Q.Given that $7x\le f(x)\le 3x^2-6$ for all $x$. Determine the value of $\displaystyle\lim_{x\to 3}f(x)$

If a function g is trapped between two other functions f and h for every x near a point a — meaning f(x) is always less than or equal to g(x), which is always less than or equal to h(x) — and if both of the bounding functions f and h converge to the very same limiting value L as x approaches a, then the trapped function g has no choice but to converge to that same value L as well; it cannot wander below f's limit or above h's limit, so it is squeezed to exactly L. This theorem is the key tool whenever a function is hard to …