A3_f2015.pdf - MATH 1500 D01/D02 Fall 2015 Assignment 3...

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MATH 1500 D01/D02 Fall 2015 Assignment 3 Total Marks: 60 Due Date: Oct 24, 2015 . SHOW ALL WORK to get full marks . Word problems should have sentence answers with units. This assignment covers sections 3.3, 3.4, 3.5, 3.6, 3.9. 1. Differentiate the following functions. DO NOT SIMPLIFY. (a) (3 points) y = 4 sin 2 x (b) (4 points) y = cos p tan( π 2 x ) (c) (4 points) y = ( ex + e - x x ) 3 / 2 (d) (3 points) f ( t ) = ln | sec( π 2 t - t 4 ) | (e) (4 points) y = log 3 (csc (5 x ) + ln ( x 2 + 1)) 2. Evaluate the following limits (a) (4 points) lim x 0 3 sin (7 x ) x - 3 x 5 (b) (4 points) lim θ 0 3 π sin θ θ - 2 sin θ 3. (5 points) Let k be a real number. Use the quotient rule to prove that d dx k cot x = - k csc 2 x. 4. (7 points) Use implicit differentiation to find the equation of the tangent line to the curve 2 xy - e y + sin ( y ) + e x = 1 at the point (ln 2 , 0). 5. (7 points) Use logarithmic differentiation to find the derivative of
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