Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of 2+((-1+x)/(3+x))^x
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Limit of (-1+x)/(x+x^2)
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Limit of ((1+x)^4-(-1+x)^4)/((1+x)^4+(-1+x)^4)
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Limit of tan(6*x)/(3*x)
- Graphing y =:
- x^4+2*x^2
- Derivative of:
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x^4+2*x^2
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Identical expressions
- x^ four + two *x^ two
- x to the power of 4 plus 2 multiply by x squared
- x to the power of four plus two multiply by x to the power of two
- x4+2*x2
- x⁴+2*x²
- x to the power of 4+2*x to the power of 2
- x^4+2x^2
- x4+2x2
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Similar expressions
- x^4-2*x^2
Limit of the function x^4+2*x^2
The solution
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/ 4 2\ lim \x + 2*x / x->-oo
$$\lim_{x \to -\infty}\left(x^{4} + 2 x^{2}\right)$$
Limit(x^4 + 2*x^2, x, -oo)
Detail solution
Let's take the limit
$$\lim_{x \to -\infty}\left(x^{4} + 2 x^{2}\right)$$
Let's divide numerator and denominator by x^4:
$$\lim_{x \to -\infty}\left(x^{4} + 2 x^{2}\right)$$ =
$$\lim_{x \to -\infty}\left(\frac{1 + \frac{2}{x^{2}}}{\frac{1}{x^{4}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to -\infty}\left(\frac{1 + \frac{2}{x^{2}}}{\frac{1}{x^{4}}}\right) = \lim_{u \to 0^+}\left(\frac{2 u^{2} + 1}{u^{4}}\right)$$
=
$$\frac{2 \cdot 0^{2} + 1}{0} = \infty$$
The final answer:
$$\lim_{x \to -\infty}\left(x^{4} + 2 x^{2}\right) = \infty$$
$$\lim_{x \to -\infty}\left(x^{4} + 2 x^{2}\right)$$
Let's divide numerator and denominator by x^4:
$$\lim_{x \to -\infty}\left(x^{4} + 2 x^{2}\right)$$ =
$$\lim_{x \to -\infty}\left(\frac{1 + \frac{2}{x^{2}}}{\frac{1}{x^{4}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to -\infty}\left(\frac{1 + \frac{2}{x^{2}}}{\frac{1}{x^{4}}}\right) = \lim_{u \to 0^+}\left(\frac{2 u^{2} + 1}{u^{4}}\right)$$
=
$$\frac{2 \cdot 0^{2} + 1}{0} = \infty$$
The final answer:
$$\lim_{x \to -\infty}\left(x^{4} + 2 x^{2}\right) = \infty$$
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
$$\lim_{x \to -\infty}\left(x^{4} + 2 x^{2}\right) = \infty$$
$$\lim_{x \to \infty}\left(x^{4} + 2 x^{2}\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(x^{4} + 2 x^{2}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{4} + 2 x^{2}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x^{4} + 2 x^{2}\right) = 3$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{4} + 2 x^{2}\right) = 3$$
More at x→1 from the right
$$\lim_{x \to \infty}\left(x^{4} + 2 x^{2}\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(x^{4} + 2 x^{2}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{4} + 2 x^{2}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x^{4} + 2 x^{2}\right) = 3$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{4} + 2 x^{2}\right) = 3$$
More at x→1 from the right
The graph