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Show that the function f(x)={{:((sinx)...

Show that the function
`f(x)={{:((sinx)/(x)+cosx", if "x!=0),(2", if "x=0):}`
is continuous at `x=0`.

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ARIHANT PUBLICATION-CONTINUITY AND DIFFERENTIABILITY -(PART I) QUESTION FOR PRACTICE (4 MARK)
  1. Show that the function f(x)=2x-|x| is continuous at x=0.

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  2. Let f(x)=x-|x-x^(2)|,x in [-1,1] find the point of discontinuity, (if ...

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  3. Show that the function f(x)={{:((sinx)/(x)+cosx", if "x!=0),(2", ...

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  4. Discuss the continuity of the following function at x=0. f(x)={{:((x...

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  5. If f(x)=(sqrt(2)cosx-1)/(cotx-1),x!=(pi)/(4). Then, find value of f((p...

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  6. Show that the function defined by g(x)=x-[x] is discontinuous at all i...

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  7. Determine f(0) so that the function f(x) defined by f(x)=((4^(x)-1)^(3...

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  8. Examine the continuity of a function f(x)={{:(|x|"cos"(1)/(x)", if ...

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

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

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

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  12. For what value of k, the function f(x)={((tan2x)/(x)", if "x!=0),(k"...

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

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  14. Find the value of a, so that the function f(x) is defined by f(x)={{...

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  15. Show that the function f(x)={(|x-a|sin(1)/(x-a)", if "x!=a),(0", ...

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  16. A car driver is driving a car on the dangerous path given by f(x)={((1...

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  17. For what value of k, the function f(x)={{:((sin2x)/(x)", "x!=0),(k"...

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  18. Find the value of k for which f(x)={{:((sqrt(1+kx)-sqrt(1-kx))/(x)", ...

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  19. find the value of k, so that the function f(x)={((2^(x+2)-16)/(4^(x)...

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  20. Find the values of a and b such that the function f defined by f(x)={:...

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