Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of 2+((-1+x)/(3+x))^x
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Limit of (-1+x)/(x+x^2)
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Limit of ((1+x)^4-(-1+x)^4)/((1+x)^4+(-1+x)^4)
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Limit of tan(6*x)/(3*x)
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Identical expressions
- (x^ two - five *x)/x
- (x squared minus 5 multiply by x) divide by x
- (x to the power of two minus five multiply by x) divide by x
- (x2-5*x)/x
- x2-5*x/x
- (x²-5*x)/x
- (x to the power of 2-5*x)/x
- (x^2-5x)/x
- (x2-5x)/x
- x2-5x/x
- x^2-5x/x
- (x^2-5*x) divide by x
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Similar expressions
- (x^2+5*x)/x
Limit of the function (x^2-5*x)/x
The solution
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[src]
/ 2 \
|x - 5*x|
lim |--------|
x->0+\ x /
$$\lim_{x \to 0^+}\left(\frac{x^{2} - 5 x}{x}\right)$$
Limit((x^2 - 5*x)/x, x, 0)
Detail solution
Let's take the limit
$$\lim_{x \to 0^+}\left(\frac{x^{2} - 5 x}{x}\right)$$
transform
$$\lim_{x \to 0^+}\left(\frac{x^{2} - 5 x}{x}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{x \left(x - 5\right)}{x}\right)$$
=
$$\lim_{x \to 0^+}\left(x - 5\right) = $$
$$-5 = $$
The final answer:
$$\lim_{x \to 0^+}\left(\frac{x^{2} - 5 x}{x}\right) = -5$$
$$\lim_{x \to 0^+}\left(\frac{x^{2} - 5 x}{x}\right)$$
transform
$$\lim_{x \to 0^+}\left(\frac{x^{2} - 5 x}{x}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{x \left(x - 5\right)}{x}\right)$$
=
$$\lim_{x \to 0^+}\left(x - 5\right) = $$
$$-5 = $$
= -5
The final answer:
$$\lim_{x \to 0^+}\left(\frac{x^{2} - 5 x}{x}\right) = -5$$
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
$$\lim_{x \to 0^-}\left(\frac{x^{2} - 5 x}{x}\right) = -5$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x^{2} - 5 x}{x}\right) = -5$$
$$\lim_{x \to \infty}\left(\frac{x^{2} - 5 x}{x}\right) = \infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{x^{2} - 5 x}{x}\right) = -4$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x^{2} - 5 x}{x}\right) = -4$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x^{2} - 5 x}{x}\right) = -\infty$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x^{2} - 5 x}{x}\right) = -5$$
$$\lim_{x \to \infty}\left(\frac{x^{2} - 5 x}{x}\right) = \infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{x^{2} - 5 x}{x}\right) = -4$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x^{2} - 5 x}{x}\right) = -4$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x^{2} - 5 x}{x}\right) = -\infty$$
More at x→-oo
One‐sided limits
[src]
/ 2 \
|x - 5*x|
lim |--------|
x->0+\ x /
$$\lim_{x \to 0^+}\left(\frac{x^{2} - 5 x}{x}\right)$$
-5
$$-5$$
= -5.0
/ 2 \
|x - 5*x|
lim |--------|
x->0-\ x /
$$\lim_{x \to 0^-}\left(\frac{x^{2} - 5 x}{x}\right)$$
-5
$$-5$$
= -5.0
= -5.0
The graph