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x^(-3/4)
Limit of the function/ x^(-3/4)

Limit of the function x^(-3/4)

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The solution

You have entered [src] 
      1  
 lim ----
x->oo 3/4
     x
lim⁡x→∞1x34\lim_{x \to \infty} \frac{1}{x^{\frac{3}{4}}} 
Limit(x^(-3/4), x, oo, dir='-')
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
02468-8-6-4-2-1010010
Plot the graph
Rapid solution [src] 
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Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→∞1x34=0\lim_{x \to \infty} \frac{1}{x^{\frac{3}{4}}} = 0
lim⁡x→0−1x34=−∞−14\lim_{x \to 0^-} \frac{1}{x^{\frac{3}{4}}} = - \infty \sqrt[4]{-1}
More at x→0 from the left
lim⁡x→0+1x34=∞\lim_{x \to 0^+} \frac{1}{x^{\frac{3}{4}}} = \infty
More at x→0 from the right
lim⁡x→1−1x34=1\lim_{x \to 1^-} \frac{1}{x^{\frac{3}{4}}} = 1
More at x→1 from the left
lim⁡x→1+1x34=1\lim_{x \to 1^+} \frac{1}{x^{\frac{3}{4}}} = 1
More at x→1 from the right
lim⁡x→−∞1x34=0\lim_{x \to -\infty} \frac{1}{x^{\frac{3}{4}}} = 0
More at x→-oo
The graph
Limit of the function x^(-3/4)
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