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Limits, Continuity and Differentiability

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  1. 101.Let f(x)=_y0((1-(xy))(xy))/(y^3).
  2. 102.The value of _x0((x^2^2x)/(x^2-^2x)) is:
  3. 103.For the function f(x)=e^|x|-|x|, xR, consider the following statements: Statement I: f is …
  4. 104.Let the function [f(x)=cases-3ax^2-2, & x<1 a^2+bx, & x1cases] be differentiable for all x…
  5. 105.Let [f(x)=cases3x, & x<0 1+x+[x], x+2[x], & 0 x2 5, & x>2cases] where [] denotes the great…
  6. 106.Let [t] be the greatest integer less than or equal to t.
  7. 107.If _x0(( x)/(x))^1/x^2=p, then 96_ep is equal to____________ Answer: 32
  8. 108.For t>-1, let _t,_t be the roots of [((t+2)^1/7-1)x^2+((t+2)^1/6-1)x+((t+2)^1/21-1)=0] If …
  9. 109.If f(x)=( x)-( x) x- x is continuous at x=0, then f(0) is equal to:
  10. 110.If =_x[((e)/(1-e))(1e-(x)/(1+x))]^x, then the value of _e1+_e equals:
  11. 111.If the function [f(x)=cases2x((k_1+1)x)+((k_2-1)x), & x<0 4, & x=0 2x_e(2+k_1x2+k_2x), & x…
  12. 112._x((2x^2-3x+5)/(3x^2+5x+4))^x/2 is equal to:
  13. 113.Let f:R-0R be a function such that f(x)-6f(1x)=353x-52.
  14. 114._x0 cosec,x(√2^2x+3 x-^2x+ x+4) is:
  15. 115._n(_k=1^n(k^3+6k^2+11k+5)/((k+3)!)) is:
  16. 116.Let f(x)=cases(1+ax)^1/x, & x<0 1+b, & x=0 (x+4)^1/2-2(x+c)^1/3-2, & x>0cases be continuou…
  17. 117._x1^+((x-1)(6+(x-1))+(1-x))/((x-1)^3)=-1, where ,R.
  18. 118.Let f:RR be a differentiable function such that f(2)=1, f'(2)=4.
  19. 119._x0^+(5x^1/3)(1+3x^2)(^-1(3 x))^2(e^5x^4/3-1) is equal to
  20. 120.Given below are two statements: Statement I: _x1x^(2)/(1-x)=1e^2 Statement II: _x0(^-1x+12…
  21. 121.Let f(x)=casesx^21x, & x0 0, & x=0cases.
  22. 122.If the function [f(x)=cases(1+| x|)^/| x|, & 0<x<2 , & x=2 e^6x/4x, & 2<x<cases] is contin…
  23. 123.Let f:(-2,2)R be defined by [f(x)=casesx[x], & -2<x<0 (x-1)[x], & 0 x<2cases] where [x] de…
  24. 124.Let f and g be two functions defined by f(x)=casesx+1, & x<0 |x-1|, & x0cases and g(x)=cas…
  25. 125.Let f(x)=cases(x-[x])x-[x], & x(-2,-1) 2x,,3[|x|], & |x|<1 1, & otherwisecases where [t] d…
  26. 126.Let f(x)=[2x^2+1] and g(x)=cases2x-3, & x<0 2x+3, & x0cases, where [t] is the greatest int…
  27. 127.Let f,g:RR be two real valued functions defined as f(x)=cases-|x+3|, & x<0 e^x, & x0cases …
  28. 128.Let f(x)=1,,1+x x, 0 x2.
  29. 129.Let f:RR be defined as [f(x)=cases[e^x], & x<0 ae^x+[x-1], & 0 x<1 b+[( x)], & 1 x<2 [e^-x…
  30. 130.Let f,g:RR be functions defined by f(x)=cases[x], & x<0 |1-x|, & x0cases and g(x)=casese^x…
  31. 131.Let f:RR be a function defined by: [f(x)=casest^3-3t: t x, & x2 x^2+2x-6, & 2<x<3 [x-3]+9,…
  32. 132.The number of points where the function [f(x)=cases|2x^2-3x-7|, & x-1[2x^2-1], & -1<x<1|x+…
  33. 133.Let f(x)=cases|4x^2-8x+5|, & if 8x^2-6x+10[4x^2-8x+5], & if 8x^2-6x+1<0cases, where [] den…
  34. 134.If f(x)=casesx+a, & x0|x-4|, & x>0cases and g(x)=casesx+1, & x<0(x-4)^2+b, & x0cases are c…
  35. 135.If for p q0, the function f(x)=[7]p(729+x)-3[3]729+qx-9 is continuous at x=0, then:
  36. 136.The function f:RR defined by [f(x)=_n(2 x)-x^2n(x-1)1+x^2n] is continuous for all x in:
  37. 137.The number of points, where the function f:RR, [f(x)=|x-1||x-2||x-1|+(x-3)|x^2-5x+4|] is N…
  38. 138.Let the function f(x)=cases_e(1+5x)-_e(1+ x)x, & x010, & x=0cases be continuous at x=0.
  39. 139.If [t] denotes the greatest integer t, then the number of points at which the function [f(…
  40. 140.Let f:RR be defined by a piecewise sine-type rule (matched to x near x=1 and x=-1).
  41. 141.Let f be any function defined on R satisfying |f(x)-f(y)|(x-y)^2 x,yR.
  42. 142.Let f(x) be a differentiable function at x=a with f'(a)=2 and f(a)=4.
  43. 143.A function f is defined on [-3,3] as f(x)=cases|x|,2-x^2, & -2 x2[|x|], & 2<|x|3cases, whe…
  44. 144.If f:RR is a function defined by f(x)=[x-1](2x-12), where [] denotes the greatest integer …
  45. 145.If f(x)=cases1|x|, & |x|1^2+b, & |x|<1cases is differentiable at every point of the domain…
  46. 146.Let f:RR be a function defined as f(x)=cases(a+1)x+2x2x, & x<0, & x=0x+bx^3-xbx^5/2, & x>0…
  47. 147.Let f:RR satisfy f(x+y)=f(x) f(y) for all x,yR and f(x)0 for any xR.
  48. 148.If the function f(x)=( x)- xx^4 is continuous at each point in its domain and f(0)=1k, the…
  49. 149.Consider the function f:RR defined by f(x)=cases(2-1x)|x|, & x00, & x=0cases.
  50. 150.Let f:RR and g:RR be defined as f(x)=casesx+a, & x<0|x-1|, & x0cases and g(x)=casesx+1, & …