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x/sqrt(16-x^4)
Limit of the function/ x/sqrt(16-x^4)

Limit of the function x/sqrt(16-x^4)

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     /     x      \
 lim |------------|
x->2+|   _________|
     |  /       4 |
     \\/  16 - x  /
$$\lim_{x \to 2^+}\left(\frac{x}{\sqrt{16 - x^{4}}}\right)$$ 
Limit(x/sqrt(16 - x^4), 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
Plot the graph
Rapid solution [src] 
-oo*I
$$- \infty i$$
Expand and simplify
One‐sided limits [src] 
     /     x      \
 lim |------------|
x->2+|   _________|
     |  /       4 |
     \\/  16 - x  /
$$\lim_{x \to 2^+}\left(\frac{x}{\sqrt{16 - x^{4}}}\right)$$ 
-oo*I
$$- \infty i$$ 
= (0.0 - 38.8352886740698j)
     /     x      \
 lim |------------|
x->2-|   _________|
     |  /       4 |
     \\/  16 - x  /
$$\lim_{x \to 2^-}\left(\frac{x}{\sqrt{16 - x^{4}}}\right)$$ 
oo
$$\infty$$ 
= 38.5477949976968
= 38.5477949976968
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 2^-}\left(\frac{x}{\sqrt{16 - x^{4}}}\right) = - \infty i$$
More at x→2 from the left
$$\lim_{x \to 2^+}\left(\frac{x}{\sqrt{16 - x^{4}}}\right) = - \infty i$$
$$\lim_{x \to \infty}\left(\frac{x}{\sqrt{16 - x^{4}}}\right) = 0$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{x}{\sqrt{16 - x^{4}}}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x}{\sqrt{16 - x^{4}}}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x}{\sqrt{16 - x^{4}}}\right) = \frac{\sqrt{15}}{15}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x}{\sqrt{16 - x^{4}}}\right) = \frac{\sqrt{15}}{15}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x}{\sqrt{16 - x^{4}}}\right) = 0$$
More at x→-oo
Numerical answer [src] 
(0.0 - 38.8352886740698j)
(0.0 - 38.8352886740698j)
The graph
Limit of the function x/sqrt(16-x^4)
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