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Show that the function f(x)={{:((e^(1//x...

Show that the function `f(x)={{:((e^(1//x)-1)/(e^(1//x)+1)", when "x!=0),(0", when "x=0):}` is discontinuous at `x=0`.

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SHARAM PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXAMPLE
  1. Discuss the continuity of f(x)={((x^2-25)/(x-5),when x!=5),(9,when x=5...

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  2. Discuss the continuity of the function f(x)={(sin 3x)/(2x),whenx!=0),(...

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  3. Show that the function f(x)={{:((e^(1//x)-1)/(e^(1//x)+1)", when "x!=0...

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  4. Examine the continuity of the function f(x)={((1)/(x+[x]),ifx<0),(-1,i...

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  5. Discuss the continuity of the function f(x)={:{((|x|)/(x)", if "x!=0...

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  6. If a function is continuous at x=a, then find lim(hto0)+1/2{f(a+h)+f(a...

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  7. Examine the continuity of f(x)= sin (pi(x))/2 at x = 0.

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  8. Find the value of a such that the function f defined by f(x)={((sinax...

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  9. If f(x)={(ax^2+b if x lt1),(1 if x=1),(2ax-b if xgt1):} is continuous...

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  10. Show that sinx is continuous for every real x.

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  11. For what value of k is the function defined by {(k(x^2+2),when xle0),(...

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  12. Find the value of k if the function f(x) defined by f(x)={(2x-1,when x...

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  13. For what value of lamda is the function f(x)={{:(lamda(x^(2)-2x)", i...

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  14. Find the value of k, so that the function defined by f(x)={(kx+1", if...

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  15. Examine the contiunity of the following functions at the indicated poi...

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  16. Examine the continuity of the function f defined by f(x)={[2x+1if x<1]...

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  17. If f(x)={(ax^2+b if x lt1),(1 if x=1),(2ax-b if xgt1):} is continuous...

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  18. Find the relationship between a and b so that thefunction defined by f...

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  19. Find the value of a and b if the function given below is continuous. ...

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  20. For what value of k the following function is continuous at x=0 ? f(...

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