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Question
Evaluate the following:
`lim_(x->a) (x^(5/8) - a^(5/8))/(x^(2/3) - a^(2/3))`
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Solution
`lim_(x->a) (x^(5/8) - a^(5/8))/(x^(2/3) - a^(2/3))`
`["Divide both numerator and denominator by x – a"; lim_(x->a) (x^n - a^n)/(x - a) = na^n]`
= `(lim_(x->a)(x^(5/8)-a^(5/8))/(x-a))/(lim_(x->a)(x^(2/3)-a^(2/3))/(x-a))`
`= (5/8 a^(5/8 - 1))/(2/3 a^(2/3 - 1))`
`= 5/8 xx 3/2 xx ("a"^((-3)/8))/("a"^((-1)/3))`
`= 15/16 xx "a"^(-1/24)`
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