Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (-6+x^2-x)/(6+x^2-5*x)
-
Limit of log(1+x^2)/(-e^(-x)+cos(3*x))
-
Limit of -2+|-2+x|/x
-
Limit of (-4-8*x+8*x^2)/(3+8*x)
- Graphing y =:
- sin(1/x)/x
- Integral of d{x}:
- sin(1/x)/x
-
Identical expressions
- sin(one /x)/x
- sinus of (1 divide by x) divide by x
- sinus of (one divide by x) divide by x
- sin1/x/x
- sin(1 divide by x) divide by x
-
Similar expressions
- (1-sin(1/x))/x
- (1-cos(x*sin(1/x)))/x
- log(1-sin(x^3*sin(1/x)))/x
Limit of the function sin(1/x)/x
The solution
You have entered
[src]
/ / 1\\
|sin|1*-||
| \ x/|
lim |--------|
x->0+\ x /
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(1 \cdot \frac{1}{x} \right)}}{x}\right)$$
Limit(sin(1/x)/x, 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
$$\lim_{x \to 0^-}\left(\frac{\sin{\left(1 \cdot \frac{1}{x} \right)}}{x}\right) = \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(1 \cdot \frac{1}{x} \right)}}{x}\right) = \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}$$
$$\lim_{x \to \infty}\left(\frac{\sin{\left(1 \cdot \frac{1}{x} \right)}}{x}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\sin{\left(1 \cdot \frac{1}{x} \right)}}{x}\right) = \sin{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin{\left(1 \cdot \frac{1}{x} \right)}}{x}\right) = \sin{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(1 \cdot \frac{1}{x} \right)}}{x}\right) = 0$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(1 \cdot \frac{1}{x} \right)}}{x}\right) = \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}$$
$$\lim_{x \to \infty}\left(\frac{\sin{\left(1 \cdot \frac{1}{x} \right)}}{x}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\sin{\left(1 \cdot \frac{1}{x} \right)}}{x}\right) = \sin{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin{\left(1 \cdot \frac{1}{x} \right)}}{x}\right) = \sin{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(1 \cdot \frac{1}{x} \right)}}{x}\right) = 0$$
More at x→-oo
Rapid solution
[src]
oo*sign(<-1, 1>)
$$\infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}$$
One‐sided limits
[src]
/ / 1\\
|sin|1*-||
| \ x/|
lim |--------|
x->0+\ x /
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(1 \cdot \frac{1}{x} \right)}}{x}\right)$$
oo*sign(<-1, 1>)
$$\infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}$$
= -3.46075922100526e-75
/ / 1\\
|sin|1*-||
| \ x/|
lim |--------|
x->0-\ x /
$$\lim_{x \to 0^-}\left(\frac{\sin{\left(1 \cdot \frac{1}{x} \right)}}{x}\right)$$
-oo*sign(<-1, 1>)
$$- \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}$$
= -3.46075922100526e-75
= -3.46075922100526e-75
The graph