Mister Exam
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- Limit of the function:
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Limit of -2+x^3+6*x
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Limit of ((-2+x)/x)^(2*x)
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Limit of (-2+x)*log(-2+x)
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Limit of -6+x^2+5*x
- Least common denominator:
- x/y+y/x
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Identical expressions
- x/y+y/x
- x divide by y plus y divide by x
- x divide by y+y divide by x
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Similar expressions
- x/y-y/x
Limit of the function x/y+y/x
The solution
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/x y\ lim |- + -| x->oo\y x/
$$\lim_{x \to \infty}\left(\frac{x}{y} + \frac{y}{x}\right)$$
Limit(x/y + y/x, x, oo, dir='-')
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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(\frac{x}{y} + \frac{y}{x}\right) = \infty \operatorname{sign}{\left(\frac{1}{y} \right)}$$
$$\lim_{x \to 0^-}\left(\frac{x}{y} + \frac{y}{x}\right) = - \infty \operatorname{sign}{\left(y \right)}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x}{y} + \frac{y}{x}\right) = \infty \operatorname{sign}{\left(y \right)}$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x}{y} + \frac{y}{x}\right) = \frac{y^{2} + 1}{y}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x}{y} + \frac{y}{x}\right) = \frac{y^{2} + 1}{y}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x}{y} + \frac{y}{x}\right) = - \infty \operatorname{sign}{\left(\frac{1}{y} \right)}$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{x}{y} + \frac{y}{x}\right) = - \infty \operatorname{sign}{\left(y \right)}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x}{y} + \frac{y}{x}\right) = \infty \operatorname{sign}{\left(y \right)}$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x}{y} + \frac{y}{x}\right) = \frac{y^{2} + 1}{y}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x}{y} + \frac{y}{x}\right) = \frac{y^{2} + 1}{y}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x}{y} + \frac{y}{x}\right) = - \infty \operatorname{sign}{\left(\frac{1}{y} \right)}$$
More at x→-oo