Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (-16+x^2-6*x)/(-2+x+x^2)
-
Limit of -1+sqrt(5)-x-2/(sqrt(2)-x)
-
Limit of (-cos(x)^3+cos(x))/(4*x*sin(x))
-
Limit of cos((1+x)/x^3)
- Graphing y =:
- x^2+5*x
- Integral of d{x}:
- x^2+5*x
- Factor polynomial:
- x^2+5*x
-
Identical expressions
- x^ two + five *x
- x squared plus 5 multiply by x
- x to the power of two plus five multiply by x
- x2+5*x
- x²+5*x
- x to the power of 2+5*x
- x^2+5x
- x2+5x
-
Similar expressions
- x^2-5*x
- (x-x^3)/(8-x^2+5*x^3)
- (3+x^2+4*x)/(6+x^2+5*x)
- (-14+x^2+5*x)/(-2+x)
- (1-x^2+5*x^4)/(3+x^4)
- (6+x^2+5*x)/(20+x^2-12*x)
Limit of the function x^2+5*x
The solution
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/ 2 \ lim \x + 5*x/ x->oo
$$\lim_{x \to \infty}\left(x^{2} + 5 x\right)$$
Limit(x^2 + 5*x, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(x^{2} + 5 x\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(x^{2} + 5 x\right)$$ =
$$\lim_{x \to \infty}\left(\frac{1 + \frac{5}{x}}{\frac{1}{x^{2}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1 + \frac{5}{x}}{\frac{1}{x^{2}}}\right) = \lim_{u \to 0^+}\left(\frac{5 u + 1}{u^{2}}\right)$$
=
$$\frac{0 \cdot 5 + 1}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(x^{2} + 5 x\right) = \infty$$
$$\lim_{x \to \infty}\left(x^{2} + 5 x\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(x^{2} + 5 x\right)$$ =
$$\lim_{x \to \infty}\left(\frac{1 + \frac{5}{x}}{\frac{1}{x^{2}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1 + \frac{5}{x}}{\frac{1}{x^{2}}}\right) = \lim_{u \to 0^+}\left(\frac{5 u + 1}{u^{2}}\right)$$
=
$$\frac{0 \cdot 5 + 1}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(x^{2} + 5 x\right) = \infty$$
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
$$\lim_{x \to \infty}\left(x^{2} + 5 x\right) = \infty$$
$$\lim_{x \to 0^-}\left(x^{2} + 5 x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{2} + 5 x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x^{2} + 5 x\right) = 6$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{2} + 5 x\right) = 6$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{2} + 5 x\right) = \infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(x^{2} + 5 x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{2} + 5 x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x^{2} + 5 x\right) = 6$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{2} + 5 x\right) = 6$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{2} + 5 x\right) = \infty$$
More at x→-oo
The graph