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Discuss the continuity and differentiabi...

Discuss the continuity and differentiability in `0,2]` of `f(x)={|2x-3|[x], xgeq1sin((pix)/2), x<1` to where [.] denotes the greatest integer function.

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BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. If f(x)= ax^2-b, |x|<1 and f(x)=-1/|x|, |x|>=1 is derivable at x=1 th...

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  2. Let f(x) be difined in the interval [-2, 2] such that f(x)={{:(-1"...

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  3. Discuss the continuity and differentiability in 0,2] of f(x)={|2x-3|...

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  4. Let a1 and a2 be two values of a for which f(x)= x*{ln(1+x)+ln(1-x)}/(...

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  5. Discuss the continuity & the derivability of 'f' where f(x)= degree ...

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  6. Consider the function f(x)=[x^2|cospi/(2x)|\ if\ x!=0 0,\ \ \ \ \ \ ...

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  7. A derivable function f : R^(+) rarr R satisfies the condition f(x) - f...

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  8. If f(x) = {{:(x - 3",",x lt 0),(x^(2)-3x + 2",",x ge 0):}"and let" g(x...

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  9. The integer ' n ' for which (lim)(xvec0)((cos x-1)(cos x-e^x))/(x^n) i...

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  10. The domain of the derivative of the function f(x)={t a n^(-1)x ,if|x|l...

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  11. Let f: Rvec be such that f(!)=3a n df^(prime)(1)=6. Then ("lim")(xvec...

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  12. Q. f={(x+a if x<0), (x-11 if x>=0) g(x)={(x+1 if x<0),(x-1)^2 if x...

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  13. If (lim)(x->0)(sin(n x)[(a-n)n x-t a n x])/(x^2)=n (n >0) then the val...

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  14. If a function f: [-2a, 2a] -> R is an odd function such that, f(x) = f...

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  15. The function given by y=||x|-1| is differentiable for all real n...

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  16. If |f(x1) - f(x2)| le (x1 - x2)^(2), AA x1 , x2 in R. Find the equatio...

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  17. Let g(x) = (x-1)^n/(log(cos^m(x-1))) ; 0 lt x lt 2 ,m and n and let p ...

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  18. If lim(x-&gt;0)[1+x1n(1+b^2)]^(1/x)=2bsin^2theta,b &gt;0,where theta...

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  19. If f(x) {-x-pi/2,xle-pi/2 and -cosx,-pi/2 < xle0 and x-1,0< x le1 and ...

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  20. Let f : R to R be a function such that f(x+y) = f(x)+f(y),Aax, y in...

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