Mister Exam
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How to use it?
- Limit of the function:
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Limit of (1+3*x)^(5/x)
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Limit of x^2/(-2+sqrt(4+x^2))
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Limit of ((5+x^2-6*x)/(5+x^2-5*x))^(2+3*x)
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Limit of (2+x^2+3*x)/(-4+x^2)
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Identical expressions
- log(x)/log(five)
- logarithm of (x) divide by logarithm of (5)
- logarithm of (x) divide by logarithm of (five)
- logx/log5
- log(x) divide by log(5)
Limit of the function log(x)/log(5)
The solution
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/log(x)\ lim |------| x->0+\log(5)/
$$\lim_{x \to 0^+}\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}}\right)$$
Limit(log(x)/log(5), x, 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
$$\lim_{x \to 0^-}\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}}\right) = -\infty$$
$$\lim_{x \to \infty}\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}}\right) = \infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}}\right) = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}}\right) = 0$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}}\right) = \infty$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}}\right) = -\infty$$
$$\lim_{x \to \infty}\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}}\right) = \infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}}\right) = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}}\right) = 0$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}}\right) = \infty$$
More at x→-oo
One‐sided limits
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/log(x)\ lim |------| x->0+\log(5)/
$$\lim_{x \to 0^+}\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}}\right)$$
-oo
$$-\infty$$
= -5.50841094543338
/log(x)\ lim |------| x->0-\log(5)/
$$\lim_{x \to 0^-}\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}}\right)$$
-oo
$$-\infty$$
= (-5.50841094543338 + 1.95198126583117j)
= (-5.50841094543338 + 1.95198126583117j)
The graph