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Examine the continuity and differenti...

Examine the continuity and differentiability of the function `f(x)=|x|+|x-1|+|x-2|x in Rdot`

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BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Find the following function is differentiable at a given point or no...

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  2. Discuss the continuity & differentiability of the function f(x) = sin ...

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  3. Examine the continuity and differentiability of the function f(x...

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  4. If the function f(x) defined as f(x)= -x^2/x, x<=0 and f(x)=x^nsin(1/x...

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  5. If the function f:[1,oo)to[1,oo) is defined by f(x)=2^(x(x-1)) then f^...

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  6. Let f(0)=0 and f'(0)=1. For a positive integral k show that lim(x->o) ...

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  7. Let f(x) = (xe)^(1/|x|+1/x); x != 0, f(0) = 0, test the continuity & ...

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

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

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

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

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

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

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

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

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

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

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  19. 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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  20. 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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