Q15 of 29 Page 1

If x = a sec3 and y = a tan3, find at .

OR


If , prove that .

Given:


•


•


So,



On differentiating we get,




Hence,


OR


Given:


•



But




On differentiating



.


Hence proved.


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Using properties of determinants, prove that

.

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If sin y = x cos (a + y), then show that

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Find the angle of intersection of the curves x2 + y2 = 4 and (x – 2)2 + y2 = 4, at the point in the first quadrant.

OR


Find the intervals in which the function f(x) = –2x3–9x2–12x + 1 is


(i) Strictly increasing (ii) Strictly decreasing.

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A window is in the form of a rectangle surmounted by a semicircular opening. The total perimeter of the window is 10 meters. Find the dimensions of the window to admit maximum light through the whole opening. How having large windows help us in saving electricity and conserving environment?