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PracticeExam3

# PracticeExam3 - Math 105 Practice Exam 3 sin(x2 y or show...

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Math 105 Practice Exam 3 1. (a) Evaluate lim ( x,y ) (1 , - 1) sin( x 2 + y ) x 2 + y or show that it doesn’t exist. (b) Consider the area function A ( x ) = R x 1 f ( t ) dt , with A (2) = 6 and A (3) = 5. Compute Z 2 3 f ( t ) dt . (c) A self-employed software engineer estimates that her annual income over the next 10 years will steadily increase according to the formula 70 , 000 e 0 . 1 t , where t is the time in years. She decides to save 10% of her income in an account paying 6% annual interest, compounded continuously. Treating the savings as a continuous income stream over a 10-year period, find the present value. (d) Draw the level curves of the graph of f ( x, y ) = 2 x 2 + y 2 at the heights 0 , 1 , 2. (e) Evaluate Z 1 0 cos( x ) x dx . (f) Let f ( x, y ) = x + y x - y . Use linear approximation to estimate f (2 . 95 , 2 . 05). 2. Evaluate Z x + 2 x ( x 2 - 1) dx . 3. Find the area of the region in the first quadrant bounded by y = 1 x , y = 4 x , and y = 1 2 x . 4. Find k such that f ( x ) = k ( x +1) 3 is a probability density function on the interval [0 , ), for some random variable X . Then compute the probability that 1
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