Find a set of functions that approximate the delta function $\delta(x-a)$ with a sequence of isosceles triangles $\delta_{\epsilon}(x-a)$, centered at $a$, that get narrower and taller as the parameter $\epsilon$ approached zero.

Using the test function $f(x)=3x^2$, find the value of $$\int_{-\infty}^{\infty} f(x)\delta_{\epsilon}(x-a)\, dx$$ Then, show that the integral approaches $f(a)$ in the limit that $\epsilon \rightarrow 0$.