Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (5+x-3*x^2)/(4-x+2*x^2)
-
Limit of (4-x^2)/(3-x^2)
-
Limit of (3+2*x)/(1-5*x)
-
Limit of (1-2*cos(x))/sin(3*x)
- Graphing y =:
- x^2+6*x
- Equation:
- x^2+6*x
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Identical expressions
- x^ two + six *x
- x squared plus 6 multiply by x
- x to the power of two plus six multiply by x
- x2+6*x
- x²+6*x
- x to the power of 2+6*x
- x^2+6x
- x2+6x
-
Similar expressions
- (8+x^2+6*x)/(12+x^2-8*x)
- (-5*x^2+6*x)/(-2*x+8*x^3)
- (3-x^2-2*x)/(2*x^2+6*x)
- x^2-6*x
- (-8+2*x^2+6*x)/(-16+x^2)
- (-7+x^2+6*x)/(2+x^2-3*x)
Limit of the function x^2+6*x
The solution
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/ 2 \ lim \x + 6*x/ x->oo
$$\lim_{x \to \infty}\left(x^{2} + 6 x\right)$$
Limit(x^2 + 6*x, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(x^{2} + 6 x\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(x^{2} + 6 x\right)$$ =
$$\lim_{x \to \infty}\left(\frac{1 + \frac{6}{x}}{\frac{1}{x^{2}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1 + \frac{6}{x}}{\frac{1}{x^{2}}}\right) = \lim_{u \to 0^+}\left(\frac{6 u + 1}{u^{2}}\right)$$
=
$$\frac{0 \cdot 6 + 1}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(x^{2} + 6 x\right) = \infty$$
$$\lim_{x \to \infty}\left(x^{2} + 6 x\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(x^{2} + 6 x\right)$$ =
$$\lim_{x \to \infty}\left(\frac{1 + \frac{6}{x}}{\frac{1}{x^{2}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1 + \frac{6}{x}}{\frac{1}{x^{2}}}\right) = \lim_{u \to 0^+}\left(\frac{6 u + 1}{u^{2}}\right)$$
=
$$\frac{0 \cdot 6 + 1}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(x^{2} + 6 x\right) = \infty$$
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
$$\lim_{x \to \infty}\left(x^{2} + 6 x\right) = \infty$$
$$\lim_{x \to 0^-}\left(x^{2} + 6 x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{2} + 6 x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x^{2} + 6 x\right) = 7$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{2} + 6 x\right) = 7$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{2} + 6 x\right) = \infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(x^{2} + 6 x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{2} + 6 x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x^{2} + 6 x\right) = 7$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{2} + 6 x\right) = 7$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{2} + 6 x\right) = \infty$$
More at x→-oo
The graph