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Find the values of a and b such that the...

Find the values of a and b such that the function f defined by `f(x)={:{((x-4)/(|x-4|)+a", if "xlt4),(a+b", if "x=4" is a"),((x-4)/(|x-4|)+b", if "xgt4):}`
continuous function at `x=4`.

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Verified by Experts

The correct Answer is:
`a=1,b=-1`
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ARIHANT PUBLICATION-CONTINUITY AND DIFFERENTIABILITY -(PART I) QUESTION FOR PRACTICE (4 MARK)
  1. Determine f(0) so that the function f(x) defined by f(x)=((4^(x)-1)^(3...

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

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

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

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

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

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

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

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

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

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

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

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

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  15. Discuss the continmuity of function f defined by f(x)={{:((1)/(2)-x"...

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  16. Discuss the continuity of the function f(x)=sin x-cos x.

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

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  18. Examine that sin|x| is a continuous function.

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  19. Show that the function f defined by f(x)=|1-x+|x||, where x is any rea...

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  20. Show that tangent function is continuous in their domain

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