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MATH151 Quiz 2 Department of Mathematics, Spring 2014 March 31, 2014 Questions: 1. Find the derivative of the following function f (x) = f " (x) = = = x5 3x + 7 ; 4 5x4 3 x3 x3 3x2 x5 4 5x7 4) 20x4 + 12 3x7 + 9x3 3x3 (x3 2x 7 3x + 7 2 (x3 4 3 (x3 4) 20x + 6x 21x2 2 4) 21x2 + 12 2 2. Find the limit lim x!0 tan 5x 7x cos (2x) 5 sin 5x = 7 (5x) cos (2x) cos (5x) 5 sin 5x 5 = lim lim = : x!0 7 cos (2x) cos (5x) x!0 5x 7 = lim x!0 3. Find the derivative of the following function f (x) = f 0 (x) = sin x2 + 5x 125 125 sin x2 + 5x ; 124 cos x2 2x + 5 4. Find the derivative of the following function. Reduce your answer to a ratio p 3 f (x) = x2 (1 x) = x2=3 (1 x) ; 2 =1=3 2 (1 x) 3x p f 0 (x) = x (1 x) x2=3 = 3 33x 2 5x p = 33x 5. Find the the equation of the tangent line to the graph of the function given implicitly x4 x2 y + y 4 = 1 1 at ( 1; 1): 4x3 2xy x2 y 0 + 4y 3 y 0 = 0; x2 y 0 4y 3 y 0 ; 4x3 2xy ; y0 = x2 4y 3 4+2 2 y 0 (( 1; 1)) = = ; 1 4 3 2 (x + 1) : y 1 = 3 4x3 2xy 2 =