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 \((x->5+)(lim)(1/x^(4/3)-1/(x-5)^4/3)=-oo\)
0

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