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Prove that, underset(xrarr0)lim (logcosx...

Prove that, `underset(xrarr0)lim (logcosx)/sin^2x = -1/2`

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UNITED BOOK HOUSE-SET 12-EXERCISE
  1. Solve:sin^(-1) cos(sin^(-1)x) = pi/3.

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  2. If A = [[4,5],[5,6]], show that A^2 = 10A + I where I is the unit matr...

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  3. Prove that, underset(xrarr0)lim (logcosx)/sin^2x = -1/2

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  4. If y = tan^(-1) (secx + tanx), find (d^2y)/(dx^2).

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  5. Prove that, underset(a)overset(b)int f(a + b - x)dx= underset(a)overse...

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  6. Solve:2^(x-y) dx + 2^(y-x) dy = 0

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  7. If x>1/2, show that the function f(x) = x(4x^2 - 3) is steadily increa...

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  8. Find the area in the fourth quadrant bounded by the curve y = x^3 - 8 ...

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  9. Can the numbers 1,2,3 be the direction ratio of a straight line? Give ...

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  10. Find the intercept form of a plane with intercepts 2,3 and 4 on the x,...

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  11. A and B are two independent events with P(A) = 2/5 and P(B) = 1/3, eva...

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  12. The mean and variance of a binomial distribution are 4 and 3 respectiv...

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  13. If tan^(-1)x, tan^(-1)y and tan^(-1)z are in A.P, find the algebric re...

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  14. Prove that, the inverse of a given square matrix, if its exists, is un...

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  15. Prove that, |(2a, a-b-c,2a),(2b,2b,b-c-a),(c-a-b,2c,2c)|=(a + b+c)^3

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  16. If sqrt(1 -x^2) + sqrt(1-y^2) = a(x-y), show that, (dy)/(dx) = sqrtfra...

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  17. Evaluate: int (xdx)/[(x^2 - a^2)(b^2-x^2)] (b^2>a^2).

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  18. Evaluate: int(sqrt x dx)/sqrt(a^3 - x^3)

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  19. Solve:(dy)/(dx)-y/x + cosec (y/x)=0, given y = 0 when x = 1

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  20. Solve: y^2 + (x - 1/y)(dy)/(dx) = 0.

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