Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
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Limit of (-3+sqrt(1+4*x))/(-2+x)
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Limit of x^2+(sqrt(1+3*x)-sqrt(1-2*x))/x
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Limit of ((11+7*x+7*x^2)/(14+9*x+13*x^2))^(4*x)
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Limit of (-1+x+6*x^2)/(1/2+x)
- Derivative of:
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7/x^2
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Identical expressions
- seven /x^ two
- 7 divide by x squared
- seven divide by x to the power of two
- 7/x2
- 7/x²
- 7/x to the power of 2
- 7 divide by x^2
Limit of the function 7/x^2
The solution
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/7 \
lim |--|
x->oo| 2|
\x /
$$\lim_{x \to \infty}\left(\frac{7}{x^{2}}\right)$$
Limit(7/x^2, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(\frac{7}{x^{2}}\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(\frac{7}{x^{2}}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{7 \frac{1}{x^{2}}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{7 \frac{1}{x^{2}}}{1}\right) = \lim_{u \to 0^+}\left(7 u^{2}\right)$$
=
$$7 \cdot 0^{2} = 0$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{7}{x^{2}}\right) = 0$$
$$\lim_{x \to \infty}\left(\frac{7}{x^{2}}\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(\frac{7}{x^{2}}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{7 \frac{1}{x^{2}}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{7 \frac{1}{x^{2}}}{1}\right) = \lim_{u \to 0^+}\left(7 u^{2}\right)$$
=
$$7 \cdot 0^{2} = 0$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{7}{x^{2}}\right) = 0$$
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
$$\lim_{x \to \infty}\left(\frac{7}{x^{2}}\right) = 0$$
$$\lim_{x \to 0^-}\left(\frac{7}{x^{2}}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{7}{x^{2}}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{7}{x^{2}}\right) = 7$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{7}{x^{2}}\right) = 7$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{7}{x^{2}}\right) = 0$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{7}{x^{2}}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{7}{x^{2}}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{7}{x^{2}}\right) = 7$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{7}{x^{2}}\right) = 7$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{7}{x^{2}}\right) = 0$$
More at x→-oo
The graph