Left Hand Limit
Trending Questions
Q. The number of real roots of the equation e6x−e4x−2e3x−12e2x+ex+1=0 is
- 1
- 2
- 6
- 4
Q. For each x∈R, let [x] be the greatest integer less than or equal to x. Then limx → 0 −x([x]+|x|) sin[x]|x| is equal to :
- −sin1
- 1
- sin1
- 0
Q. Evaluate the given limit :
limx→3x4−812x2−5x−3
limx→3x4−812x2−5x−3
Q. If f(x)=⎧⎪⎨⎪⎩sin[x][x], x≠00 , x=0, then limx→0f(x) equals (where [.] denotes greatest integer function)
- sin1
- 1
- −1
- limit does not exist.
Q. Value of limit lim x→0+a√x−a1/√xa√x+a1/√x, a>1, is
- 4
- 2
- −1
- 0
Q. If α=limx→π/4tan3x−tanxcos(x+π4) and β=limx→0(cosx)cotx
are the roots of the equation, ax2+bx−4=0, then the ordered pair (a, b) is
are the roots of the equation, ax2+bx−4=0, then the ordered pair (a, b) is
- (−1, −3)
- (−1, 3)
- (1, 3)
- (1, −3)
Q. Evaluate the limit:
limx→0cos3x−cos7xx2
limx→0cos3x−cos7xx2
Q. The function f:R→R defined by f(x)=x3+2 is
- one-one and onto
- onto but not one-one
- one-one but not onto
- neither one-one nor onto
Q. Let a, b, c∈R such that a+b+c=π. If f(x)=⎧⎪
⎪
⎪
⎪⎨⎪
⎪
⎪
⎪⎩sin(ax2+bx+c)x2−1, if x<1−1, if x=1a sgn(x+1)cos(2x−2)+bx2, if 1<x≤2 is continuous at x=1, then the value of (a2+b2) is
[Here, sgn(k) denotes signum function of k]
[Here, sgn(k) denotes signum function of k]
Q. If f(x)=⎧⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪⎨⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪⎩(12)sin8xcot4x, x<0b−6, x=0(1+|sin2x|)a|cot3x|b, x>0 is continuous at x=0, then the value of (a+b) is
Q. If f(x)={x2−3, 2<x<32x+5, 3<x<4, the equation whose roots are limx→3−f(x) and limx→3+f(x) is
- x2 - 26x + 66 = 0
- x2 - 17x + 66 = 0
- x2 - 22x + 121 = 0
- x2 - 12x + 36 = 0
Q. Evaluate the given limit limx→3(x+3)
Q.
The range of f(x)=35+4sin3x is
Q. If f(x)=⎧⎪⎨⎪⎩tan([x]+x)[x]−2x, x≠00 , x=0, then limx→0f(x) equal to
(where [.] denotes the greatest integer function)
(where [.] denotes the greatest integer function)
- −12
- π4
- 1
- does not exist
Q. Differentiate from first principle:
(vii) sin(x+1)
(vii) sin(x+1)
Q. If [x] is the greatest integer less than or equal to x, for all x∈R, then evaluate limx→1+1−|x|+sin|1−x||1−x|[1−x]
- 3
- 0
- 6
- −5
Q. If f(x)=⎧⎪
⎪⎨⎪
⎪⎩[sin[x−3][x−3]], x≠00, x=0, then
(where [.] represents the greatest integer function)
(where [.] represents the greatest integer function)
- f(x) is continuous at x=0
- f(x) is discontinuous at x=0
- limx→0+f(x)=−1
- limx→0+f(x)=0
Q. Evaluate the limit:
limx→0ex−1+sinxx
limx→0ex−1+sinxx
Q. lf α, β(α>β) are the roots of the equation 4x2+2x−1=0, then β is equal to
- 4α2+α−1
- 4α3−3α
- −2α−1
- 4α2−3α
Q. Evaluate the given limit:
limx→−2(1x+12)x+2
.
limx→−2(1x+12)x+2
.
Q. If f(x)=[x]sin(π[x+1]), where [.] denotes the greatest integer function, then the points of discontinuity of f in the domain are
- Z−{0}
- R−[1, 0)
- Z
- None of these
Q.
Graph of f(x) is given. Find the value of left hand limit as x approaches 3.
2
-2
0
does not exist
Q. If f(x)={x2−3, 2<x<32x+5, 3<x<4, the equation whose roots are limx→3−f(x) and limx→3+f(x) is
- x2−12x+36=0
- x2−26x+66=0
- x2−17x+66=0
- x2−22x+121=0
Q.
limx→1 sin| ||x|−2|−3|is
sin 2
sin 1
0
Does not exist
Q. Evaluate the limit:
limx→0sin24x2x4
limx→0sin24x2x4
Q.
Graph of f(x) is given. Find the value of left hand limit as x approaches 3.
-2
does not exist
0
2
Q. 10∑λ=1sin−1(sin(λπ−π6)) is equal to
- 5π3
- π2
- 0
- 5π
Q. If f(x)=[x]sin(π[x+1]), where [.] denotes the greatest integer function, then the point of discontinuity of f in the domain are
- Z
- Z\{0}
- R\[-1, 0)
- None of these
Q.
The value of limx→1[sin sin−1x] is
1
does not exist
π/2
0
Q. Consider f(x)=⎧⎪
⎪
⎪
⎪⎨⎪
⎪
⎪
⎪⎩[2(sinx−sin3x)+∣∣sinx−sin3x∣∣2(sinx−sin3x)−∣∣sinx−sin3x∣∣], x≠π2forx∈(0, π)3x=π2, where [] denotes the greatest integer function, then-
- f is continuous and differentiable at x=π/2
- f is continuous but not differentiable at x=π/2
- f is neither continuous not differentiable at x=π/2
- None of these