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x+4/x^2
Limit of the function/ x+4/x^2

Limit of the function x+4/x^2

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     /    4 \
 lim |x + --|
x->0+|     2|
     \    x /
lim⁡x→0+(x+4x2)\lim_{x \to 0^+}\left(x + \frac{4}{x^{2}}\right) 
Limit(x + 4/x^2, 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
02468-8-6-4-2-1010-100000100000
Plot the graph
Other limits x→0, -oo, +oo, 1
lim⁡x→0−(x+4x2)=∞\lim_{x \to 0^-}\left(x + \frac{4}{x^{2}}\right) = \infty
More at x→0 from the left
lim⁡x→0+(x+4x2)=∞\lim_{x \to 0^+}\left(x + \frac{4}{x^{2}}\right) = \infty
lim⁡x→∞(x+4x2)=∞\lim_{x \to \infty}\left(x + \frac{4}{x^{2}}\right) = \infty
More at x→oo
lim⁡x→1−(x+4x2)=5\lim_{x \to 1^-}\left(x + \frac{4}{x^{2}}\right) = 5
More at x→1 from the left
lim⁡x→1+(x+4x2)=5\lim_{x \to 1^+}\left(x + \frac{4}{x^{2}}\right) = 5
More at x→1 from the right
lim⁡x→−∞(x+4x2)=−∞\lim_{x \to -\infty}\left(x + \frac{4}{x^{2}}\right) = -\infty
More at x→-oo
Rapid solution [src] 
oo
∞\infty
Expand and simplify
One‐sided limits [src] 
     /    4 \
 lim |x + --|
x->0+|     2|
     \    x /
lim⁡x→0+(x+4x2)\lim_{x \to 0^+}\left(x + \frac{4}{x^{2}}\right) 
oo
∞\infty 
= 91204.0066225166
     /    4 \
 lim |x + --|
x->0-|     2|
     \    x /
lim⁡x→0−(x+4x2)\lim_{x \to 0^-}\left(x + \frac{4}{x^{2}}\right) 
oo
∞\infty 
= 91203.9933774834
= 91203.9933774834
Numerical answer [src] 
91204.0066225166
91204.0066225166
The graph
Limit of the function x+4/x^2
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