Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (-3+x^2-2*x)/(-3+x)
-
Limit of 5^x-cos(x)
-
Limit of (x/2)^(1/(-2+x))
-
Limit of (1-3/x)^x
- How do you in partial fractions?:
- -1/(2*x^2)
-
Identical expressions
- - one /(two *x^ two)
- minus 1 divide by (2 multiply by x squared )
- minus one divide by (two multiply by x to the power of two)
- -1/(2*x2)
- -1/2*x2
- -1/(2*x²)
- -1/(2*x to the power of 2)
- -1/(2x^2)
- -1/(2x2)
- -1/2x2
- -1/2x^2
- -1 divide by (2*x^2)
-
Similar expressions
- 1/(2*x^2)
Limit of the function -1/(2*x^2)
The solution
You have entered
[src]
/-1 \
lim |----|
x->oo| 2|
\2*x /
$$\lim_{x \to \infty}\left(- \frac{1}{2 x^{2}}\right)$$
Limit(-1/(2*x^2), x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(- \frac{1}{2 x^{2}}\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(- \frac{1}{2 x^{2}}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{\left(-1\right) \frac{1}{2} \frac{1}{x^{2}}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{\left(-1\right) \frac{1}{2} \frac{1}{x^{2}}}{1}\right) = \lim_{u \to 0^+}\left(- \frac{u^{2}}{2}\right)$$
=
$$- \frac{0^{2}}{2} = 0$$
The final answer:
$$\lim_{x \to \infty}\left(- \frac{1}{2 x^{2}}\right) = 0$$
$$\lim_{x \to \infty}\left(- \frac{1}{2 x^{2}}\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(- \frac{1}{2 x^{2}}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{\left(-1\right) \frac{1}{2} \frac{1}{x^{2}}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{\left(-1\right) \frac{1}{2} \frac{1}{x^{2}}}{1}\right) = \lim_{u \to 0^+}\left(- \frac{u^{2}}{2}\right)$$
=
$$- \frac{0^{2}}{2} = 0$$
The final answer:
$$\lim_{x \to \infty}\left(- \frac{1}{2 x^{2}}\right) = 0$$
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
$$\lim_{x \to \infty}\left(- \frac{1}{2 x^{2}}\right) = 0$$
$$\lim_{x \to 0^-}\left(- \frac{1}{2 x^{2}}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- \frac{1}{2 x^{2}}\right) = -\infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- \frac{1}{2 x^{2}}\right) = - \frac{1}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- \frac{1}{2 x^{2}}\right) = - \frac{1}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- \frac{1}{2 x^{2}}\right) = 0$$
More at x→-oo
$$\lim_{x \to 0^-}\left(- \frac{1}{2 x^{2}}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- \frac{1}{2 x^{2}}\right) = -\infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- \frac{1}{2 x^{2}}\right) = - \frac{1}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- \frac{1}{2 x^{2}}\right) = - \frac{1}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- \frac{1}{2 x^{2}}\right) = 0$$
More at x→-oo
The graph