Science:Math Exam Resources/Courses/MATH100/December 2012/Question 06 (e)/Solution 1

As given in the original statement, the function has domain of all nonzero reals. The function itself is only not continuous at 0 so we check there for an asymptote.

The value

${\begin{aligned}\lim _{x\to 0^{+}}(2x^{3/5}+3x^{-2/5})=\infty \end{aligned}}$ since this function when we plug in values of x slightly bigger than 0, the first term tends to 0 and the second term tends to positive infinity.

Notice that the left hand limit is also positive infinity since the second term can be written as $\displaystyle 3x^{-2/5}={\frac {3}{\sqrt[{5}]{x^{2}}}}$ which is always positive.