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y = [x + sqrt(x^2 + 1)]^p , prove that (...

`y = [x + sqrt(x^2 + 1)]^p` , prove that `(x^2 + 1)y_2 + xy_1 - p^2y = 0`

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

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

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  3. y = [x + sqrt(x^2 + 1)]^p , prove that (x^2 + 1)y2 + xy1 - p^2y = 0

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

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  5. Verify Rolle's theorem for the following functions f(x)=(x-2)(x-6) i...

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  6. Verify Rolle's theorem for the following functions f(x)=(x-2)(x-4)^2...

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  7. Verify Rolle's theorem for the following functions f(x)=(x - 1)(x - ...

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  8. Discuss the continuity of the following function: f(x) = sinx - cosx

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  9. Discuss the continuity of the following function: f(x) = sinx cdot cos...

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  10. Discuss the continuity of the following functions f(x) = {{:(x + 2",...

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  11. Determine the value of k so that following functions are continuous at...

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  12. Determine, k if the following function is continuous at x = 0 f(x) =...

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  13. Differentiate the following w.r.t. x ((3x - 1)/(3x + 1))^2

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  14. Differentiate the following w.r.t. x log (x + sqrt(1 + x^2))

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

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

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

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

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

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

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