Mister Exam
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- Limit of the function:
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Limit of (2^(1+2*x)+3^(2+x))/(5+4^(2+x))
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Limit of 1/(x*(3+x))
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Limit of 1+x*log(2+x)
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Limit of ((1+x^2)^(1/3)-x*cot(x))/(x*sin(x))
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Identical expressions
- one /(x*(three +x))
- 1 divide by (x multiply by (3 plus x))
- one divide by (x multiply by (three plus x))
- 1/(x(3+x))
- 1/x3+x
- 1 divide by (x*(3+x))
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Similar expressions
- cos(1/x)^(3+x^2)
- 1/(x*(3-x))
- e^(1/x)*(3+x)/(-1+x)
Limit of the function 1/(x*(3+x))
The solution
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1 lim --------- x->oox*(3 + x)
$$\lim_{x \to \infty} \frac{1}{x \left(x + 3\right)}$$
Limit(1/(x*(3 + 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
The graph
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty} \frac{1}{x \left(x + 3\right)} = 0$$
$$\lim_{x \to 0^-} \frac{1}{x \left(x + 3\right)} = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{x \left(x + 3\right)} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \frac{1}{x \left(x + 3\right)} = \frac{1}{4}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{x \left(x + 3\right)} = \frac{1}{4}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{x \left(x + 3\right)} = 0$$
More at x→-oo
$$\lim_{x \to 0^-} \frac{1}{x \left(x + 3\right)} = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{x \left(x + 3\right)} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \frac{1}{x \left(x + 3\right)} = \frac{1}{4}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{x \left(x + 3\right)} = \frac{1}{4}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{x \left(x + 3\right)} = 0$$
More at x→-oo
The graph