Mister Exam
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How to use it?
- 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*log(two +x)
- 1 plus x multiply by logarithm of (2 plus x)
- one plus x multiply by logarithm of (two plus x)
- 1+xlog(2+x)
- 1+xlog2+x
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Similar expressions
- 1-x*log(2+x)
- 1+x*log(2-x)
- x/((1+x)*log(2+x)^2)
- -log(1+x)+(1+x)*log(2+x)
- log(-x^2-2*x)/((1+x)*log(2+x))
- x*log(1+x)/((1+x)*log(2+x))
- 1/((1+x)*log(2+x))
Limit of the function 1+x*log(2+x)
The solution
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[src]
lim (1 + x*log(2 + x)) x->-2+
$$\lim_{x \to -2^+}\left(x \log{\left(x + 2 \right)} + 1\right)$$
Limit(1 + x*log(2 + x), x, -2)
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
$$\lim_{x \to -2^-}\left(x \log{\left(x + 2 \right)} + 1\right) = \infty$$
More at x→-2 from the left
$$\lim_{x \to -2^+}\left(x \log{\left(x + 2 \right)} + 1\right) = \infty$$
$$\lim_{x \to \infty}\left(x \log{\left(x + 2 \right)} + 1\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(x \log{\left(x + 2 \right)} + 1\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x \log{\left(x + 2 \right)} + 1\right) = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x \log{\left(x + 2 \right)} + 1\right) = 1 + \log{\left(3 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x \log{\left(x + 2 \right)} + 1\right) = 1 + \log{\left(3 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x \log{\left(x + 2 \right)} + 1\right) = -\infty$$
More at x→-oo
More at x→-2 from the left
$$\lim_{x \to -2^+}\left(x \log{\left(x + 2 \right)} + 1\right) = \infty$$
$$\lim_{x \to \infty}\left(x \log{\left(x + 2 \right)} + 1\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(x \log{\left(x + 2 \right)} + 1\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x \log{\left(x + 2 \right)} + 1\right) = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x \log{\left(x + 2 \right)} + 1\right) = 1 + \log{\left(3 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x \log{\left(x + 2 \right)} + 1\right) = 1 + \log{\left(3 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x \log{\left(x + 2 \right)} + 1\right) = -\infty$$
More at x→-oo
One‐sided limits
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lim (1 + x*log(2 + x)) x->-2+
$$\lim_{x \to -2^+}\left(x \log{\left(x + 2 \right)} + 1\right)$$
oo
$$\infty$$
= 18.7040401084166
lim (1 + x*log(2 + x)) x->-2-
$$\lim_{x \to -2^-}\left(x \log{\left(x + 2 \right)} + 1\right)$$
oo
$$\infty$$
= (18.6966614522551 - 6.3004815912505j)
= (18.6966614522551 - 6.3004815912505j)
The graph