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Show that the function 'f' given by: f...

Show that the function 'f' given by:
`f(x) = |x| + |x-1|, x in R` is continuous both at x = 0 and x=1

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Show that the following functions are continuous: f(x) = cos(x^2)

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  2. Show that the following functions are continuous: f(x) = |cosx|

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  3. Show that the function 'f' given by: f(x) = |x| + |x-1|, x in R is c...

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  4. Show that the function 'f' given by: f(x) = |x-1|+|x-2|, x in R is c...

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  5. Locate the points of discontinuity of the function: f(x) = {:{((x^4-...

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  6. Examine the derivability of the following functions at the specified p...

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  7. Examine the derivability of the following functions at the specified p...

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  8. Examine the derivability of the following functions at the specified p...

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  9. Examine the derivability of the following functions at the specified p...

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

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  11. If F(x) = f(Ax) and f(ax) is differentiable , then prove that F'(x) = ...

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  12. If f(x) = {:{(xsin(1/x),xne0),(0,x=0):} Show that 'f' is not different...

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  13. Show that the function defined by: f(x) : {:{(3-2x,ifx<2),(3x-7,ifxg...

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  14. Discuss the continuity of fx) at x =0, when: f(x) = {:{((e^(1//x) -1...

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  15. Show that the function: f(x) = {:{(2+x,ifxge0),(2-x,ifx<0):} is cont...

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  16. Show that the function 'f' defined as follows, is continuous at x = 2,...

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  17. The function 'f' defined as: f(x) = {:{(x^2+3x+a,ifxle1),(bx+2,ifx>1...

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  18. For what values of 'a' and 'b' the function: f(x) = {:{(x^2,xlec),(a...

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  19. Let f: R rarr R(R is the set of real numbers) be defined as follows: ...

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  20. Show that f(x) = |x-3|, x in R is continuous but not differentiable at...

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