Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
-
Limit of (7+n)/(5+n)
-
Limit of (9+3*x^2+4*x)/(7-7*x+3*x^2)
-
Limit of -2+x^3+6*x
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Limit of -x+(-2+x)^4/(3+x)^4
- Factor polynomial:
- x^2-10*x
-
Identical expressions
- x^ two - ten *x
- x squared minus 10 multiply by x
- x to the power of two minus ten multiply by x
- x2-10*x
- x²-10*x
- x to the power of 2-10*x
- x^2-10x
- x2-10x
-
Similar expressions
- x^2+10*x
Limit of the function x^2-10*x
The solution
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/ 2 \ lim \x - 10*x/ x->oo
$$\lim_{x \to \infty}\left(x^{2} - 10 x\right)$$
Limit(x^2 - 10*x, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(x^{2} - 10 x\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(x^{2} - 10 x\right)$$ =
$$\lim_{x \to \infty}\left(\frac{1 - \frac{10}{x}}{\frac{1}{x^{2}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1 - \frac{10}{x}}{\frac{1}{x^{2}}}\right) = \lim_{u \to 0^+}\left(\frac{1 - 10 u}{u^{2}}\right)$$
=
$$\frac{1 - 0}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(x^{2} - 10 x\right) = \infty$$
$$\lim_{x \to \infty}\left(x^{2} - 10 x\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(x^{2} - 10 x\right)$$ =
$$\lim_{x \to \infty}\left(\frac{1 - \frac{10}{x}}{\frac{1}{x^{2}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1 - \frac{10}{x}}{\frac{1}{x^{2}}}\right) = \lim_{u \to 0^+}\left(\frac{1 - 10 u}{u^{2}}\right)$$
=
$$\frac{1 - 0}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(x^{2} - 10 x\right) = \infty$$
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
$$\lim_{x \to \infty}\left(x^{2} - 10 x\right) = \infty$$
$$\lim_{x \to 0^-}\left(x^{2} - 10 x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{2} - 10 x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x^{2} - 10 x\right) = -9$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{2} - 10 x\right) = -9$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{2} - 10 x\right) = \infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(x^{2} - 10 x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{2} - 10 x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x^{2} - 10 x\right) = -9$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{2} - 10 x\right) = -9$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{2} - 10 x\right) = \infty$$
More at x→-oo
The graph