Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (-2*x^2+4*x^3+5*x)/(3*x^2+7*x)
-
Limit of (-cos(5*x)+cos(3*x))/x^2
-
Limit of (-1+cos(7*x))/(-1+cos(3*x))
-
Limit of (16+x^2+10*x)/(-6+x^2-x)
- Derivative of:
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x^2+3*x
- Factor polynomial:
- x^2+3*x
-
Identical expressions
- x^ two + three *x
- x squared plus 3 multiply by x
- x to the power of two plus three multiply by x
- x2+3*x
- x²+3*x
- x to the power of 2+3*x
- x^2+3x
- x2+3x
-
Similar expressions
- x^2-3*x
- (-1-x^2+3*x)/x
- (-40+x^2+3*x)/(15+3*x)
- (-4+x^2+3*x)/(4+x)
- 1-7*x+2*x^2+3*x^3+x^4/3
- (x^2+3*x)/sin(3*x)
Limit of the function x^2+3*x
The solution
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/ 2 \ lim \x + 3*x/ x->oo
$$\lim_{x \to \infty}\left(x^{2} + 3 x\right)$$
Limit(x^2 + 3*x, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(x^{2} + 3 x\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(x^{2} + 3 x\right)$$ =
$$\lim_{x \to \infty}\left(\frac{1 + \frac{3}{x}}{\frac{1}{x^{2}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1 + \frac{3}{x}}{\frac{1}{x^{2}}}\right) = \lim_{u \to 0^+}\left(\frac{3 u + 1}{u^{2}}\right)$$
=
$$\frac{0 \cdot 3 + 1}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(x^{2} + 3 x\right) = \infty$$
$$\lim_{x \to \infty}\left(x^{2} + 3 x\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(x^{2} + 3 x\right)$$ =
$$\lim_{x \to \infty}\left(\frac{1 + \frac{3}{x}}{\frac{1}{x^{2}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1 + \frac{3}{x}}{\frac{1}{x^{2}}}\right) = \lim_{u \to 0^+}\left(\frac{3 u + 1}{u^{2}}\right)$$
=
$$\frac{0 \cdot 3 + 1}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(x^{2} + 3 x\right) = \infty$$
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
$$\lim_{x \to \infty}\left(x^{2} + 3 x\right) = \infty$$
$$\lim_{x \to 0^-}\left(x^{2} + 3 x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{2} + 3 x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x^{2} + 3 x\right) = 4$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{2} + 3 x\right) = 4$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{2} + 3 x\right) = \infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(x^{2} + 3 x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{2} + 3 x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x^{2} + 3 x\right) = 4$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{2} + 3 x\right) = 4$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{2} + 3 x\right) = \infty$$
More at x→-oo
The graph