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If y = sqrt(5^x+sqrt(5^x+sqrt(5^x+…........

If `y = sqrt(5^x+sqrt(5^x+sqrt(5^x+….......oo)))`, then prove that : `(2y-1)dy/dx = 5^x log5`.

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BETTER CHOICE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-PREVIOUS YEARS BOARDS QUESTIONS FOR PRACTICE (MULTIPLE CHOICE QUESTIONS)
  1. Differentiate the following w.r.t. x log (x + sqrt(1 + x^2))

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  2. If y = sqrt(2^x+sqrt(2^x+sqrt(2^x+….......oo))), then prove that : (2y...

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  3. If y = sqrt(5^x+sqrt(5^x+sqrt(5^x+….......oo))), then prove that : (2y...

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  4. Differentiate the function w.r.t. x : sqrt ((x-1)(x-2))/((x-3)(x-4)(...

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  5. Differentiate the following w.r.t. x. (sin x)^(cos x) + (cos x)^(sin...

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  6. Differentiate the following w.r.t. x. (sin x)^(tan x) + (cos x)^(sec...

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  7. Differentiate cos^(-1)((1)/(sqrt(1 + x^2))) w.r.t.x.

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  8. Diferentiate tan^(-1)((x)/(sqrt(1 - x^2))) w.r.t.x.

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

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

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

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

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

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

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

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

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

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

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

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

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