Indeterminate Forms
Trending Questions
Q.
limx→0(sin xx)(sin xx−sin x) equals
1
e
e−1
e−2
Q. Let f be a biquadratic function of x given by f(x)=Ax4+Bx3+Cx2+Dx+E, where A, B, C, D, E∈R and A≠0. If limx→0(f(−x)2x3)1/x=e−3, then
- A+4B=0
- A−3B=0
- f(1)=8
- f′(1)=−30
Q. limx → ∞sin4 x−sin2 x+1cos4 x−cos2 x+1is equal to
- 0
- 1
- 13
- Does not exist
Q.
limx→∞(x5+5x+3x2+x+2)x equals
e4
e2
e3
e
Q. ___
limx→1logxx−1 is equal to
Q. limx → ∞(1e−x1+x)x is equal to
- e1−e
- 0
- ee1−e
- Does not exist
Q. Let a1>a2>a3>…>an>1; p1>p2>p3>⋯>pn>0 be such that p1+p2+p3+⋯+pn=1. If F(x)=(p1ax1+p2ax2+⋯+pnaxn)1/x, then
- limx→0F(x)=ap11ap22…apnn
- limx→0F(x)=ap11+ap22+⋯+apnn
- limx→∞F(x)=a1
- limx→−∞F(x)=an
Q.
limn→∞ n((2n+1)2)(n+2)(n2+3n−1) =
0
2
4
∞
Q. limx→∞(2+x)40(4+x)5(2−x)45
- −1
- 1
- 16
- 32
Q.
k = limx→∞⎛⎜ ⎜⎝1000∑k=1(x+k)mxm+101000⎞⎟ ⎟⎠ is (m > 101)
10
102
103
104
Q. The value of limn→∞3n+2n3n−2n is
- −1
- 1
- 0
- ∞
Q.
limn→∞ n((2n+1)2)(n+2)(n2+3n−1) =
0
2
4
∞
Q.
The value of limx→∞[√x+√x+√x−√x]is.
1/2
1
0
-1/2
Q.
limx→∞√x2+1−3√x2+14√x4+1−5√x4−1isequalto
1
-1
0
1/2
Q. limx→0 100∑r=1[xr]1+|x|=
- 0
- 1
- −1
- does not exist
Q.
limx→∞(√n)(√n+(√n+1)) =
1
12
0
∞
Q.
The limiting value of(cos x)1/sin xas x→0 is
1
e
0
1/e
Q.
limn→∞1−2+3−4+5−6+.......2n√n2+1+√4n2−1is equal to:
1/3
-1/3
-1/5
1/5
Q. limn→∞2.3n−3.5n3.3n+4.5n=
- 23
- −34
- 1
- 0
Q. The value of limx→1(tanxπ4)tanπx2 is
- e−2
- e−1
- e
- 1
Q.
The limiting value of(cos x)1/sin xas x→0 is
1
e
0
1/e
