Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (-4+x^2)/(x^3+2*x)
-
Limit of (x^2-11*x)/x
-
Limit of (x^2+10*x)/tan(5*x)
-
Limit of (1+x)/x^2
-
Identical expressions
- (x^ two - eleven *x)/x
- (x squared minus 11 multiply by x) divide by x
- (x to the power of two minus eleven multiply by x) divide by x
- (x2-11*x)/x
- x2-11*x/x
- (x²-11*x)/x
- (x to the power of 2-11*x)/x
- (x^2-11x)/x
- (x2-11x)/x
- x2-11x/x
- x^2-11x/x
- (x^2-11*x) divide by x
-
Similar expressions
- (x^2+11*x)/x
Limit of the function (x^2-11*x)/x
The solution
You have entered
[src]
/ 2 \
|x - 11*x|
lim |---------|
x->0+\ x /
$$\lim_{x \to 0^+}\left(\frac{x^{2} - 11 x}{x}\right)$$
Limit((x^2 - 11*x)/x, x, 0)
Detail solution
Let's take the limit
$$\lim_{x \to 0^+}\left(\frac{x^{2} - 11 x}{x}\right)$$
transform
$$\lim_{x \to 0^+}\left(\frac{x^{2} - 11 x}{x}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{x \left(x - 11\right)}{x}\right)$$
=
$$\lim_{x \to 0^+}\left(x - 11\right) = $$
$$-11 = $$
The final answer:
$$\lim_{x \to 0^+}\left(\frac{x^{2} - 11 x}{x}\right) = -11$$
$$\lim_{x \to 0^+}\left(\frac{x^{2} - 11 x}{x}\right)$$
transform
$$\lim_{x \to 0^+}\left(\frac{x^{2} - 11 x}{x}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{x \left(x - 11\right)}{x}\right)$$
=
$$\lim_{x \to 0^+}\left(x - 11\right) = $$
$$-11 = $$
= -11
The final answer:
$$\lim_{x \to 0^+}\left(\frac{x^{2} - 11 x}{x}\right) = -11$$
Lopital's rule
There is no sense to apply Lopital's rule to this function since there is no indeterminateness of 0/0 or oo/oo type
The graph
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{x^{2} - 11 x}{x}\right) = -11$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x^{2} - 11 x}{x}\right) = -11$$
$$\lim_{x \to \infty}\left(\frac{x^{2} - 11 x}{x}\right) = \infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{x^{2} - 11 x}{x}\right) = -10$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x^{2} - 11 x}{x}\right) = -10$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x^{2} - 11 x}{x}\right) = -\infty$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x^{2} - 11 x}{x}\right) = -11$$
$$\lim_{x \to \infty}\left(\frac{x^{2} - 11 x}{x}\right) = \infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{x^{2} - 11 x}{x}\right) = -10$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x^{2} - 11 x}{x}\right) = -10$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x^{2} - 11 x}{x}\right) = -\infty$$
More at x→-oo
One‐sided limits
[src]
/ 2 \
|x - 11*x|
lim |---------|
x->0+\ x /
$$\lim_{x \to 0^+}\left(\frac{x^{2} - 11 x}{x}\right)$$
-11
$$-11$$
= -11.0
/ 2 \
|x - 11*x|
lim |---------|
x->0-\ x /
$$\lim_{x \to 0^-}\left(\frac{x^{2} - 11 x}{x}\right)$$
-11
$$-11$$
= -11.0
= -11.0
The graph