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azatkgz
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Homework Statement
Find all values of the parameter a>0 such that the function
[tex]f(x)=\left\{\begin{array}{cc}\frac{a^x+a^{-x}-2}{x^2},x>0\\3ln(a-x)-2,x\leq0\end{array}\right[/tex]
The Attempt at a Solution
[tex]\lim_{x\rightarrow 0}\frac{a^x+a^{-x}-2}{x^2}=0[/tex]
[tex]0=3ln(a-0)-2\rightarrow a=e^{2/3}[/tex]