Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (1+x^2+9*x)/(-5+2*x+7*x^2)
-
Limit of (-tan(2*x)+sin(2*x))/x^3
-
Limit of 3/n^4
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Limit of (1-cos(x)^2)/(x^2*sin(x)^2)
- Derivative of:
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3*x^5
- Integral of d{x}:
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3*x^5
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Identical expressions
- three *x^ five
- 3 multiply by x to the power of 5
- three multiply by x to the power of five
- 3*x5
- 3*x⁵
- 3x^5
- 3x5
-
Similar expressions
- (5+x^5-2*x^3)/(6+3*x^5)
- ((1+3*x)/(-2+3*x))^(5+x)
- -2+5*x+(-5+3*x)^5/x^2
Limit of the function 3*x^5
The solution
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/ 5\ lim \3*x / x->oo
$$\lim_{x \to \infty}\left(3 x^{5}\right)$$
Limit(3*x^5, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(3 x^{5}\right)$$
Let's divide numerator and denominator by x^5:
$$\lim_{x \to \infty}\left(3 x^{5}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{1}{3} \frac{1}{x^{5}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{1}{3} \frac{1}{x^{5}}} = \lim_{u \to 0^+}\left(\frac{3}{u^{5}}\right)$$
=
$$\frac{3}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(3 x^{5}\right) = \infty$$
$$\lim_{x \to \infty}\left(3 x^{5}\right)$$
Let's divide numerator and denominator by x^5:
$$\lim_{x \to \infty}\left(3 x^{5}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{1}{3} \frac{1}{x^{5}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{1}{3} \frac{1}{x^{5}}} = \lim_{u \to 0^+}\left(\frac{3}{u^{5}}\right)$$
=
$$\frac{3}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(3 x^{5}\right) = \infty$$
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
$$\lim_{x \to \infty}\left(3 x^{5}\right) = \infty$$
$$\lim_{x \to 0^-}\left(3 x^{5}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(3 x^{5}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(3 x^{5}\right) = 3$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(3 x^{5}\right) = 3$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(3 x^{5}\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(3 x^{5}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(3 x^{5}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(3 x^{5}\right) = 3$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(3 x^{5}\right) = 3$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(3 x^{5}\right) = -\infty$$
More at x→-oo
The graph