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