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115-exam1-sample

# 115-exam1-sample - C x = 8 x where x is the number of items...

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Sample Exam I Math 115 1. (10 points) Find the domain for the function f ( x ) = x 4 - x 2 2. (10 points) 1. People are willing to pay 100 - x dollars for a limited edition etching, where x is the number sold. What is the domain of x ? 3. (15 points) Find ( a ) lim x →∞ x + 3 x 2 - 9 ( b ) lim x 7 x - 7 x 2 - 49 ( c ) lim x 3 x 3 - 8 x - 3 4. (10 points) Let f ( x ) = x 2 ( x + 1). Find the equation of the line tangent to the curve f ( x ) at x = 1 whithout using the rules of differentiation .

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5. (10 points) Determine all values of x, if any, for which f ( x ) is discon- tinuous. f ( x ) = x + 1 , x 1 - x 2 + 4 x - 1 , x > 1 6. (15 points) The graph of a function f is sketched below Y 0 ! 3 ! 2 ! 1 2 1 3 4 X (i) Find the points at which f has no limit; explain your reasoning. (ii) Find the points at which f is not continuous; explain your reasoning. (iii) Find the points at which f has no derivative; explain your reasoning.
7. (10 points) If the price of a product per item is given by p ( x ) = x 2 +2 x +4 and the total cost function is given by
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Unformatted text preview: C ( x ) = 8 + x where x is the number of items produced and sold. Find the proﬁt function P ( x ). What is the proﬁt when the production and sales are x = 6? 8. (10 points) Suppose an egg is thrown straight upward from the ground with initial velocity 96 feet/second and the egg’s height at time t is given by the function s ( t ) = 96 t-16 t 2 . Find the velocity at any time t whithout using the rules of diﬀerentiation . What is the velocity of the egg when t=3 seconds? 9. (10 points) The monthly demand and supply functions for the Luminar desk lamp are given by p = d ( x ) =-1 . 1 x 2 + x + 40 and p = s ( x ) = 0 . 1 x 2 + 15 respectively, where p is measured in dollars and x in units of a thousand. Find the equilibrium quantity and price....
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