Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (5+x-3*x^2)/(4-x+2*x^2)
-
Limit of (4-x^2)/(3-x^2)
-
Limit of (3+2*x)/(1-5*x)
-
Limit of (1-2*cos(x))/sin(3*x)
- Derivative of:
-
sin(pi*x/4)
- Integral of d{x}:
- sin(pi*x/4)
-
Identical expressions
- sin(pi*x/ four)
- sinus of ( Pi multiply by x divide by 4)
- sinus of ( Pi multiply by x divide by four)
- sin(pix/4)
- sinpix/4
- sin(pi*x divide by 4)
-
Similar expressions
- sin(pi*x)/(4+sqrt(x))
Limit of the function sin(pi*x/4)
The solution
You have entered
[src]
/pi*x\ lim sin|----| x->2+ \ 4 /
$$\lim_{x \to 2^+} \sin{\left(\frac{\pi x}{4} \right)}$$
Limit(sin((pi*x)/4), x, 2)
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]
/pi*x\ lim sin|----| x->2+ \ 4 /
$$\lim_{x \to 2^+} \sin{\left(\frac{\pi x}{4} \right)}$$
1
$$1$$
= 1.0
/pi*x\ lim sin|----| x->2- \ 4 /
$$\lim_{x \to 2^-} \sin{\left(\frac{\pi x}{4} \right)}$$
1
$$1$$
= 1.0
= 1.0
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 2^-} \sin{\left(\frac{\pi x}{4} \right)} = 1$$
More at x→2 from the left
$$\lim_{x \to 2^+} \sin{\left(\frac{\pi x}{4} \right)} = 1$$
$$\lim_{x \to \infty} \sin{\left(\frac{\pi x}{4} \right)} = \left\langle -1, 1\right\rangle$$
More at x→oo
$$\lim_{x \to 0^-} \sin{\left(\frac{\pi x}{4} \right)} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} \sin{\left(\frac{\pi x}{4} \right)} = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-} \sin{\left(\frac{\pi x}{4} \right)} = \frac{\sqrt{2}}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \sin{\left(\frac{\pi x}{4} \right)} = \frac{\sqrt{2}}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \sin{\left(\frac{\pi x}{4} \right)} = \left\langle -1, 1\right\rangle$$
More at x→-oo
More at x→2 from the left
$$\lim_{x \to 2^+} \sin{\left(\frac{\pi x}{4} \right)} = 1$$
$$\lim_{x \to \infty} \sin{\left(\frac{\pi x}{4} \right)} = \left\langle -1, 1\right\rangle$$
More at x→oo
$$\lim_{x \to 0^-} \sin{\left(\frac{\pi x}{4} \right)} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} \sin{\left(\frac{\pi x}{4} \right)} = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-} \sin{\left(\frac{\pi x}{4} \right)} = \frac{\sqrt{2}}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \sin{\left(\frac{\pi x}{4} \right)} = \frac{\sqrt{2}}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \sin{\left(\frac{\pi x}{4} \right)} = \left\langle -1, 1\right\rangle$$
More at x→-oo
The graph