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CBSE Questions for Class 11 Commerce Applied Mathematics Limits And Continuity     Quiz 9 - MCQExams.com

Ltn3nr=2n+1nr2n2 is equal to :
  • ln23
  • ln32
  • ln23
  • ln32
The value of limx11x(cos1x)2
  • 14
  • 1/2
  • 2
  • None of these
limI(π2)=t0tanθcosθln(cosθ)dθ is equal to
  • 4
  • 4
  • 2
  • Does not exists
If f (0) = 0 and f(x) is a differentiable and increasing function,then lim x0  x.f(x2)f(x)
  • is always equal to zero
  • may not exist as left hand limit may not exist
  • may not exist as left hand limit may not exist
  • right hand limit is always zero
Consider f(x)=limnxnsinxnxn+sinxn for x>0,x1,f(1)=0 then
  • f is continuous at x=1
  • f has a discontinuity at x=1
  • f has an infinite or oscillatory discontinuity at x=1
  • f has a removal type of discontinuity at x=1
If kr=1cos1β=kπ2 for any k1 and A=kr=1(βr)r, then limxA(1+x)1/3(12x)1/4x+x2 is equal to
  • 0
  • 12
  • π2
  • 56
limx0aex+bcosx+c.exsin2x=4 then b =
  • 2
  • 4
  • -2
  • -4
limxπ62sin2x+sinx12sin2x3sinx+1
  • 6
  • -6
  • -3
  • 3
Let f:R(0,1) be a continuous function.. Then, which of the following function(s) has (have) the value zero at some point in the interval (0,1)?
  • ex10f(t)sintdt
  • f(x)+10f(t)sintdt
  • xπ2x0f(t)costdt
  • x3f(x)
limxa+{x}sin(xa)(xa)2 

is equal to (where {.} denotes the fraction
part of x and aN

  • 0
  • 1
  • does not exist
  • none of thes
If f(x)={1|x|1+x,x11,x=1   then f([2x]), where [] represents the greatest integer function , is 
  • discontinuous at x=1
  • continuous at x=0
  • continuous at x=12
  • continuous at x=1
If f:RR is defined by
f(x)={x+2x2+3x+2ifxR{1,1}1ifx=20ifx=1 then f(x) continuous on the set 
  • R
  • R{2}
  • R{1,2}
  • R{1}
If l=limn3x29x2+74 and m=limn3x29x2+74, then
  • lm
  • l=2m
  • l=m
  • l=m
Letf(θ)=1tan9θ(1+tanθ)10+(2+tanθ)10+....+(20+tanθ)1020tanθ. The left hand limit of f(θ) as θπ2 is:
  • 1900
  • 2000
  • 2100
  • 2200
Consider A=[cosθsinθsinθcosθ], then the value of limnAnn (where θR) is equal to 
  • 10
  • zero matrix
  • symmetric matrix
  • 4
If limxλ(2λx)λtan(πx2λ)=1e, then λ is equal to-
  • π
  • π
  • π2
  • 2π
limx01xx(a arc tanxab arc tanxb) has the value equal to
  • ab3
  • 0
  • (a2b2)6a2b2
  • a2b23a2b2
limx2360+x24sin(x2)
  • 14
  • 0
  • 112
  • Does not exist
if(x)= greatest integer x, then limx2(1)[x]isequalto is equal to-
  • 0
  • -1
  • +1
  • none of these
The value of limx0csc4xx20ln(1+4t)t2+1dt is 
  • 1
  • 2
  • 3
  • 4
The value of limnn(n{ln(n)ln(n+1)}+1) is?
  • e
  • 1e
  • 12
  • 14
limxx2sin(logecosπx)
  • 0
  • π22
  • π24
  • π28
limxπ2cotxcosx(π2x)3 equals
  • 124
  • 116
  • 18
  • 14
limxπ2(1sinx)(8x2π3)cosx(π2x)4
  • π216
  • 3π216
  • π216
  • 3π216
limx0[x2cosec(x2)0]is equal to :
  • π180
  • π90
  • 0
  • 90π
The value of limx1πcos1xx+1 is given by 
  • 12π
  • 12π
  • 1
  • 0
If limx0asinxbx+cx2+x32x2log(1+x)2x3+x4 exists and is finite, then the value of a,b,c are respectively 
  • 0,6,6
  • 6,0,6
  • 6,6,0
  • 0,0,6
 \underset { x\rightarrow a }{ lim } \cfrac { sin\quad x-sin\quad a }{ \sqrt [ 3 ]{ x } -\sqrt [ 3 ]{ a }  } 
  • \sqrt [ 3 ]{ a\quad cos\quad a }
  • 2\sqrt [ 3 ]{ a }
  • { 3a }^{ { 2 /}{ 3 } }cos\quad a
  • \sqrt [ 2 ]{ a\quad cos\quad a }
The value of \displaystyle \lim_{x\rightarrow 0}\dfrac {1-\cos^{3}x}{x\sin x\cos x} is
  • \dfrac {2}{5}
  • \dfrac {3}{5}
  • \dfrac {3}{2}
  • \dfrac {3}{4}
Integrate:
 lim_{x\rightarrow 0}\dfrac{(1-\cos{2x})^{2}}{2x\tan{x}-x\tan{2x}}
  • 2
  • \dfrac{-1}{2}
  • -2
  • \dfrac{1}{2}
\displaystyle \lim_{x\rightarrow 0^{+}}{(\csc x)^{1/\log x}}=
  • e
  • e^{-1}
  • e^{2}
  • 1
The value of \lim_{x \rightarrow 0} \left(\dfrac{\tan x}{x}\right)^{1/x^{3}} is-
  • 0
  • \infty
  • e^{1/4}
  • Does\ not\ exist
The value of \underset { x\rightarrow \frac { x }{ 2 }  }{ lim } \frac { log\sin { x }  }{ { \left( \frac { \pi  }{ 2 } -x \right)  }^{ 2 } } is 
  • 0
  • \frac{1}{2}
  • -\frac{1}{2}
  • -2
\lim_{n\rightarrow \infty}\dfrac{1}{n^{2}}\left[\sin^{3}\dfrac{\pi}{4n}+2\sin^{3}\dfrac{2\pi}{4n}+3\sin^{3}\dfrac{3\pi}{4n}+....+n\sin^{3}\dfrac{n\pi}{4n}\right]=
  • \dfrac{\sqrt{2}}{9\pi^{2}}\left(52-15\pi\right)
  • \dfrac{\sqrt{2}}{9\pi^{2}}\left(52+15\pi\right)
  • \dfrac{\sqrt{2}}{9\pi}\left(52-17\pi\right)
  • \dfrac{\sqrt{2}}{9\pi^{2}}\left(52+17\pi\right)
If \alpha \quad and \beta are the roots of the equation  {ax}^{2}+bx+c=0 , then 
  \underset { x\rightarrow \cfrac { \pi  }{ 2 }  }{ lim } \cfrac { tan\left[ \left( \alpha +\beta  \right) x \right]  }{ sin\left[ \left( \alpha \beta  \right) x \right]  }  is equal to :
  • \cfrac {c} {b}
  • - \cfrac {b} {c}
  • \cfrac {a} {b}
  • - \cfrac {a} {b}
\begin{matrix} lim \\ n\rightarrow \infty  \end{matrix}\int _{ 0 }^{ 1 }{ \frac { { nx }^{ n-1 } }{ 1+{ x }^{ 2 } }  } dx=
  • 0
  • 1
  • 2
  • \frac { 1 }{ 2 }
Arrange the following limits in the ascending order :
(1)  \lim _ { x \rightarrow \infty } \left( \dfrac { 1 + x } { 2 + x } \right) ^ { x + 2 }

(2)  \lim _ { x \rightarrow 0 } ( 1 + 2 x ) ^ { 3 / x }

(3)  \lim _ { \theta \rightarrow 0 } \dfrac { \sin \theta } { 2 \theta }

(4)  \lim _ { x \rightarrow 0 } \dfrac { \log _ { e } ( 1 + x ) } { x }
  • 1,2,3,4
  • 1,3,4,2
  • 1,4,3,2
  • 3,4,1,2
\mathop{\lim}\limits_{x \to 0} \left(\dfrac{3+x}{3-x}\right)^{\dfrac{x+1}{x}} is equal to 
  • e^{2/3}
  • e^{1/3}
  • e^3
  • e^2
If \mathop {\lim }\limits_{x \to 0} \frac{{x\left( {1 + a\cos x} \right) - b\sin x}}{{{x^3}}} = 1, then
  • a = \frac{5}{2}
  • b = \frac{{ - 5}}{2}
  • a + b = 4
  • a + b = -4
\lim_{x\rightarrow 0 }(\frac{p^{\frac{1}{x}}+q^{\frac{1}{x}}+r^{\frac{1}{x}}+s^{\frac{1}{x}}}{4})3x where p,q,r,s> 0 is equal to
  • pqrs
  • (pqrs)^{3}
  • (pqrs)\frac{3}{2}
  • (pqrs)\frac{3}{4}
\lim- {x\to 0} \dfrac{1- cos(1 - cos4x)}{x^4} is equal to : 
  • 4
  • 16
  • 32
  • None of these
The value of \displaystyle\lim_{x\to 0} |x|^{sinx} equals 
  • 0
  • -1
  • 1
  • does not exist
If \displaystyle \lim _{ x\rightarrow 0 }{ \dfrac { \left( \sin { nx }  \right) \left[ (a-n)nx-tanx \right]  }{ { x }^{ 2 } }  } =0, then the value of a
  • \dfrac { 1 }{ n }
  • n-\dfrac { 1 }{ n }
  • n+\dfrac{1}{n}
  • None\ of\ these
\lim _ { x \rightarrow 0 } \frac { 1 - \cos x \cos 2 x \cos 3 x } { \sin ^ { 2 } 2 x } =
  • \frac { 3 } { 2 }
  • \frac { 5 } { 2 }
  • \frac { 7 } { 4 }
  • \frac { 9 } { 2 }
The value of lim_{x \to 0} (\dfrac{1}{x^2} - cotx) equals 
  • 1
  • 0
  • \infty
  • Does not exist
\displaystyle \lim _{ x-\infty  }{ sgn\left( \cot{\dfrac { { \pi x }^{ 2019 } }{ { x }^{ 2019 }+7 }}  \right)  }
  • Equals -1
  • Equals 1
  • equals 0
  • Does not exit
\displaystyle\lim_{x \to \pi/2} (sec x +tan x) is equal to 
  • 1
  • -1
  • \dfrac{1}{2}
  • 0
\underset { x\rightarrow \pi/2 }{ lim } \left(\dfrac{cosec x-1}{cot^2x}\right)=
  • 0
  • -\dfrac{1}{2}
  • \dfrac{1}{2}
  • 1
\underset { x\rightarrow 0 }{ lim } \dfrac { x\tan { 2x } -2\tan { 2x }  }{ { \left( 1-cos2x \right)  } } equals:
  • \dfrac{1}{4}
  • 1
  • \dfrac{1}{2}
  • -\dfrac{1}{2}
\displaystyle\lim_{x\to \pi/2} \dfrac{sinx-(sinx)^{sin x}}{1-sin x + In sin x} is equal to
  • 4
  • 2
  • 1
  • none of these
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Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers