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

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

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

If y = e^(a cos^(-1)x) show that (1-x^(2)) (d^(2)y)/(dx^(2))-x (dy)/(dx) -a^(2)y= 0 . Where -1 le x le 1

If y= e^(cos^(-1)x), -1 le x le 1 , then prove that (1-x^(2)) (d^(2)y)/(dx^(2))-x (dy)/(dx)- y= 0

If y=log (x + sqrt(x^(2) + 1)) then show that, (x^(2) + 1) (d^(2)y)/(dx^(2)) + x (dy)/(dx)= 0

If y= e^(tan x) then show that, (cos^(2)x) (d^(2)y)/(dx^(2))- (1+ sin 2x) (dy)/(dx)=0

If x=tan(1/alogy)\ , show that (1+x^2)(d^2\ y)/(dx^2)+(2x-a)(dy)/(dx)=0

If y= sin (sin x) then show that, (d^(2)y)/(dx^(2)) + (tan x) (dy)/(dx) + y cos^(2)x = 0

If y= Ae^(mx) + Be^(nx) , show that (d^(2)y)/(dx^(2))- (m + n) (dy)/(dx) + mny= 0

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

If y=Acos(logx)+B sin(logx) then prove that x^(2)(d^(2)y)/(dx^(2))+x(dy)/(dx)+y=0 .

KUMAR PRAKASHAN-CONTINUITY AND DIFFERENTIABILITY-Textbook Illustrations for Practice Work
  1. If y= A sin x + B cos x, then prove that (d^(2)y)/(dx^(2)) +y= 0

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  2. If y= 3e^(2x) + 2e^(3x), prove that (d^(2)y)/(dx^(2))-5 (dy)/(dx) + 6y...

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

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  4. Verify Rolle's theorem for the function y= x^(2) + 2, a = - 2 and b= 2

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  5. Verify Mean value Theorem for the function f(x)= x^(2) in the interval...

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  6. Differentiate w.r.t x, the following function: (i) sqrt(3x+2) + (1)...

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  7. Differentiate the following w.r.t x. (i) cos^(-1) (sin x) (ii) tan^...

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  8. Find f'(x) if f(x)= (sin x)^(sin x) for all 0 lt x lt pi.

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  9. For a positive constant a find (dy)/(dx), where y= a^(t + (1)/(t)), an...

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  10. Differentiate sin^(2)x w.r.t e^(cos x)

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  11. Examine the continuity of the function f(x)= 2x + 3 " at " x=1

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  12. Prove that the function f(x)= x^(2) is continuous at x=0.

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  13. Discuss the continuity of the function f given by f(x)= |x| " at " x=0...

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  14. Show that f(x)= {(x^(3)+3",",x ne0),(1",",x=0):} is a discontinuous fu...

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  15. Check the points where the constant function f(x)= k is continuous

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  16. Prove that the identity function on real numbers given by f(x)=x is co...

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  17. Is the function defined by f(x)= |x|, a continuous function

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  18. Discuss the continuity of the function f given by f(x)= x^(3) + x^(2)-...

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  19. Discuss the continuity of the function f defined by f(x)= (1)/(x), x n...

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  20. Discuss the continuity of the function f defined by f(x)= {(x+2",","if...

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