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Limits, Continuity and Differentiability

Showing 50 of 401 · 401 total
  1. 301.[ _x 0 ( ^2x ) x^2] is equal to :
  2. 302.Let [p = _x 0^ + ( 1 + ^2 x )^1 2x] then log p is equal to :
  3. 303.[ _x 0 ,( 1 - 2x )^2 2x, x, - x 2x] is :
  4. 304.If [ _x ( 1 + a x - 4 x^2 )^2x = e^3,] then 'a' is equal to :
  5. 305.[ _x 2 x - x ( - 2x )^3] equals
  6. 306.[ _x 3 ] [ 3x - 3 2x - 4 - 2 ] is equal to :
  7. 307.For each t [ R], let [t] be the greatest integer less than or equal to t.
  8. 308.Let f(x) be a polynomial of degree 4 having extreme values at x = 1 and x = 2. If [ lim_x …
  9. 309.[ _x 0 x 2x - 2x x ( 1 - 2x )^2] equals :
  10. 310.[ _x 0 ,,( 27 + x )^1 3 - 3 9 - ( 27 + x )^2 3] equals.
  11. 311.If the function f defined as [f( x ) = 1 x - k - 1 e^2x - 1,x 0,] is continuous at x = 0, …
  12. 312.If [ _x 1 x^2 - ax + b x - 1 = 5], then a + b is equal to :
  13. 313.If [ _x 1 x^4 - 1 x - 1 = _x k x^3 - k^3 x^2 - k^2], then k is :
  14. 314.For each t [ ] R , let [t] be the greatest integer less than or equal to t Then [ _x 1^ + …
  15. 315.Let K be the set of all real values of x where the function f(x) = sin |x| -- |x| + 2(x --…
  16. 316.[ _x 0 x ( 4x ) ^2x ^2( 2x )] is equal to :
  17. 317.Let [x] denote the greatest integer less than or equal to x.
  18. 318.Let f(x) = 5 -- |x -- 2| and g(x) = |x + 1|, x [ ] R.
  19. 319.If [ ] and [ ] are the roots of the equation 375x2 -- 25x -- 2 = 0, then [ _n _r = 1^n ^r …
  20. 320.[ _x 1^ - - 2 ^ - 1x 1 - x ] is equal to :
  21. 321.[ _x /4 ^3x - x ( x + 4 )] is :
  22. 322.Let f : R [ ] R be a differentiable function satisfying f'(3) + f'(2) = 0.
  23. 323.Let f : [--1,3] [ ] R be defined as [f(x) = pmatrix | x | + [ x ] & , & - 1 x < 1 x + | x …
  24. 324.[ _x 0 ^2x 2 - 1 + x ] equals:
  25. 325.If [f(x) = [x] - [ x 4 ]] ,x [ ] 4 , where [x] denotes the greatest integer function, then
  26. 326.If the function [f(x) = pmatrix a| - x| + 1,x 5 b|x - , + 3,x > 5 pmatrix .] is continuous…
  27. 327.Let f(x) = 15 -- |x -- 10|; x [ ] R.
  28. 328.For each x[ ]R, let [x] be the greatest integer less than or equal to x.
  29. 329.[ _y 0 1 + 1 + y^4 - 2 y^4]
  30. 330.[ _x 0 ( ( 4 + x ) )^1 x] is equal to :
  31. 331.[ _x a ( a + 2x )^1 3 - ( 3x )^1 3 ( 3a + x )^1 3 - ( 4x )^1 3] (a [ ] 0) is equal to :
  32. 332.Let [t] denote the greatest integer [ ] t.
  33. 333.Let [f:( 0, ) ( 0, )] be a differentiable function such that f(1) = e and [ _t x t^2f^2(x)…
  34. 334.[ _x 0 x( e^( 1 + x^2 + x^4 - 1 )/x - 1 ) 1 + x^2 + x^4 - 1]
  35. 335.If [ ] is positive root of the equation, p(x) = x2 - x - 2 = 0, then [ _x ^ + 1 - ( p( x )…
  36. 336.Let f : R [ ] R be a function defined by f(x) = max x, x2.
  37. 337.[ _x 0 ( 3x^2 + 2 7x^2 + 2 )^1 x^2] is equal to
  38. 338.Let [t] denote the greatest integer [ ] t and [ _x 0 x[ 4 x ] = A].
  39. 339.Let f be any function continuous on [a, b] and twice differentiable on (a, b).
  40. 340.The value of [ _n [r] + [2r] + ...
  41. 341.The value of [ _x 0^ + ^ - 1(x - [x]^2). ^ - 1(x - [x]^2) x - x^3], where [ x ] denotes th…
  42. 342.If [ _x 0 ^ - 1x - ^ - 1x 3x^3] is equal to L, then the value of (6L + 1) is
  43. 343.If [f:R R] is given by f(x) = x + 1, then the value of [ _n 1 n[ f(0) + f( 5 n ) + f( 10 n…
  44. 344.[ _n ( 1 + 1 + 1 2 + ........
  45. 345.Let [t] denote the greatest integer less than or equal to t.
  46. 346.[ _x 2 ( _n = 1^9 x n(n + 1)x^2 + 2(2n + 1)x + 4 )] is equal to :
  47. 347.Let [f(x) = ^ - 1x] and [g(x) = x^2 - x - 2 2x^2 - x - 6].
  48. 348.The value of [ _h 0 2 3 ( 6 + h ) - ( 6 + h ) 3 h( 3 - ) ] is :
  49. 349.If [ _x ( x^2 - x + 1 - ax ) = b], then the ordered pair (a, b) is :
  50. 350.If [], [] are the distinct roots of x2 + bx + c = 0, then [ _x e^2(x^2 + bx + c) - 1 - 2(x…