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A function f : R rarr R satisfies the eq...

A function `f : R rarr R` satisfies the equation `f(x = y) = f(x) . f(y)` for all, `f(x) ne 0`. Suppose that the function is differentiable at x = 0 and f'(0) = 2. Then,

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Examine the differentiability of the function f(x) = {:{(x[x], if 0 le...

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  2. Show that |x-5| is continuous but not differentiable at x =5.

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  3. A function f : R rarr R satisfies the equation f(x = y) = f(x) . f(y) ...

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

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  5. Verify the Lagrange's Mean Value Theorem for the functions: f(x) = 1...

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  6. Verify LMV Theorem for the following: f(x) = sin x - sin 2x in[0,pi]

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  7. Verify LMV Theorem for the following: f(x) = sqrt(25-x^2)in[1,5]

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  8. The function f(x) = {{:(("sin x")/(x)+ cos x ,if x != 0),(k , if x = 0...

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  9. The function f(x) = [x], where [x] denotes the greatest integer functi...

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  10. The value of 'k' which makes the function defined by : f(x) = {:{(sin(...

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  11. If u = sin^-1(2x/(1+x)^2) and v = tan^-1(2x/(1-x^2)), the du/dv is

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  12. If x=t^2, y = t^3, then (d^2y)/(dx^2) is

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  13. The value of 'c' in Rolle's Theorem for the function f(x) =x^3 - 3x in...

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  14. The value of 'c' in mean Value Theorem for the function f(x) =x(x-2) i...

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  15. The derivative of f(x) =|x | at x=0 is

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  16. The derivative of log(ax+b) is

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  17. If f(x) = {:{(kx+1,xle5),(3x-5,x>5):} s is a continuous function then ...

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  18. The derivative of sin^3 (x^5) w.r.t. x is

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  19. If y = log(cose^x), then dy/dx = ……….

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  20. If y =e^(sin(logx), then the value of dy/dx is

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