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CBSE Questions for Class 11 Commerce Applied Mathematics Limits And Continuity     Quiz 1 - MCQExams.com

Evaluate limx34x3 using the properties of limits.
  • 281/4
  • 251/4
  • 271/4
  • 261/4
IfAi=xai|xai|,i=1,2,3,.....n and a1<a2<a3....<an,then
limxam(A1A2......An),1mn
  • is equal to (1)m
  • is equal to (1)m+1
  • is equal to (1)nm
  • is equal to (1)nm1
limxπ2cotxcosx(π2x)3
  • 12
  • 12
  • 2
  • 1
f(x)=xsin1x, forx0
       =0, forx=0
Then.
  • f(0+)exit but f(0) does not exit
  • f(0+) and f(0) do not exit
  • f(0+)=f(0) 
  • none of these
limx0sin1xtan1xx3 is equal to 
  • 0
  • 1
  • 1
  • 12
If limx(x2+x+1x+1axb)=4,then
  • a=1,b=4
  • a=1,b=4
  • a=2,b=3
  • a=2,b=3
limn(tanθ+12tanθ2+122tanθ22+...+12ntanθ2n) equals?
  • 1θ
  • 1θ2cot2θ
  • 2cot2θ
  • None of these
Let p= limx0+(1+tan2x)12x then log p is equal to :
  • 1
  • 12
  • 14
  • 2
limxπ4(sin2x)sec22x is equal to 
  • 12
  • 12
  • e12
  • e12
limθπ/21sinθ(π/2θ)cosθ is equal to
  • 1
  • 1
  • 1/2
  • 1/2
If limx(1+ax4x2)2x=e3 , then 'a' is equal to :
  • 2
  • 32
  • 23
  • 12
The value of limx0sin(πcos2x)x2 equals 
  • π
  • π
  • π2
  • 2π
limx1xtan(x[x])x1 is:
  • 1
  • 0
  • -1
  • does not exist
The value of limθπ2(secθtanθ) equals 
  • 0
  • 1
  • 2
The value of limx01cos3xxsinxcosx is
  • 25
  • 35
  • 32
  • 34
The value of limxaxsin(bax) where a>1 is 
  • bloga
  • alogb
  • b
  • a
The value of limx3(x3+27)loge(x2)x29 is
  • 9
  • 18
  • 27
  • 13
The value of limxx442(cosx+sinx)51sin2x is
  • 0
  • 2
  • 52
  • 3
limx0([5sinxx]+[6sinxx])  (where  [.]  denotes greatest integer function) is equal to
  • 0
  • 12
  • 1
  • 2
If limx0x3a+x(bxsinx)=1, a > 0, then a + b is equal to 
  • 36
  • 37
  • 38
  • 40
limx0sinx5sin4x=
  • 0
  • 1
  • 1
limx0(1cos2x)sin5xx2sin3x=?
  • 10/3
  • 3/10
  • 6/5
  • 56
limx01cos2xcos2xcos8x is equal to 
  • 1/15
  • 1/10
  • 1/15
  • 15
limx1cos2cos2xx2|x|  is equal to :
  • 0
  • cos2
  • 2sin2
  • None
limx0x.10xx1cosx=
  • log10
  • 2log10
  • 3log10
  • 4log10
limx031+sinx31sinxx=
  • 0
  • 1
  • 23
  • 32
limx0sin(6x2)Incos(2x2x)=
  • 12
  • -12
  • 6
  • -6
limx1(log33x)logx3=?
  • e1
  • e
  • 1
  • 1
Let  f(β)=limαβsin2αsin2βα2β2,  then  f(π4)  is greater than-
  • limx01cos3xxsin2x
  • limxπ/2cotxcosx(π2x)3
  • limx(cosx+1cosx)
  • limxaa+2x3x3a+x2x where a>0
limx(3x4+2x2)sin(1x)+|x|3+5|x|3+|x|2+|x|+1=
  • 2
  • 1
  • -2
  • -3
The value f limxπ/41sin2xπ4x=
  • 14
  • 14
  • 12
  • None of these
If L=limx0asinxsin2xtan3x is finite, then the value of L is :
  • 1
  • 2
  • 3
  • -1
If limx0aexbcosx12cxxcosx=2 then the value of a+b+c is-
  • 4
  • 4
  • 2
  • 2
limx0sin2x+3x2x+sin3x is equal to
  • 1
  • 15
  • 2
  • Does not exist
If f(x) is continuous and f(92)=29, then limx0f(1cos3xx2) is equal to :
  • 92
  • 29
  • 0
  • 89
The function f:(R0) R given by f(x)=1x2e2x1 can be made continuous at x=0 by defining f(0) as
  • 2
  • 1
  • 0
  • 1
If the function f(x)= \left\{\begin{matrix}\dfrac {\sqrt {2+\cos x}-1}{(\pi-x)^2} & x\neq \pi \\ k & x=\pi \end{matrix}\right. is continuous at x=\pi, then k equals :
  • 0
  • \dfrac {1}{2}
  • 2
  • \dfrac {1}{4}
If   f:R\rightarrow R   is a function defined by   f(x)=[x]\displaystyle \cos\left(\frac{2x-1}{2}\pi\right),   where   [{x}]   denotes the greatest integer function, then   {f}   is:
  • continuous for every real x
  • discontinuous only at x = 0
  • discontinuous only at non-zero integral values of x
  • continuous only at x = 0
\displaystyle \lim_{x\rightarrow 0}x^{2}\displaystyle \sin\frac{\pi}{x}=
  • 1
  • 0
  • does not exist
  • \infty
\displaystyle \lim _{ x\rightarrow 0 }{ \cfrac { x{ e }^{ x }-\sin { x }  }{ x }  } is equal to
  • 3
  • 1
  • 0
  • 2
Use limit properties to evaluate \displaystyle\lim_{x\to4}\dfrac{3x^2\tan \dfrac {\pi}{x}}x
  • 12
  • 14
  • 16
  • 18
For every integer n, let a_{n} and b_{n} be real numbers. Let function f: IR \rightarrow IR be given by
f(x)=\left\{\begin{array}{l} a_{n}+\sin\pi x,\ for\ x\in[2n,\ 2n+1]\\ b_{n}+\cos\pi x,\ for\ x\ \in(2n-1,2n)                   \end{array}\right., for\ all\ integers\ n.
lf f is continuous, then which of the following hold(s) for all n?
  • a_{n-1}-b_{n-1}=0
  • a_{n}-b_{n}=1
  • a_{n}-b_{n+1}=1
  • a_{n-1}-b_{n}=-1
If \lim _{ x\rightarrow \infty  }{ x\sin { \left( \cfrac { 1 }{ x }  \right)  }  } =A and \lim _{ x\rightarrow 0 }{ x\sin { \left( \cfrac { 1 }{ x }  \right)  }  } =B, then which one of the following is correct?
  • A=1 and B=0
  • A=0 and B=1
  • A=0 and B=0
  • A=1 and B=1
The function f\left( x \right)=\left[ x \right] ,  at { x }=5 is:
  • left continuous
  • right continuous
  • continuous
  • cannot be determined
f(x)=\left\{\begin{matrix} 2x-1& if &x>2 \\ k & if &x=2 \\  x^{2}-1& if & x<2\end{matrix}\right.is continuous at x= 2 then k =
  • 1
  • 2
  • 3
  • 4
Evaluate \displaystyle \lim_{x \rightarrow -2} \displaystyle \frac{x^2 - 1}{2x + 4}.
  • 0
  • 1
  • 2
  • \infty
If f(x)=\displaystyle \frac{\sin x}{x},x\neq 0 is to be continuous at {x}=0 then \mathrm{f}({0})=
  • 0
  • 1
  • -1
  • 2
Say true or false.
Every continuous function is always differentiable.
  • True
  • False
\displaystyle \lim_{x\rightarrow \infty} \sin x equals
  • 1
  • 0
  • \infty
  • does not exist

 The function \displaystyle \mathrm{f}({x})=\frac{|x-3|}{x-3} at {x}=3, is
  • Left continuous
  • Right continuous
  • continuous
  • discontinuous
0:0:2


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