Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of ((-4+3*x)/(2+3*x))^(1+x)/3
-
Limit of (-16+2^x)/(-1+5*sqrt(x)*(5-x))
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Limit of (-14+x^2-5*x)/(-6+x+2*x^2)
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Limit of (3+x^2+4*x)/(1+x^3)
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Identical expressions
- (x^ two + six *x)/x
- (x squared plus 6 multiply by x) divide by x
- (x to the power of two plus six multiply by x) divide by x
- (x2+6*x)/x
- x2+6*x/x
- (x²+6*x)/x
- (x to the power of 2+6*x)/x
- (x^2+6x)/x
- (x2+6x)/x
- x2+6x/x
- x^2+6x/x
- (x^2+6*x) divide by x
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Similar expressions
- (x^2-6*x)/x
Limit of the function (x^2+6*x)/x
The solution
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[src]
/ 2 \
|x + 6*x|
lim |--------|
x->0+\ x /
$$\lim_{x \to 0^+}\left(\frac{x^{2} + 6 x}{x}\right)$$
Limit((x^2 + 6*x)/x, x, 0)
Detail solution
Let's take the limit
$$\lim_{x \to 0^+}\left(\frac{x^{2} + 6 x}{x}\right)$$
transform
$$\lim_{x \to 0^+}\left(\frac{x^{2} + 6 x}{x}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{x \left(x + 6\right)}{x}\right)$$
=
$$\lim_{x \to 0^+}\left(x + 6\right) = $$
$$6 = $$
The final answer:
$$\lim_{x \to 0^+}\left(\frac{x^{2} + 6 x}{x}\right) = 6$$
$$\lim_{x \to 0^+}\left(\frac{x^{2} + 6 x}{x}\right)$$
transform
$$\lim_{x \to 0^+}\left(\frac{x^{2} + 6 x}{x}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{x \left(x + 6\right)}{x}\right)$$
=
$$\lim_{x \to 0^+}\left(x + 6\right) = $$
$$6 = $$
= 6
The final answer:
$$\lim_{x \to 0^+}\left(\frac{x^{2} + 6 x}{x}\right) = 6$$
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
$$\lim_{x \to 0^-}\left(\frac{x^{2} + 6 x}{x}\right) = 6$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x^{2} + 6 x}{x}\right) = 6$$
$$\lim_{x \to \infty}\left(\frac{x^{2} + 6 x}{x}\right) = \infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{x^{2} + 6 x}{x}\right) = 7$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x^{2} + 6 x}{x}\right) = 7$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x^{2} + 6 x}{x}\right) = -\infty$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x^{2} + 6 x}{x}\right) = 6$$
$$\lim_{x \to \infty}\left(\frac{x^{2} + 6 x}{x}\right) = \infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{x^{2} + 6 x}{x}\right) = 7$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x^{2} + 6 x}{x}\right) = 7$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x^{2} + 6 x}{x}\right) = -\infty$$
More at x→-oo
One‐sided limits
[src]
/ 2 \
|x + 6*x|
lim |--------|
x->0+\ x /
$$\lim_{x \to 0^+}\left(\frac{x^{2} + 6 x}{x}\right)$$
6
$$6$$
= 6.0
/ 2 \
|x + 6*x|
lim |--------|
x->0-\ x /
$$\lim_{x \to 0^-}\left(\frac{x^{2} + 6 x}{x}\right)$$
6
$$6$$
= 6.0
= 6.0
The graph