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CBSE Questions for Class 11 Commerce Applied Mathematics Limits And Continuity     Quiz 7 - MCQExams.com

Evaluate
limx01cos(1cos2x)x4
  • 4
  • 2
  • 1
  • 12
Evaluate the following limits.
limx2x2x2.
  • 23
  • 22
  • 25
  • None of these
If limx0x(1+acosx)bsinxx3=1 then
  • a=5/2, b=1/2
  • a=3/2, b=1/2
  • a=3/2, b=5/2
  • a=5/2, b=3/2
limx0  (1cos2x)22xtanxxtan2x is :
  • 2
  • 12
  • 12
  • 2
limx032x23xx is equal to
  • log32
  • 1
  • log98
  • 0
Let f(x)=ax+bx+1,limx0f(x)=2 and limxf(x)=1 then f(2)=
  • 1
  • 2
  • 1
  • 0
Evaluate the limit, limx0x((1+x)1/xe)x((1+x2)1/x2e)
  • 0
  • 1
  • 2
  • DNE
limx(x2x+1axb)=0,   then the values of  a  and  b  are given by
  • a=1,b=1/2
  • a=1,b=1/2
  • a=1,b=1/2
  • None of these
The value of limx y In (sin(x+1/y)sinx) when 0<x<π/2 is
  • cos x
  • cot x
  • does not exist
limxπ/4cot3xtanxcos(x+π/4)  is
  • 4
  • 82
  • 8
  • 42
limn{n!(kn)n}1n,k0, is equal to?
  • ke
  • ek
  • 1ke
  • None of these
Let f(x)=limnn1r=0x(rx+1){(r+1)x+1}, then?
  • f(x) is continuous but not differentiable at x=0
  • f(x) is both continuous and differentiable at x=0
  • f(x) is neither continuous nor differentiable at x=0
  • f(x) is a periodic function
limx0tan(sinx)xtanx3 is equal to 
  • 16
  • 13
  • 12
  • 1
limx[nn2+12+nn2+22+nn2+32+....+1n5]
  • π/4
  • tan1(2)
  • π/2
  • tan1(3)
The value of nlim1.n+2.(n1)+3.(n2)+...+n.112+22+...+n2 is
  • 1
  • 1
  • 12
  • 12
limx0x2esin1x equals 
  • 1
  • 0
  • Does not exist
Evaluate: limxπ4cot3xtanxcos(x+π/4)
  • 8
  • 82
  • 4
  • 42
limx1(1+cosπ)cot2πx=
  • 1
  • -1
  • 12
  • 0
Let f:(0,)R be a differentiable function such that f(x)=2f(x)x for all x(0,) and f(1)1. Then 
  • limx0+f(1x)=1
  • limx0+xf(1x)=2
  • limx0+x2f(x)=0
  • |f(x)|2 for all X(0,2)
limxπ2cotxcosx(π2x)3 equals?
  • 14
  • 124
  • 116
  • 18
Let f:RR be a differentiable function satisfying f(3)+f(2)=0.
Then limx0(1+f(3+x)f(3)1+f(2x)f(2))1x is equal to 
  • e2
  • e
  • e1
  • 1
If the function f(x) satisfies the relation f(x+y)=y|x1|(x1)f(x)+f(y) with f(1)=2, then limx1f(x) is?
  • 2
  • 2
  • 0
  • Limit do not exixst
Evaluate the following limits.
limxax+ax+a.
  • 1a
  • 1a
  • 12a
  • 1a
Evaluate the following limits.
limx0x2/39x27.
  • 13
  • 12
  • 15
  • None of these
Evaluate the following limits.
limx03x+1x+3.
  • 13
  • 23
  • 53
  • None of these
Evaluate the following limits.
limx1x21+x1x21,x>1.
  • 2+12
  • 212
  • 2+12
  • None of these
Evaluate the following limits.
limx0ax+bcx+d,d0.
  • ac
  • ad
  • bd
  • None of these
Evaluate the following limits.
limx0a2+x2ax2.
  • 1a
  • 12a
  • 1a
  • 12a
Evaluate the following limits.
limx02xa+xax.
  • 2a
  • a
  • 2a
  • None of these
Evaluate the following limits.
limx0a+xaxa2+ax.
  • 12a
  • 12aa
  • 12a
  • None of these
Evaluate the following limits.
limx42x4x.
  • 14
  • 12
  • 13
  • None of these
Evaluate the following limits.
limx21+4x5+2xx2.
  • 12
  • 13
  • 14
  • 15
Evaluate the following limits.
limx02x2+xx.
  • 12
  • 13
  • 12
  • 12
Evaluate the following limits.
If limxax5a5xa=405, find all possible values of a.
  • a=3,3
  • a=2,2
  • a=5,5
  • None of these
Evaluate the following limits.
If limxax9a9xa=9, find all possible values of a.
  • 2,2.
  • 1,1.
  • 1,0.
  • None of these
Evaluate the following limit.
limx08x2xx.
  • log4
  • log6
  • log5
  • None of these
If f:R(0,) is an increasing function and if limx2018f(3x)f(x)=1, then limx2018f(2x)f(x) is equal to 
  • 23
  • 32
  • 2
  • 3
  • 1
limx0(3x2+27x2+2)1/x2 is equal to:
  • 1e2
  • 1e
  • e2
  • e
If f is differentiable at x=1 and limh01hf(1+h)=5,f(1)=
  • 0
  • 1
  • 3
  • 4
  • 5
The value of limxπ1+cos3xsin2x is
  • 1/3
  • 2/3
  • -1/4
  • 3/2
limx0x(ex1)1cosx is equal to
  • 0
  • -2
  • 2
limxπ/2[xtanx(π2)secx] is equal to 
  • 1
  • -1
  • 0
  • None of these
limxx2tan1x8x2+7x+1 is equal to
  • 122
  • 122
  • 12
  • Does not exist
limn(n1)1/nn equals?
  • 1
  • e
  • e1
  • None of these
If f(x)=cosx(1sinx)1/3, then
  • limxπ2f(x)=
  • limxπ+2f(x)=
  • limxπ2f(x)=
  • none of these
limx0sinxn(sinx)m,(m<n) is equal to
  • 1
  • 0
  • n/m
  • None of these
limx11+sinπ(3x1+x2)1+cosπx is equal to
  • 0
  • 1
  • 2
  • 4
The value of limx22x+23x62x21x is
  • 16
  • 8
  • 4
  • 2
 The value oflimx1(2x)tanπx2 is
  • e2π
  • e1/π
  • e2/π
  • e1/π
limx11x2sin2πx is equal to 
  • 12π
  • 1π
  • 2π
  • None of these
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