Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
-
Limit of (9+3*x^2+4*x)/(7-7*x+3*x^2)
-
Limit of (1+2*n)/(-1+3*n)
-
Limit of (x^3-3^x)/(-3+x)
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Limit of -x+(-2+x)^4/(3+x)^4
- Derivative of:
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2*x^5
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Identical expressions
- two *x^ five
- 2 multiply by x to the power of 5
- two multiply by x to the power of five
- 2*x5
- 2*x⁵
- 2x^5
- 2x5
-
Similar expressions
- ((3+2*x)/(1+2*x))^(5+3*x)
- 2-x^2-5*x^3+2*x^5-x^4/3
- (1-1/(3+2*x))^(5+x)
- (1+3/(2*x))^(5*x)
Limit of the function 2*x^5
The solution
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/ 5\ lim \2*x / x->oo
$$\lim_{x \to \infty}\left(2 x^{5}\right)$$
Limit(2*x^5, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(2 x^{5}\right)$$
Let's divide numerator and denominator by x^5:
$$\lim_{x \to \infty}\left(2 x^{5}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{1}{2} \frac{1}{x^{5}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{1}{2} \frac{1}{x^{5}}} = \lim_{u \to 0^+}\left(\frac{2}{u^{5}}\right)$$
=
$$\frac{2}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(2 x^{5}\right) = \infty$$
$$\lim_{x \to \infty}\left(2 x^{5}\right)$$
Let's divide numerator and denominator by x^5:
$$\lim_{x \to \infty}\left(2 x^{5}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{1}{2} \frac{1}{x^{5}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{1}{2} \frac{1}{x^{5}}} = \lim_{u \to 0^+}\left(\frac{2}{u^{5}}\right)$$
=
$$\frac{2}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(2 x^{5}\right) = \infty$$
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
$$\lim_{x \to \infty}\left(2 x^{5}\right) = \infty$$
$$\lim_{x \to 0^-}\left(2 x^{5}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(2 x^{5}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(2 x^{5}\right) = 2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(2 x^{5}\right) = 2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(2 x^{5}\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(2 x^{5}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(2 x^{5}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(2 x^{5}\right) = 2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(2 x^{5}\right) = 2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(2 x^{5}\right) = -\infty$$
More at x→-oo
The graph