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# finalp2 - Math 16A Short Calculus section 2 Practice Final...

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Math 16A Short Calculus, section 2 Practice Final Exam 1. Continuity For each of the following functions, state: the range, the inter- val(s) on which the function is continuous, and for each disconti- nuity whether or not the discontinuity is removable. (a) y = x 2 + 4 (b) y = x +2 x 2 - 4 (c) y = 2 b x c (d) y = 4 cos( θ ) + 1

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2. Slope and Derivative (a) Find an equation of the line tangent to f ( x ) = x 2 + 1 with slope - 2. (b) Use the limit definition to find the derivative of the following functions. i. f ( x ) = x 2 - 1 ii. h ( t ) = 2 t
3. Rates of Change (a) The profit P from selling x units of a product is given by P = 15 + 12 x - 81 x . i. Find the average rate of change of P on the interval [1 , 9]. ii. Find a formula for the marginal profit. What is the marginal profit for x = 9? (b) A sphere of radius 3 has its radius changing at a rate of 4 inches per second. How quickly is the volume of the sphere changing?

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4. Derivative Tests (a) Apply the Second-Derivative Test to find the relative extrema of f ( x ) = x 3 - 3 x 2 + 1. Show all of your work.
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finalp2 - Math 16A Short Calculus section 2 Practice Final...

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