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If y = tan^(-1)((sqrt(1 + x^2) - sqrt(1 ...

If `y = tan^(-1)((sqrt(1 + x^2) - sqrt(1 - x^2))/(sqrt(1 + x^2) + sqrt(1 - x^2)))` , then show that `(dy)/(dx) = x/(sqrt(1 - x^4))`

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. If f(x) = {:{((x^2-(a+2)x+a)/(x-2), x ne2),(2,x=2):} is continuous at ...

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  2. Let g(x) = ((x-1)^3)/(log(x-1)) Find g(5).

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  3. Let y be an implict function of x defined by x^(2x) - 2x^x cot y -1 =0...

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  4. Let f: (-1,1) rarr R be a differentiable function with f(0) = -1 and ...

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  5. If 'f' is differentiable at x = a, find (underset(xrarra)lim(x^2f(a)-a...

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  6. If f: R rarr R is a function defined by: f(x) = [x] cos((2x-1)/2)pi, ...

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  7. Let f(x)={x^2|(cos)pi/x|, x!=0 and 0,x=0,x in RR, then f is a. differ...

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  8. If y = sec(tan^-1x), then dy/dx at x =1 is equal to

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  9. If g is te inverse of a function f and f'(x) = 1/(1+x^5) then g'(x) is...

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  10. If the function g(x) = {{:(k sqrt(x + 1)",", 0 le x le 3),(mx + 2",",3...

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  11. For x in R, f(x) = |log 2 - sin x| and g(x) = f(f(x)), then

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  12. A function f: R rarr R is defined as follows: f(x) = {:{(x,ifxle1),(...

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  13. If sqrtx+sqrty=4, then dy/dx is

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  14. Find dy/dx when x = 4t, y = 4/t

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  15. The funtion f(x) is defined as follows: f(x) = {:{(x^2+ax+b,0lex<2),...

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  16. If y = tan^(-1)((sqrt(1 + x^2) - sqrt(1 - x^2))/(sqrt(1 + x^2) + sqrt(...

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  17. If x^Y = e^[X - Y], prove that dy/dx= log x/(1+logx)^2.

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  18. If y = e^[ax] sin bx, prove that d^2y/dx^2 - 2a dy/dx +(a^2 + b^2 ) y ...

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  19. Verify Rolle's theorem for function f(x) = sin x + cos x in the interv...

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  20. Finddy/dx, if y^x+x^y+x^x = a^b

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