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

If `y = sin(2 cos^(-1)x)`, then prove that `(1 - x^2)(d^2y)/(dx) -x dy/dx + 4y = 0`

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BETTER CHOICE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-PREVIOUS YEARS BOARDS QUESTIONS FOR PRACTICE (MULTIPLE CHOICE QUESTIONS)
  1. Diferentiate tan^(-1)((x)/(sqrt(1 - x^2))) w.r.t.x.

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  2. If y = cos(2 cos^(-1)x), then prove that (1 - x^2)(d^2y)/(dx) -xdy/dx ...

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

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  4. Verify Rolle's theorem for the function : f(x) = (x+1)(x-4) in the int...

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  5. Verify Rolle's theorem for the following functions f(x)=(x + 2)(x-3)...

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  6. Verify Rolle's theorem for the following functions f(x) = (x+3)(x-6)...

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  7. Find the values of k so that the function f is continuous at the indic...

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  8. Find the values of k so that the function f is continuous at the indic...

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  9. If (cos x)^y = (cos y)^x, find dy/dx .

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  10. Differentiate the following w.r.t. x : (x + 1/x)^x + x^(x + 1/x)

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  11. Differentiate the following w.r.t. x : x^(x^2 - 3) + (x - 3)^(x^2) ,...

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  12. For what value of k, function f (x) is continuous at x = 0 where f(x) ...

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  13. Find (dy)/(dx) when x^y + y^x = a^b

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  14. Differentiate tan^(-1) ((sqrt(1 + sin x) + sqrt(1 - sin x))/(sqrt(1 + ...

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  15. y = e^(m sin^(-1)x), prove that (1 - x^2) y2 - xy1 = m^2y

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  16. If y = e^(m tan^-1 x), then show that (1 +x^2) y2 + (2x - m) y1= 0.

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  17. Examine the continuity of f(x) = {{:((x)/(|x| )"," ,"if " x != 0),(0",...

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  18. If xy = e^(x - y), prove that (dy)/(dx) = (y (x - 1))/(x (y + 1))

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  19. Differentiate e^(sec^2 x) + 3 cos^(-1) x w.r.t.x.

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  20. Find k so that f(x) = {{:((x^2 -25 )/(x -5)"," ,"if " x != 5),(k",","...

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