# Science:Math Exam Resources/Courses/MATH100/December 2014/Question 10

MATH100 December 2014
Other MATH100 Exams

### Question 10

Let ${\displaystyle a}$ be a real number, and let

${\displaystyle f(x)=\left\{{\begin{array}{ll}x&\quad \mathrm {if} x\leq 0\\x^{a}\sin {\Bigl (}{\frac {1}{x}}{\Bigr )}&\quad \mathrm {if} x>0\end{array}}\right.}$

For what values ${\displaystyle a}$ is the function ${\displaystyle f(x)}$ continuous at ${\displaystyle x=0}$?