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Unformatted text preview: Math 105 Practice Final Exam 1 1(a). Evaluate the limit lim ( x, y ) (0 , 0) xy 1 / 2 x 2 y if the limit exists. (b). Suppose F ( x ) = e x 2 1 f ( t ) d t and f ( e ) = 4. Find F (1). (c). Which of the following equations describes an elliptic paraboloid. Find the equations of and sketch the level curves corresponding to height , 1 ,- 1 if there is any. (A). z = x 2 4 + y 2 9 . (B). z = x 2 4- y 2 9 . (C). z 2 +1 = x 2 4 + y 2 9 . (d). Evaluate xe x 2 dx , if it is convergent. (e). Use linear approximation to find the distance between (2 . 98 , 4 . 01) and the origin point. 2(a). Evaluate / 2 e x sin x dx . (b). Use trapezoid rule with n = 2 to approximate the above definite integral. 3. Find the area of the region bounded by y = x 2 , y = x 2- 4 x + 4, x = 0 and x = 3. 4. Suppose a kind of dear in a region has no natural enemy and its num- ber grows exponentially at a rate of 12% per year. To control the number of the dear, it is allowed to hunt A dears. Suppose at the beginning there arethe dear, it is allowed to hunt A dears....
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