Answer to Question #194250 in Calculus for Maureen

Question

Evaluate the limits

Lim

X to 2

of

Xcube -8 over x-2

Answer 1

We need to calculate $\overset{lim}{(x\to2)}$ $\frac {(x^3-8)} {(x-2)}$

So here this is in $\frac 0 0$ form after putting 2 in place of x. So L-Hospital's rule is applicable here.

= $\overset {lim}{(x\to2)}$ $\frac {\frac {d} {dx} (x^3-8)} {\frac {d} {dx} (x-2)}$

=$\overset {lim} {x\to2} { ( \frac {3x^2} {1})}$ (As $\frac{d} {dx} (x^n)=n.x^{n-1} )$ & $(\frac {d} {dx} (constant)=0)$

= $\frac {3(2)^2} {1}$

=$3*4=12$ (Ans)