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

2022 · 26 Jun · Shift 2 · Q27
Guest · try one question or challengeGuest · try one question or challenge
  1. PYQ Library
  2. /JEE Main
  3. /Mathematics
  4. /Limits Continuity and Differentiability
  5. /2022 · 26 Jun · Shift 2 · Q27

Limits Continuity and Differentiability question

2022 · 26 Jun · Shift 2 · Q27

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1
lim⁡x→0cos⁡(sin⁡x)−cos⁡xx4\mathop {\lim }\limits_{x \to 0} {{\cos (\sin x) - \cos x} \over {{x^4}}}x→0lim​x4cos(sinx)−cosx​ is equal to :
  1. A
    13{1 \over 3}31​
  2. B
    14{1 \over 4}41​
  3. C
    16{1 \over 6}61​
  4. D
    112{1 \over 12}121​
PreviousNext

More from Limits Continuity and Differentiability

  • Let f(x) = min {1, 1 + x sin x}, 0 ≤ x ≤ 2 π. If m is the number of points, where f is not differentiable and n is the number of points, where f is not continuous, then the ordered pair (m, n) is equal to2022 · MCQ
  • If for peqqeq0, the function f(x)=3729+qx​−97p(729+x)​−3​ is continuous at x=0, then :2022 · MCQ
  • Let a be an integer such that x→7lim​[x−3a]18−[1−x]​ exists, where [t] is greatest integer ≤ t. Then a is equal to :2022 · MCQ
  • Let [t] denote the greatest integer ≤ t and {t} denote the fractional part of t. The integral value of α for which the left hand limit of the function f(x)=[1+x]+2[x]+{x}α2[x]+{x}+[x]−1​…2022 · Numerical
  • Let f:[0,1]→R be a twice differentiable function in (0,1) such that f(0)=3 and f(1)=5. If the line y=2x+3 intersects the graph of f at only two distinct points in (0,1), then the least number of points…2022 · Numerical
  • x→0lim​((x+2)3+2(x+2)2+3sin(x+2)(x+2cosx)3+2(x+2cosx)2+3sin(x+2cosx)​)x100​ is equal to ​.2022 · Numerical
  • The function f:R→R defined by f(x)=n→∞lim​1+x2n+1−x2ncos(2πx)−x2nsin(x−1)​ is continuous for all x in :2022 · MCQ
  • Let f : R → R be defined as f(x)=⎩⎨⎧​[ex],aex+[x−1],b+[sin(πx)],[e−x]−c,​x<00≤x<11≤x<2x≥2​ where a, b, c ∈…2022 · MCQ