Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (3+x^2-4*x)/(-9+x^2)
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Limit of (-6+x^2-x)/(9+x^2-6*x)
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Limit of (-x+tan(x))/(x+2*sin(x))
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Limit of sin(-2+2*x)/(-1+x)
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Identical expressions
- cosh(one /x)/(x*(one +x^ two))
- hyperbolic co sinus of e of ine of (1 divide by x) divide by (x multiply by (1 plus x squared ))
- hyperbolic co sinus of e of ine of (one divide by x) divide by (x multiply by (one plus x to the power of two))
- cosh(1/x)/(x*(1+x2))
- cosh1/x/x*1+x2
- cosh(1/x)/(x*(1+x²))
- cosh(1/x)/(x*(1+x to the power of 2))
- cosh(1/x)/(x(1+x^2))
- cosh(1/x)/(x(1+x2))
- cosh1/x/x1+x2
- cosh1/x/x1+x^2
- cosh(1 divide by x) divide by (x*(1+x^2))
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Similar expressions
- cosh(1/x)/(x*(1-x^2))
Limit of the function cosh(1/x)/(x*(1+x^2))
The solution
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[src]
/ /1\ \
| cosh|-| |
| \x/ |
lim |----------|
x->0+| / 2\|
\x*\1 + x //
$$\lim_{x \to 0^+}\left(\frac{\cosh{\left(\frac{1}{x} \right)}}{x \left(x^{2} + 1\right)}\right)$$
Limit(cosh(1/x)/((x*(1 + x^2))), 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
One‐sided limits
[src]
/ /1\ \
| cosh|-| |
| \x/ |
lim |----------|
x->0+| / 2\|
\x*\1 + x //
$$\lim_{x \to 0^+}\left(\frac{\cosh{\left(\frac{1}{x} \right)}}{x \left(x^{2} + 1\right)}\right)$$
oo
$$\infty$$
= -0.0213505581546171
/ /1\ \
| cosh|-| |
| \x/ |
lim |----------|
x->0-| / 2\|
\x*\1 + x //
$$\lim_{x \to 0^-}\left(\frac{\cosh{\left(\frac{1}{x} \right)}}{x \left(x^{2} + 1\right)}\right)$$
-oo
$$-\infty$$
= 0.0213505581546171
= 0.0213505581546171
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{\cosh{\left(\frac{1}{x} \right)}}{x \left(x^{2} + 1\right)}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\cosh{\left(\frac{1}{x} \right)}}{x \left(x^{2} + 1\right)}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{\cosh{\left(\frac{1}{x} \right)}}{x \left(x^{2} + 1\right)}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\cosh{\left(\frac{1}{x} \right)}}{x \left(x^{2} + 1\right)}\right) = \frac{1 + e^{2}}{4 e}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\cosh{\left(\frac{1}{x} \right)}}{x \left(x^{2} + 1\right)}\right) = \frac{1 + e^{2}}{4 e}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\cosh{\left(\frac{1}{x} \right)}}{x \left(x^{2} + 1\right)}\right) = 0$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\cosh{\left(\frac{1}{x} \right)}}{x \left(x^{2} + 1\right)}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{\cosh{\left(\frac{1}{x} \right)}}{x \left(x^{2} + 1\right)}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\cosh{\left(\frac{1}{x} \right)}}{x \left(x^{2} + 1\right)}\right) = \frac{1 + e^{2}}{4 e}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\cosh{\left(\frac{1}{x} \right)}}{x \left(x^{2} + 1\right)}\right) = \frac{1 + e^{2}}{4 e}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\cosh{\left(\frac{1}{x} \right)}}{x \left(x^{2} + 1\right)}\right) = 0$$
More at x→-oo
The graph