Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (-5+7*n)/(2+n)
-
Limit of (-64+4^x)/(-3+x)
-
Limit of (-7+3*x^2+5*x)/(1+x+3*x^2)
-
Limit of (-2+2*x^3+7*x)/(-4-x+3*x^3)
- Graphing y =:
- 12*x^2
- Integral of d{x}:
- 12*x^2
- Derivative of:
-
12*x^2
-
Identical expressions
- twelve *x^ two
- 12 multiply by x squared
- twelve multiply by x to the power of two
- 12*x2
- 12*x²
- 12*x to the power of 2
- 12x^2
- 12x2
-
Similar expressions
- (32+x^4-12*x^2)/(-2+x)
Limit of the function 12*x^2
The solution
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/ 2\ lim \12*x / x->oo
$$\lim_{x \to \infty}\left(12 x^{2}\right)$$
Limit(12*x^2, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(12 x^{2}\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(12 x^{2}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{1}{12} \frac{1}{x^{2}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{1}{12} \frac{1}{x^{2}}} = \lim_{u \to 0^+}\left(\frac{12}{u^{2}}\right)$$
=
$$\frac{12}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(12 x^{2}\right) = \infty$$
$$\lim_{x \to \infty}\left(12 x^{2}\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(12 x^{2}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{1}{12} \frac{1}{x^{2}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{1}{12} \frac{1}{x^{2}}} = \lim_{u \to 0^+}\left(\frac{12}{u^{2}}\right)$$
=
$$\frac{12}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(12 x^{2}\right) = \infty$$
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
$$\lim_{x \to \infty}\left(12 x^{2}\right) = \infty$$
$$\lim_{x \to 0^-}\left(12 x^{2}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(12 x^{2}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(12 x^{2}\right) = 12$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(12 x^{2}\right) = 12$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(12 x^{2}\right) = \infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(12 x^{2}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(12 x^{2}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(12 x^{2}\right) = 12$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(12 x^{2}\right) = 12$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(12 x^{2}\right) = \infty$$
More at x→-oo
The graph