Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (-10+x^2+3*x)/(16+x^2-10*x)
-
Limit of ((-1+x^2)/(2+x^2))^(1+x^2)
-
Limit of (x^2+10*x)/tan(5*x)
-
Limit of (x/(5+10*x))^x
-
Identical expressions
- (x/(five + ten *x))^x
- (x divide by (5 plus 10 multiply by x)) to the power of x
- (x divide by (five plus ten multiply by x)) to the power of x
- (x/(5+10*x))x
- x/5+10*xx
- (x/(5+10x))^x
- (x/(5+10x))x
- x/5+10xx
- x/5+10x^x
- (x divide by (5+10*x))^x
-
Similar expressions
- (x/(5-10*x))^x
Limit of the function (x/(5+10*x))^x
The solution
You have entered
[src]
x
/ x \
lim |--------|
x->oo\5 + 10*x/
$$\lim_{x \to \infty} \left(\frac{x}{10 x + 5}\right)^{x}$$
Limit((x/(5 + 10*x))^x, x, oo, dir='-')
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
$$\lim_{x \to \infty} \left(\frac{x}{10 x + 5}\right)^{x} = 0$$
$$\lim_{x \to 0^-} \left(\frac{x}{10 x + 5}\right)^{x} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \left(\frac{x}{10 x + 5}\right)^{x} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \left(\frac{x}{10 x + 5}\right)^{x} = \frac{1}{15}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(\frac{x}{10 x + 5}\right)^{x} = \frac{1}{15}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(\frac{x}{10 x + 5}\right)^{x} = \infty$$
More at x→-oo
$$\lim_{x \to 0^-} \left(\frac{x}{10 x + 5}\right)^{x} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \left(\frac{x}{10 x + 5}\right)^{x} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \left(\frac{x}{10 x + 5}\right)^{x} = \frac{1}{15}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(\frac{x}{10 x + 5}\right)^{x} = \frac{1}{15}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(\frac{x}{10 x + 5}\right)^{x} = \infty$$
More at x→-oo
The graph