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The function f(x)={:{(x^(2)/a", if ...

The function `f(x)={:{(x^(2)/a", if "0lexlt1),(a", if "1lexltsqrt(2)),((2b^(2)-4b)/(x^(2))", if "sqrt(2)lexltoo):}` is continuous on `(0,oo)`. Find the most suitable value of a and b.

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The correct Answer is:
`a=-1,b=1` or `a=1,b=1pmsqrt(2)`
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ARIHANT PUBLICATION-CONTINUITY AND DIFFERENTIABILITY -CHAPTER PRACTICE (4 MARK)
  1. Find all points of discontinuity of f, where f is defined by f(x)={:{(...

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  2. Find the value of k so that the function f is continuous at x=pi//2,f(...

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  3. The function f(x)={:{(x^(2)/a", if "0lexlt1),(a", if "1...

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  4. If the function f(x) defined by f(x)={((log(1+ax)-log(1-bx))/(k)", if ...

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  5. Examine the continuity of the following function f(x)={{:((x)/(2|x|)",...

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  6. Find the point of discontinuity, if any of the following function f(x)...

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  7. Find the point of discontinuity of the function f(x)={:{((sin2x)/(x)",...

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  8. If function f(x)=|x-3|+|x-4|, then show that f(x) is not differentiabl...

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  9. Differentiate tan^(-1)((sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sq...

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  10. If y=x^(sinx-cosx)+(x^(2)-1)/(x^(2)+1), then find (dy)/(dx)

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  11. If y=(sinx)^(x)+sin^(-1)sqrt(x), then find (dy)/(dx).

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  12. Find (dy)/(dx), if y=(cosx)^(x)+(sinx)^(1//x).

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  13. If x=alphasin2t(1+cos2t) and y=betacos 2t(1-cos2t), then show that (dy...

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  14. Find the derivative of the function w.r.t. x at x=1, cos^(-1)[sinsqrt(...

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  15. If y=e^(m sin ^(-1)x), then show that (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)...

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  16. Test the continuity and differentiability at x=1 of the function f def...

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  17. Show that the function f(x)=|x-1|+|x-2| is not differentiable at x=2.

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  18. If a function f is differentiable at a point c, then prove that it is ...

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  19. If x=acos^(3)theta,y=a sin^(3)theta,then find (d^2y)/dx^(2)

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  20. Find the derivative of (x+sinx)/(x+cosx) w.r.t. x.

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