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Examine the continuity of the function: ...

Examine the continuity of the function:
`f(x) = {:((x-4)/(2(x-4)), if x ne4),(0, if x =4):}` at x =4

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Find the co-ordinates of the point at which the tangent to the curve g...

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  2. Use Lagrange's Mean value Theorem to determine a point P on the curve ...

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  3. Examine the continuity of the function: f(x) = {:((x-4)/(2(x-4)), if...

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  4. Find the value of 'k', such that the function : f(x) = {:{(2x^(x+2)-...

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  5. Given f(x) =1/(x-1). Find the points of discontinuity of the composite...

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  6. Find f' (x) when f(x) = 2^(cos^2x)

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  7. Find f' (x) when f(x) = sin^-1(1/sqrt(x+1))

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  8. If sinx = (2t)/(1+t^2), tan y = (2t)/(1-t^2), find dy/dx

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  9. If y=sec^-1(1/(4x^3 -3x)), find dy/dx

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  10. Find dy/dx when tan^-1(x^2+y^2)=0

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  11. Examine the differentiability of the function f(x) = {:{(x[x], if 0 le...

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

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

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

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

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

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

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

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

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

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