Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
- Limit of (1-cos(a*x))/(1-cos(b*x))
-
Limit of cot(x)*log(x+e^x)
-
Limit of (x^2-x)/(-1+x^2)
-
Limit of 6/x
- Derivative of:
-
3*x^4
- Graphing y =:
- 3*x^4
-
Identical expressions
- three *x^ four
- 3 multiply by x to the power of 4
- three multiply by x to the power of four
- 3*x4
- 3*x⁴
- 3x^4
- 3x4
-
Similar expressions
- (1+3*x^4)/(5-4*x^2)
- (1+x^2+x^4)/(x^2-x+3*x^4)
- (2+x+x^3)/(3+3*x^4+6*x)
- 1-11*x+43*x^4/8
- (1+3*x)^(4/x)
Limit of the function 3*x^4
The solution
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/ 4\ lim \3*x / x->oo
$$\lim_{x \to \infty}\left(3 x^{4}\right)$$
Limit(3*x^4, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(3 x^{4}\right)$$
Let's divide numerator and denominator by x^4:
$$\lim_{x \to \infty}\left(3 x^{4}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{1}{3} \frac{1}{x^{4}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{1}{3} \frac{1}{x^{4}}} = \lim_{u \to 0^+}\left(\frac{3}{u^{4}}\right)$$
=
$$\frac{3}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(3 x^{4}\right) = \infty$$
$$\lim_{x \to \infty}\left(3 x^{4}\right)$$
Let's divide numerator and denominator by x^4:
$$\lim_{x \to \infty}\left(3 x^{4}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{1}{3} \frac{1}{x^{4}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{1}{3} \frac{1}{x^{4}}} = \lim_{u \to 0^+}\left(\frac{3}{u^{4}}\right)$$
=
$$\frac{3}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(3 x^{4}\right) = \infty$$
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
$$\lim_{x \to \infty}\left(3 x^{4}\right) = \infty$$
$$\lim_{x \to 0^-}\left(3 x^{4}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(3 x^{4}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(3 x^{4}\right) = 3$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(3 x^{4}\right) = 3$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(3 x^{4}\right) = \infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(3 x^{4}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(3 x^{4}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(3 x^{4}\right) = 3$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(3 x^{4}\right) = 3$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(3 x^{4}\right) = \infty$$
More at x→-oo
The graph