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sin(|x|)/x
Limit of the function/ sin(|x|)/x

Limit of the function sin(|x|)/x

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You have entered [src] 
     /sin(|x|)\
 lim |--------|
x->0+\   x    /
lim⁡x→0+(sin⁡(∣x∣)x)\lim_{x \to 0^+}\left(\frac{\sin{\left(\left|{x}\right| \right)}}{x}\right) 
Limit(sin(|x|)/x, x, 0)
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02468-8-6-4-2-10102-2
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Rapid solution [src] 
1
11
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→0−(sin⁡(∣x∣)x)=1\lim_{x \to 0^-}\left(\frac{\sin{\left(\left|{x}\right| \right)}}{x}\right) = 1
More at x→0 from the left
lim⁡x→0+(sin⁡(∣x∣)x)=1\lim_{x \to 0^+}\left(\frac{\sin{\left(\left|{x}\right| \right)}}{x}\right) = 1
lim⁡x→∞(sin⁡(∣x∣)x)=0\lim_{x \to \infty}\left(\frac{\sin{\left(\left|{x}\right| \right)}}{x}\right) = 0
More at x→oo
lim⁡x→1−(sin⁡(∣x∣)x)=sin⁡(1)\lim_{x \to 1^-}\left(\frac{\sin{\left(\left|{x}\right| \right)}}{x}\right) = \sin{\left(1 \right)}
More at x→1 from the left
lim⁡x→1+(sin⁡(∣x∣)x)=sin⁡(1)\lim_{x \to 1^+}\left(\frac{\sin{\left(\left|{x}\right| \right)}}{x}\right) = \sin{\left(1 \right)}
More at x→1 from the right
lim⁡x→−∞(sin⁡(∣x∣)x)=0\lim_{x \to -\infty}\left(\frac{\sin{\left(\left|{x}\right| \right)}}{x}\right) = 0
More at x→-oo
One‐sided limits [src] 
     /sin(|x|)\
 lim |--------|
x->0+\   x    /
lim⁡x→0+(sin⁡(∣x∣)x)\lim_{x \to 0^+}\left(\frac{\sin{\left(\left|{x}\right| \right)}}{x}\right) 
1
11 
= 1.0
     /sin(|x|)\
 lim |--------|
x->0-\   x    /
lim⁡x→0−(sin⁡(∣x∣)x)\lim_{x \to 0^-}\left(\frac{\sin{\left(\left|{x}\right| \right)}}{x}\right) 
-1
−1-1 
= -1.0
= -1.0
Numerical answer [src] 
1.0
1.0
The graph
Limit of the function sin(|x|)/x
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