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 e0 . 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 10 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
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This note was uploaded on 01/14/2012 for the course MATH 105 taught by Professor Malabikapramanik during the Fall '10 term at The University of British Columbia.