11-27-2011, 04:41 PM
MTH 301 MIDTERM PAPER
(DATE 26NOVEMBER2011)
Total 26 Questions:
20 MCQS. (Which is mostly from past papers)
6 Long questions:
Long Questions are here:
Q: 21: Write down the equation of a plane passing through the point (3,-4, 2) and perpendicular to the vector n=4i+3j+6k
Q: 22: Lets xyz is three positive integers, whose sum is 18 and the product of two integers with square of third integers will be maximum. Wright the function to be maximized in the function x and y.
Q: 23: Find the critical point for the function f(x, y) =x²+y²along the line y+2-2xat which the absolute extrema of the function can exist.
Q: 24: Find the equation of normal line (symmetric form) to the surface f(x, y) =x²+y²+z²-6 at the point (-1, 2, 1).
Q: 25: Using second partial derivative test show that the function f(x, y) =xy (24-x-y) is maximum at x=8 and y=8.
Q: 26: Find the gradient of the f(x, y, z) =yz³- 2x².
(DATE 26NOVEMBER2011)
Total 26 Questions:
20 MCQS. (Which is mostly from past papers)
6 Long questions:
Long Questions are here:
Q: 21: Write down the equation of a plane passing through the point (3,-4, 2) and perpendicular to the vector n=4i+3j+6k
Q: 22: Lets xyz is three positive integers, whose sum is 18 and the product of two integers with square of third integers will be maximum. Wright the function to be maximized in the function x and y.
Q: 23: Find the critical point for the function f(x, y) =x²+y²along the line y+2-2xat which the absolute extrema of the function can exist.
Q: 24: Find the equation of normal line (symmetric form) to the surface f(x, y) =x²+y²+z²-6 at the point (-1, 2, 1).
Q: 25: Using second partial derivative test show that the function f(x, y) =xy (24-x-y) is maximum at x=8 and y=8.
Q: 26: Find the gradient of the f(x, y, z) =yz³- 2x².
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