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Prove that f(x) = {sinx/x ; x != 0 and ...

Prove that `f(x) = {sinx/x ; x != 0 and 1 ; x=0`. is continuous at `x=0`.

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NAGEEN PRAKASHAN-Continuity and Differentiability-Exercies 5a
  1. Discuss the continuiy of the function f(x)={(1/x ", " x ne 0),(1...

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  2. Discuss the continuity of the function f(x)={((|x|)/x", " xne 0)...

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  3. (i) Dissusse the continuity of the function f(x)={(|x-a|", " xne a...

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  4. Show that f(x) = sinx is continuous for all values of x.

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  5. Prove that f(x) = {sinx/x ; x != 0 and 1 ; x=0. is continuous at x=0...

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  6. If f(x) ={:{((sin 3x)/(sin 5x)", "x ne 0),(0", " x= 0):}, then d...

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  7. Show that the function f(x) ={:{((sin 3x)/(x)", "x ne 0),(1", " ...

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  8. Discuss the continuity of f(x) ={:{((sin^2 2x)/(x^2)", "x ne 0),(1", ...

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  9. Discuss the continuity of f(x) ={:{(cos""(1)/(x)", "x ne 0),(" "1",...

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  10. Discuss the continuity of f(x) ={:{(sin""(1)/(x)", "x ne 0),(" "1", ...

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  11. Discuss the continutiy of f(x) ={:{(xcos""(1)/(x)", "x ne 0),(" "0...

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  12. Disuss the continutiy of f(x) ={:{((sin^2 x)/(x^2)", "x ne 0),(" "0"...

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  13. If the function f(x) ={:{((3x^3-2x^2-1)/(x-1)", "x ne 1),(" "K", ...

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  14. For what value of k, the function f(x) ={:{(Kx^2", " x le 2 ),(" ...

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  15. For what value of k, the function f(x) ={:{((x^2-4)/(x-2)", " x ne 2...

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  16. For what value of k, the function f(x) ={:{(2x+1", "x gt2),(" ...

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  17. If the function f(x) given by f(x)={(3a x+b,"if "x >1), (11,"if "x=1),...

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  18. Discuss the continuity of the function f(x) ={:{((1+cos x)/(tan^2 x...

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  19. Discuss the continuity of the function f(x) ={:{((Sinx)/(x) ", "x ...

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  20. Prove that the function f(x)=2x-|x| is continuous at x=0.

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