Mister Exam
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How to use it?
- Limit of the function:
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Limit of sin(3)^2/x
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Limit of x^4+2*cos(x)^2
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Limit of x*2^x*3^(-x)
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Limit of log(1+3*x^2)/(x^3-5*x^2)
- Integral of d{x}:
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1/cosh(x)
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Identical expressions
- one /cosh(x)
- 1 divide by hyperbolic co sinus of e of ine of (x)
- one divide by hyperbolic co sinus of e of ine of (x)
- 1/coshx
- 1 divide by cosh(x)
Limit of the function 1/cosh(x)
The solution
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1 lim ------- x->oocosh(x)
$$\lim_{x \to \infty} \frac{1}{\cosh{\left(x \right)}}$$
Limit(1/cosh(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
$$\lim_{x \to \infty} \frac{1}{\cosh{\left(x \right)}} = 0$$
$$\lim_{x \to 0^-} \frac{1}{\cosh{\left(x \right)}} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{\cosh{\left(x \right)}} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \frac{1}{\cosh{\left(x \right)}} = \frac{2 e}{1 + e^{2}}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{\cosh{\left(x \right)}} = \frac{2 e}{1 + e^{2}}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{\cosh{\left(x \right)}} = 0$$
More at x→-oo
$$\lim_{x \to 0^-} \frac{1}{\cosh{\left(x \right)}} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{\cosh{\left(x \right)}} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \frac{1}{\cosh{\left(x \right)}} = \frac{2 e}{1 + e^{2}}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{\cosh{\left(x \right)}} = \frac{2 e}{1 + e^{2}}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{\cosh{\left(x \right)}} = 0$$
More at x→-oo
The graph