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sin(2+x)/(2-x)
Limit of the function/ sin(2+x)/(2-x)

Limit of the function sin(2+x)/(2-x)

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      /sin(2 + x)\
 lim  |----------|
x->-2+\  2 - x   /
lim⁡x→−2+(sin⁡(x+2)2−x)\lim_{x \to -2^+}\left(\frac{\sin{\left(x + 2 \right)}}{2 - x}\right) 
Limit(sin(2 + x)/(2 - x), 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
-4.0-3.0-2.0-1.04.00.01.02.03.0-5050
Plot the graph
Rapid solution [src] 
0
00
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→−2−(sin⁡(x+2)2−x)=0\lim_{x \to -2^-}\left(\frac{\sin{\left(x + 2 \right)}}{2 - x}\right) = 0
More at x→-2 from the left
lim⁡x→−2+(sin⁡(x+2)2−x)=0\lim_{x \to -2^+}\left(\frac{\sin{\left(x + 2 \right)}}{2 - x}\right) = 0
lim⁡x→∞(sin⁡(x+2)2−x)=0\lim_{x \to \infty}\left(\frac{\sin{\left(x + 2 \right)}}{2 - x}\right) = 0
More at x→oo
lim⁡x→0−(sin⁡(x+2)2−x)=sin⁡(2)2\lim_{x \to 0^-}\left(\frac{\sin{\left(x + 2 \right)}}{2 - x}\right) = \frac{\sin{\left(2 \right)}}{2}
More at x→0 from the left
lim⁡x→0+(sin⁡(x+2)2−x)=sin⁡(2)2\lim_{x \to 0^+}\left(\frac{\sin{\left(x + 2 \right)}}{2 - x}\right) = \frac{\sin{\left(2 \right)}}{2}
More at x→0 from the right
lim⁡x→1−(sin⁡(x+2)2−x)=sin⁡(3)\lim_{x \to 1^-}\left(\frac{\sin{\left(x + 2 \right)}}{2 - x}\right) = \sin{\left(3 \right)}
More at x→1 from the left
lim⁡x→1+(sin⁡(x+2)2−x)=sin⁡(3)\lim_{x \to 1^+}\left(\frac{\sin{\left(x + 2 \right)}}{2 - x}\right) = \sin{\left(3 \right)}
More at x→1 from the right
lim⁡x→−∞(sin⁡(x+2)2−x)=0\lim_{x \to -\infty}\left(\frac{\sin{\left(x + 2 \right)}}{2 - x}\right) = 0
More at x→-oo
One‐sided limits [src] 
      /sin(2 + x)\
 lim  |----------|
x->-2+\  2 - x   /
lim⁡x→−2+(sin⁡(x+2)2−x)\lim_{x \to -2^+}\left(\frac{\sin{\left(x + 2 \right)}}{2 - x}\right) 
0
00 
= -4.99767881278251e-33
      /sin(2 + x)\
 lim  |----------|
x->-2-\  2 - x   /
lim⁡x→−2−(sin⁡(x+2)2−x)\lim_{x \to -2^-}\left(\frac{\sin{\left(x + 2 \right)}}{2 - x}\right) 
0
00 
= 1.44732464584506e-32
= 1.44732464584506e-32
Numerical answer [src] 
-4.99767881278251e-33
-4.99767881278251e-33
The graph
Limit of the function sin(2+x)/(2-x)
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