Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-2+x)/(-2+x^2-x)
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Limit of cos(5*x)*sin(2*x)/tan(x)
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Limit of 3*sin(x)^2/(4*x)
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Limit of log(1+e^x)
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Identical expressions
- three *sin(x)^ two /(four *x)
- 3 multiply by sinus of (x) squared divide by (4 multiply by x)
- three multiply by sinus of (x) to the power of two divide by (four multiply by x)
- 3*sin(x)2/(4*x)
- 3*sinx2/4*x
- 3*sin(x)²/(4*x)
- 3*sin(x) to the power of 2/(4*x)
- 3sin(x)^2/(4x)
- 3sin(x)2/(4x)
- 3sinx2/4x
- 3sinx^2/4x
- 3*sin(x)^2 divide by (4*x)
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Similar expressions
- 3*sinx^2/(4*x)
Limit of the function 3*sin(x)^2/(4*x)
The solution
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[src]
/ 2 \
|3*sin (x)|
lim |---------|
pi \ 4*x /
x->--+
2
$$\lim_{x \to \frac{\pi}{2}^+}\left(\frac{3 \sin^{2}{\left(x \right)}}{4 x}\right)$$
Limit(3*sin(x)^2/((4*x)), x, pi/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]
/ 2 \
|3*sin (x)|
lim |---------|
pi \ 4*x /
x->--+
2
$$\lim_{x \to \frac{\pi}{2}^+}\left(\frac{3 \sin^{2}{\left(x \right)}}{4 x}\right)$$
3 ---- 2*pi
$$\frac{3}{2 \pi}$$
= 0.477464829275686
/ 2 \
|3*sin (x)|
lim |---------|
pi \ 4*x /
x->---
2
$$\lim_{x \to \frac{\pi}{2}^-}\left(\frac{3 \sin^{2}{\left(x \right)}}{4 x}\right)$$
3 ---- 2*pi
$$\frac{3}{2 \pi}$$
= 0.477464829275686
= 0.477464829275686
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \frac{\pi}{2}^-}\left(\frac{3 \sin^{2}{\left(x \right)}}{4 x}\right) = \frac{3}{2 \pi}$$
More at x→pi/2 from the left
$$\lim_{x \to \frac{\pi}{2}^+}\left(\frac{3 \sin^{2}{\left(x \right)}}{4 x}\right) = \frac{3}{2 \pi}$$
$$\lim_{x \to \infty}\left(\frac{3 \sin^{2}{\left(x \right)}}{4 x}\right) = 0$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{3 \sin^{2}{\left(x \right)}}{4 x}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{3 \sin^{2}{\left(x \right)}}{4 x}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{3 \sin^{2}{\left(x \right)}}{4 x}\right) = \frac{3 \sin^{2}{\left(1 \right)}}{4}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{3 \sin^{2}{\left(x \right)}}{4 x}\right) = \frac{3 \sin^{2}{\left(1 \right)}}{4}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{3 \sin^{2}{\left(x \right)}}{4 x}\right) = 0$$
More at x→-oo
More at x→pi/2 from the left
$$\lim_{x \to \frac{\pi}{2}^+}\left(\frac{3 \sin^{2}{\left(x \right)}}{4 x}\right) = \frac{3}{2 \pi}$$
$$\lim_{x \to \infty}\left(\frac{3 \sin^{2}{\left(x \right)}}{4 x}\right) = 0$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{3 \sin^{2}{\left(x \right)}}{4 x}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{3 \sin^{2}{\left(x \right)}}{4 x}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{3 \sin^{2}{\left(x \right)}}{4 x}\right) = \frac{3 \sin^{2}{\left(1 \right)}}{4}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{3 \sin^{2}{\left(x \right)}}{4 x}\right) = \frac{3 \sin^{2}{\left(1 \right)}}{4}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{3 \sin^{2}{\left(x \right)}}{4 x}\right) = 0$$
More at x→-oo
The graph