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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
limxasinxsina3x3a
  • 3acosa
  • 23a
  • 3a2/3cosa
  • 2acosa
The value of limx01cos3xxsinxcosx is
  • 25
  • 35
  • 32
  • 34
Integrate:
 limx0(1cos2x)22xtanxxtan2x
  • 2
  • 12
  • 2
  • 12
limx0+(cscx)1/logx=
  • e
  • e1
  • e2
  • 1
The value of limx0(tanxx)1/x3 is-
  • 0
  • e1/4
  • Does not exist
The value of limxx2logsinx(π2x)2 is 
  • 0
  • 12
  • 12
  • 2
limn1n2[sin3π4n+2sin32π4n+3sin33π4n+....+nsin3nπ4n]=
  • 29π2(5215π)
  • 29π2(52+15π)
  • 29π(5217π)
  • 29π2(52+17π)
If αandβ are the roots of the equation  ax2+bx+c=0, then 
 limxπ2tan[(α+β)x]sin[(αβ)x] is equal to :
  • cb
  • bc
  • ab
  • ab
limn10nxn11+x2dx=
  • 0
  • 1
  • 2
  • 12
Arrange the following limits in the ascending order :
(1)  limx(1+x2+x)x+2

(2)  limx0(1+2x)3/x

(3)  limθ0sinθ2θ

(4)  limx0loge(1+x)x
  • 1,2,3,4
  • 1,3,4,2
  • 1,4,3,2
  • 3,4,1,2
limx0(3+x3x)x+1x is equal to 
  • e2/3
  • e1/3
  • e3
  • e2
If limx0x(1+acosx)bsinxx3=1, then
  • a=52
  • b=52
  • a+b=4
  • a+b=4
limx0(p1x+q1x+r1x+s1x4)3x where p,q,r,s>0 is equal to
  • pqrs
  • (pqrs)3
  • (pqrs)32
  • (pqrs)34
limx0 1cos(1cos4x)x4 is equal to : 
  • 4
  • 16
  • 32
  • None of these
The value of limx0|x|sinx equals 
  • 0
  • 1
  • 1
  • does not exist
If limx0(sinnx)[(an)nxtanx]x2=0, then the value of a
  • 1n
  • n1n
  • n+1n
  • None of these
limx01cosxcos2xcos3xsin22x=
  • 32
  • 52
  • 74
  • 92
The value of limx0(1x2cotx) equals 
  • 1
  • 0
  • Does not exist
limxsgn(cotπx2019x2019+7)
  • Equals 1
  • Equals 1
  • equals 0
  • Does not exit
limxπ/2(secx+tanx) is equal to 
  • 1
  • 1
  • 12
  • 0
limxπ/2(cosecx1cot2x)=
  • 0
  • 12
  • 12
  • 1
limx0xtan2x2tan2x(1cos2x) equals:
  • 14
  • 1
  • 12
  • 12
limxπ/2sinx(sinx)sinx1sinx+Insinx is equal to
  • 4
  • 2
  • 1
  • none of these
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