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If y=sin^(-1) x, prove that (1-x^2)(d^2...

If `y=sin^(-1)` x, prove that `(1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)=0`

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PATHFINDER-APPLICATION OF DERIVATIVE-QUESTION BANK
  1. Differentiate tan ^(-1)((sqrt(1+x^2 )-1)/x) w,r,t. tan ^(-1)x

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  2. If e^y(x+1)=1, prove that (d^2y)/(dx^2)=((dy)/(dx))^2

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  3. If y=sin^(-1) x, prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)=0

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  4. If x=a(theta+sin theta) and y=a(1-costheta), find (d^2y)/(dx^2)"at"the...

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  5. A particle moves along the curve y=2/3x^3. Find the points on the curv...

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  6. A man of height 1.6m, walks at a rate of 30m/sec away from a lamp whic...

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  7. Water is leaking from a conical funnel at the rate of 5cm^3//sec. If t...

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  8. Find the approximate value of log(10)10.1 it being given that log10e=0...

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  9. The time T of of oscillation of a simple pendulum of length l is given...

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  10. If in a triangle ABC, the side c and the angle C remain constant while...

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  11. Find the interval in which f(x)=2x^3+3x^2-12x+1 is increasing.

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  12. Find the interval in which f(x)=x^3-3x^2-9x+30 is strictly increasing ...

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  13. The function f(x)=sin^4x+cos^4x increasing if :

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  14. Let f(x)=int0^xe^t(t-1)(t-2)dt, Then f decreases in the interval

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  15. If f(x)=x.e^(x(1-x)), then f(x) is

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  16. Let f(x)=3x+5 then show f(x) is strictly increasing and f^(-1)(x) exis...

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  17. If alt0, and f(x)=e^(ax)+e^(-ax) Is monotonically decreasing. Find the...

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  18. If f''(x)gt0 and f'(1)=0 such that g(x)=f(cot^2x+2cotx+2), where 0ltxl...

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  19. Using calculus find the order relation between x and tan^(-1) x when "...

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  20. The number of critical points of f(x)=(|x-1|)/X^2 is

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