Mister Exam
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How to use it?
- Limit of the function:
- Limit of x+y
-
Limit of (-36+x^2)/(-6+x)
-
Limit of (9-x+2*x^2)/(5-x)
-
Limit of ((1+x)^4-(-1+x)^4)/((1+x)^3+(-1+x)^3)
- Equation:
- x+y
- Canonical form:
- x+y
- x+y
-
Identical expressions
- x+y
- x plus y
-
Similar expressions
- x-y
Limit of the function x+y
The solution
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lim (x + y) x->oo
$$\lim_{x \to \infty}\left(x + y\right)$$
Limit(x + y, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(x + y\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(x + y\right)$$ =
$$\lim_{x \to \infty}\left(\frac{1 + \frac{y}{x}}{\frac{1}{x}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1 + \frac{y}{x}}{\frac{1}{x}}\right) = \lim_{u \to 0^+}\left(\frac{u y + 1}{u}\right)$$
=
$$\frac{0 y + 1}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(x + y\right) = \infty$$
$$\lim_{x \to \infty}\left(x + y\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(x + y\right)$$ =
$$\lim_{x \to \infty}\left(\frac{1 + \frac{y}{x}}{\frac{1}{x}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1 + \frac{y}{x}}{\frac{1}{x}}\right) = \lim_{u \to 0^+}\left(\frac{u y + 1}{u}\right)$$
=
$$\frac{0 y + 1}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(x + y\right) = \infty$$
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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(x + y\right) = \infty$$
$$\lim_{x \to 0^-}\left(x + y\right) = y$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x + y\right) = y$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x + y\right) = y + 1$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x + y\right) = y + 1$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x + y\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(x + y\right) = y$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x + y\right) = y$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x + y\right) = y + 1$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x + y\right) = y + 1$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x + y\right) = -\infty$$
More at x→-oo