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