. Word problems should have sentence answers with units. 1
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1. [17] Differentiate the following functions. DO NOT SIMPLIFY. (a) y x x e tan x ` cot x . (b) y sec ´ a cos p πx ´ 1 q ¯ (c) y “ p sin p x q ` e x 3 ? x q 3 (d) f p t q “ ln |p π 2 ´ t 2 ´ t 5 q| (e) y log 5 p csc 3 x ´ ln π 2 ` x q 2. [6] Evaluate the following limits (a) lim θ Ñ 0 3 sin θ θ ` 2 tan θ (b) lim t Ñ´ 1 t sin p t ` 1 q t 3 ` 3 t 2 ` 2 t 3. [5] Let c and k be any two distinct real numbers. Prove that if f and g are both differentiable, then p c f p x q ` k g p x qq 1 c f 1 p x q ` k g 1 p x q . 4. [3] Let h p x q “ 2 b tan p x q` 1 . For what value of b is h 1 p π q “ 1 . 5. [7] Use implicit differentiation to find the equation of the tangent line to the curve ? x ` sin p xy q ´ e y ´ π 0 at the point p 1 , π q . 6. [8] Use logarithmic differentiation to find the derivative of
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