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Determine the values of x for which the ...

Determine the values of x for which the following functions fails to be continuous or differentiable
`f(x) = {((1-x), x lt 1), ((1-x)(2-x), 1lexle2 ), ((3-x), x gt 2):}`

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PATHFINDER-LIMIT, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. Let f(x) be a continuous function in [-1, 1] and satisfies f(2x^2 - 1)...

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  2. Let g(x) =int0^x f(t) dt where f is such that 1//2lef(t)le1 for tin[0,...

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  3. Determine the values of x for which the following functions fails to b...

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  4. In a function f : [-2a, 2a] rarr R is an odd function such that f(x) =...

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  5. lim(xrarr0)sqrt(1-cos2x)/(sqrt2x) is equal to

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  6. lim(xrarr2)(-1)^x (where [x] is the greatest integer function ), is eq...

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  7. lim(xrarr1([x]+[x]) , (where [.] denotes the greatest integer function...

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  8. If zr=cos(ralpha/n^2)+i"sin"(ralpha/n^2), where r=1,2,3,…n, then lim(n...

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  9. lim((xrarrinfty)((x+1))^(x//3) is given by

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  10. If lim(xrarrinfty)(sqrt(x^2-x+1 )-ax-b) = 0 then the values of a and b...

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  11. lim(xrarr0)[(In cosx)/((1+x^2)^(1/4)-1))] is equal to

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  12. If lim(nrarrinfty)(an-frac(1+n^2)(1+n))=b a finite number then

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  13. The integer n for which lim(x rarr0)((cos x-1)(cosx-e^x))/x^n is a fin...

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  14. The value of lim(xrarrinfty)frac(x+cosx)(x+sinx is

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  15. The value of f(0) so that the function f(x)=frac(2x-sin^-1x)(2x+tan^-1...

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  16. Which of the following function has finite number of points of discont...

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  17. Let f (x) = [3+2 cos x] , x in (-frac(pi)(2),frac(pi)(2)) where [.] de...

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  18. If y = frac(1)(t^2-t-6 and t = frac(1)(x-2) then the values of x wh...

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  19. The function f(x) = [x]^2-[x^2] (where [.] denotes the greatest integ...

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  20. f + g may be continuous function, if

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