Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (x^2-5*x^3)/(x-2*x^2+6*x^3)
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Limit of (-1+x^2+5*x)/(2+3*x)
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Limit of (x^2-4*x)/(-6+x)
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Limit of (-4+x^2)/(-6+3*x)
- Graphing y =:
- x-log(1+x^2)
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Identical expressions
- x-log(one +x^ two)
- x minus logarithm of (1 plus x squared )
- x minus logarithm of (one plus x to the power of two)
- x-log(1+x2)
- x-log1+x2
- x-log(1+x²)
- x-log(1+x to the power of 2)
- x-log1+x^2
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Similar expressions
- x-log(1-x^2)
- x+log(1+x^2)
Limit of the function x-log(1+x^2)
The solution
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/ / 2\\ lim \x - log\1 + x // x->-oo
$$\lim_{x \to -\infty}\left(x - \log{\left(x^{2} + 1 \right)}\right)$$
Limit(x - log(1 + x^2), x, -oo)
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
$$\lim_{x \to -\infty}\left(x - \log{\left(x^{2} + 1 \right)}\right) = -\infty$$
$$\lim_{x \to \infty}\left(x - \log{\left(x^{2} + 1 \right)}\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(x - \log{\left(x^{2} + 1 \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x - \log{\left(x^{2} + 1 \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x - \log{\left(x^{2} + 1 \right)}\right) = 1 - \log{\left(2 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x - \log{\left(x^{2} + 1 \right)}\right) = 1 - \log{\left(2 \right)}$$
More at x→1 from the right
$$\lim_{x \to \infty}\left(x - \log{\left(x^{2} + 1 \right)}\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(x - \log{\left(x^{2} + 1 \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x - \log{\left(x^{2} + 1 \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x - \log{\left(x^{2} + 1 \right)}\right) = 1 - \log{\left(2 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x - \log{\left(x^{2} + 1 \right)}\right) = 1 - \log{\left(2 \right)}$$
More at x→1 from the right
The graph