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x^sin(2*x)
Limit of the function/ x^sin(2*x)

Limit of the function x^sin(2*x)

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      sin(2*x)
 lim x        
x->0+
$$\lim_{x \to 0^+} x^{\sin{\left(2 x \right)}}$$ 
Limit(x^sin(2*x), x, 0)
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
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Rapid solution [src] 
1
$$1$$
Expand and simplify
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-} x^{\sin{\left(2 x \right)}} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} x^{\sin{\left(2 x \right)}} = 1$$
$$\lim_{x \to \infty} x^{\sin{\left(2 x \right)}} = \infty^{\left\langle -1, 1\right\rangle}$$
More at x→oo
$$\lim_{x \to 1^-} x^{\sin{\left(2 x \right)}} = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} x^{\sin{\left(2 x \right)}} = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty} x^{\sin{\left(2 x \right)}} = \left(-\infty\right)^{\left\langle -1, 1\right\rangle}$$
More at x→-oo
One‐sided limits [src] 
      sin(2*x)
 lim x        
x->0+
$$\lim_{x \to 0^+} x^{\sin{\left(2 x \right)}}$$ 
1
$$1$$ 
= 0.997118825634446
      sin(2*x)
 lim x        
x->0-
$$\lim_{x \to 0^-} x^{\sin{\left(2 x \right)}}$$ 
1
$$1$$ 
= (1.00381659102748 - 0.00170318471994232j)
= (1.00381659102748 - 0.00170318471994232j)
Numerical answer [src] 
0.997118825634446
0.997118825634446
The graph
Limit of the function x^sin(2*x)
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