Doubts
Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents
Sign in to save progress →
Doubts
Sign in

Limits Continuity and Differentiability question

2011 · Shift 2 · Q36
Guest · try one question or challengeGuest · try one question or challenge
  1. PYQ Library
  2. /JEE Advanced
  3. /Mathematics
  4. /Limits Continuity and Differentiability
  5. /2011 · Shift 2 · Q36

Limits Continuity and Differentiability question

2011 · Shift 2 · Q36

JEE AdvancedMathematicsLimits Continuity and DifferentiabilityMultiple correct+4 / −1
If f(x)={−x−π2,x≤−π2−cos⁡x−π21f(x) = \left\{ {\begin{matrix} { - x - {\pi \over 2},} & {x \le - {\pi \over 2}} \\ { - \cos x} & { - {\pi \over 2} 1} \\ \end{matrix} } \right.f(x)={−x−2π​,−cosx​x≤−2π​−2π​1​, then
  1. A
    f(x) is continuous at x = −π-\pi−π/2.
  2. B
    f(x) is not differentiable at x = 0.
  3. C
    f(x) is differentiable at x = 1.
  4. D
    f(x) is differentiable at x = −-− 3/2.
PreviousNext

More from Limits Continuity and Differentiability

  • Let L=x→0lim​x4a−a2−x2​−4x2​​,a>0. If L is finite, then2009 · Multiple correct
  • Let f(x) be a non-constant twice differentiable function defined on (−∞,∞) such that f(x)=f(1−x) and f′(41​)=0. Then,2008 · Multiple correct
  • Let g(x)=logcosm(x−1)(x−1)n​;00, and let p be the left hand derivative of ∣x−1∣ at x=1. If x→1+lim​g(x)=p, then2008 · MCQ
  • Consider the function f:(−∞,∞)→(−∞,∞) defined by f(x)=x2+ax+1x2−ax+1​,0<a<2.Which of the following is true?2008 · MCQ
  • Let the function g:(−∞,∞)→(−2π​,2π​) be given by g(u)=2tan−1(eu)−2π​. Then, g is2008 · MCQ
  • In the following [x] denotes the greatest integer less than or equal to x. Match the functions in Column I with the properties Column II. Includes table2007 · MCQ
  • Let R denote the set of all real numbers. Define the function f:R→R by f(x)={2−2x2−x2sinx1​2​ if xeq0, if x=0.​…2025 · MCQ
  • Let α and β be the real numbers such that x→0lim​x31​(2α​0∫x​1−t21​dt+βxcosx)=2. Then the value of α + β is ​.2025 · Numerical