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