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Prove that the function f(x) = {{:(x cos...

Prove that the function `f(x) = {{:(x cos 1/x"," , "when " x != 0),(0",", "when " x = 0):}` is continuous at `x = 0`

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BETTER CHOICE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-PREVIOUS YEARS BOARDS QUESTIONS FOR PRACTICE (MULTIPLE CHOICE QUESTIONS)
  1. y = e^(m sin^(-1)x), prove that (1 - x^2) y2 - xy1 = m^2y

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

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

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

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

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

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  7. If f(x) is continuous at x = 0 , find a, where f(x) = {{:((1 - cos ax)...

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

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  9. Differentiate tan^(-1)((sqrt(1 + a^2 x^2) - 1)/(ax)) w.r.t.x.

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  10. Verify LMV theorem for the following functions f(x) = x(x-1)(x - 2) i...

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  11. Verify LMV theorem for the following functions f(x) = x^2 + x - 1 "...

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  12. Discuss the continuly of the following functions f(x) = {{:(2x"," , ...

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  13. Discuss the continuly of the following functions f(x) = {{:(2"," , "...

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  14. Find (dy)/(dx) if ax + by^2 = cos y

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  15. Find (dy)/(dx) if 2x + 3y = sin x

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  16. Find (dy)/(dx) if x^y = y^x.

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  17. y = 5 cos x - 3 sin x, prove that (d^2 y)/(dx^2) + y = 0

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  18. Prove that the function f(x) = {{:(x cos 1/x"," , "when " x != 0),(0",...

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  19. Discuss the continuity of the function f(x) = {{:(3"," , "if " 0 le x ...

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  20. Differentiate x^(sin x) + (sin x)^(cos x) w.r.t.x.

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