Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (2+x^2+3*x)/(2+2*x^2+5*x)
-
Limit of (-51+x^2-14*x)/(-21+x^2-4*x)
-
Limit of (28+x^2+11*x)/(-16+x^2)
-
Limit of (-1+x)/(3-2*x)
-
Identical expressions
- cos(one /z)
- co sinus of e of (1 divide by z)
- co sinus of e of (one divide by z)
- cos1/z
- cos(1 divide by z)
-
Similar expressions
- (z-i)*cos(1)/(z*(1+z))
- (1+z-i/z)*cos(1)/z
Limit of the function cos(1/z)
The solution
You have entered
[src]
/1\ lim cos|-| z->0+ \z/
$$\lim_{z \to 0^+} \cos{\left(\frac{1}{z} \right)}$$
Limit(cos(1/z), z, 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 z→0, -oo, +oo, 1
$$\lim_{z \to 0^-} \cos{\left(\frac{1}{z} \right)} = \left\langle -1, 1\right\rangle$$
More at z→0 from the left
$$\lim_{z \to 0^+} \cos{\left(\frac{1}{z} \right)} = \left\langle -1, 1\right\rangle$$
$$\lim_{z \to \infty} \cos{\left(\frac{1}{z} \right)} = 1$$
More at z→oo
$$\lim_{z \to 1^-} \cos{\left(\frac{1}{z} \right)} = \cos{\left(1 \right)}$$
More at z→1 from the left
$$\lim_{z \to 1^+} \cos{\left(\frac{1}{z} \right)} = \cos{\left(1 \right)}$$
More at z→1 from the right
$$\lim_{z \to -\infty} \cos{\left(\frac{1}{z} \right)} = 1$$
More at z→-oo
More at z→0 from the left
$$\lim_{z \to 0^+} \cos{\left(\frac{1}{z} \right)} = \left\langle -1, 1\right\rangle$$
$$\lim_{z \to \infty} \cos{\left(\frac{1}{z} \right)} = 1$$
More at z→oo
$$\lim_{z \to 1^-} \cos{\left(\frac{1}{z} \right)} = \cos{\left(1 \right)}$$
More at z→1 from the left
$$\lim_{z \to 1^+} \cos{\left(\frac{1}{z} \right)} = \cos{\left(1 \right)}$$
More at z→1 from the right
$$\lim_{z \to -\infty} \cos{\left(\frac{1}{z} \right)} = 1$$
More at z→-oo
One‐sided limits
[src]
/1\ lim cos|-| z->0+ \z/
$$\lim_{z \to 0^+} \cos{\left(\frac{1}{z} \right)}$$
<-1, 1>
$$\left\langle -1, 1\right\rangle$$
= -1.83036708622755e-76
/1\ lim cos|-| z->0- \z/
$$\lim_{z \to 0^-} \cos{\left(\frac{1}{z} \right)}$$
<-1, 1>
$$\left\langle -1, 1\right\rangle$$
= -1.83036708622755e-76
= -1.83036708622755e-76
The graph