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# Find Infinite limit (Rational Function) underset (x->5^+)(lim)(1/x^(4/3)-1/(x-5)^(4/3))

Question
Rational functions
asked 2020-11-03
Find Infinite limit (Rational Function)
underset $$(x->5^+)(lim)(1/x^(4/3)-1/(x-5)^(4/3))$$

## Answers (1)

2020-11-04
Given:
underset $$(x->5^+)(lim)(1/x^(4/3)-1/(x-5)^(4/3))$$
It is known that
underset $$(x->a)(lim)[f(x)+-g(x)]=underset(x->a)(lim)f(x)+-underset (x->a)(lim)g(x)$$
Then above can be written as
$$=underset(x->5+)(lim)(1/x^(4/3))-underset(x->5+)(lim)(1/(x-5)^4/3)$$
Plug Limits
$$(1/5^4/3)-(oo)(since,(x-5)^(4/3)>0)$$
$$-oo(since, c-oo=-oo)$$
Hence,
underset $$(x->5+)(lim)(1/x^(4/3)-1/(x-5)^4/3)=-oo$$

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