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sin(1/(-1+x))
Limit of the function/ sin(1/(-1+x))

Limit of the function sin(1/(-1+x))

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        /  1   \
 lim sin|------|
x->1+   \-1 + x/
$$\lim_{x \to 1^+} \sin{\left(\frac{1}{x - 1} \right)}$$ 
Limit(sin(1/(-1 + x)), x, 1)
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
Plot the graph
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 1^-} \sin{\left(\frac{1}{x - 1} \right)} = \left\langle -1, 1\right\rangle$$
More at x→1 from the left
$$\lim_{x \to 1^+} \sin{\left(\frac{1}{x - 1} \right)} = \left\langle -1, 1\right\rangle$$
$$\lim_{x \to \infty} \sin{\left(\frac{1}{x - 1} \right)} = 0$$
More at x→oo
$$\lim_{x \to 0^-} \sin{\left(\frac{1}{x - 1} \right)} = - \sin{\left(1 \right)}$$
More at x→0 from the left
$$\lim_{x \to 0^+} \sin{\left(\frac{1}{x - 1} \right)} = - \sin{\left(1 \right)}$$
More at x→0 from the right
$$\lim_{x \to -\infty} \sin{\left(\frac{1}{x - 1} \right)} = 0$$
More at x→-oo
Rapid solution [src] 
<-1, 1>
$$\left\langle -1, 1\right\rangle$$
Expand and simplify
One‐sided limits [src] 
        /  1   \
 lim sin|------|
x->1+   \-1 + x/
$$\lim_{x \to 1^+} \sin{\left(\frac{1}{x - 1} \right)}$$ 
<-1, 1>
$$\left\langle -1, 1\right\rangle$$ 
= 1.61429919914458e-75
        /  1   \
 lim sin|------|
x->1-   \-1 + x/
$$\lim_{x \to 1^-} \sin{\left(\frac{1}{x - 1} \right)}$$ 
<-1, 1>
$$\left\langle -1, 1\right\rangle$$ 
= 1.22571286411748e-76
= 1.22571286411748e-76
Numerical answer [src] 
1.61429919914458e-75
1.61429919914458e-75
The graph
Limit of the function sin(1/(-1+x))
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