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Limits and Derivatives Test - 6

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Limits and Derivatives Test - 6
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Weekly Quiz Competition
  • Question 1
    1 / -0
    If x = , y = , then  equals
  • Question 2
    1 / -0

    Solution

  • Question 3
    1 / -0
    If 2x + 2y = 2x + y, then  =
  • Question 4
    1 / -0
    If xpyq = (x + y)p + q, then  =
  • Question 5
    1 / -0
    If = 2, then a and b, respectively are
  • Question 6
    1 / -0

    Ltx→0(sinx−x/x4)sinx equal to

    Solution

    Ltx→0(sinx−x/x3).(sinx/x)=Ltx→0(sinx−x/x3)

    Now using L'Hospital we have, cosx−1/3x2

    Again using L'Hospital, −sinx/6x

    Again using L'hospital; −1/6

  • Question 7
    1 / -0
    The function f(x) = 1+ |sin x| is
  • Question 8
    1 / -0
    If x = a cos4and y = a sin4, then  at  =  is equal to
  • Question 9
    1 / -0
  • Question 10
    1 / -0
  • Question 11
    1 / -0
    If y = a emx + b e -mx, then y'' is equal to
  • Question 12
    1 / -0

    Let f (x) = x sin1x, x≠0, then the value of the function at x = 0, so that f is continuous at x = 0, is

    Solution

    Here, if we directly put x= 0, f(0) = 0 * sin (1/0) = 0.

    At L.H.L, put x=0-h ,Ltx→0x.sin1x f(0-h) = = 0.

    At R.H.L, put x = 0+h ,Ltx→0x.sin1/x , f(0+h) =  = 0.

    Hence, L.H.L = f(0) = R.H.L.

    f(x) is continuous at x=0.

  • Question 13
    1 / -0

    Solution

  • Question 14
    1 / -0

    Solution

  • Question 15
    1 / -0

    Solution

  • Question 16
    1 / -0

    Solution

  • Question 17
    1 / -0

    Solution

  • Question 18
    1 / -0

    Solution

  • Question 19
    1 / -0

    Solution

  • Question 20
    1 / -0

    Solution

  • Question 21
    1 / -0
     is equal to
  • Question 22
    1 / -0
     is equal to
  • Question 23
    1 / -0
    If f be a function, such that f(9) = 9 and f'(9) = 3, then   is equal to
  • Question 24
    1 / -0
     is equal to
  • Question 25
    1 / -0
    The derivative of f(x) = |x| at x = 0 is
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