#### Zargawee

**[SOLVED] Small Limits Question**

Hi There,

I have this Simple Question In Limits :

If lim

_{x->3}(f(x) - 2) / (x - 3) = 7

Then lim

_{x->3}(x

^{2}f(x) - 18) / (x-3) = ??

I solved the question this way :

Since the denominator equals Zero , and limit exists , then the numerator equals zero .

[4]f(x) - 2 = 0 ---> f(x) = 2

lim

_{x->3}(x

^{2}f(x) - 18) / (x-3) =

lim

_{x->3}(2x

^{2}- 18) / (x-3) =

lim

_{x->3}2(x

^{2}- 9) / (x-3) =

lim

_{x->3}2(x-3) (x+3) / (x-3) =

lim

_{x->3}2(x+3) =

2 (3+3) = 12

But I also solved in this way :

lim

_{x->3}(x

^{2}f(x) - 18) / (x-3) =

lim

_{x->3}(x

^{2}f(x) - 2x

^{2}+ 2x

^{2}- 18) / (x-3)

lim

_{x->3}(x

^{2}f(x) + (2x

^{2}) /(x-3) - 2x

^{2}- 18) / (x-3)

lim

_{x->3}(x

^{2}) (f(x) + 2) /(x-3) - 2(x

^{2}- 9) / (x-3)

lim

_{x->3}(x

^{2}) (f(x) + 2) /(x-3) - 2(x

^{2}- 9) / (x-3)

lim

_{x->3}(x

^{2}) 7 - lim

_{x->3}2(x-3)(x+3) / (x-3)

lim

_{x->3}(x

^{2}) 7 - lim

_{x->3}2(x-3)(x+3) / (x-3)

3

^{2}* 7 + lim

_{x->3}(x+3)

(9 * 7) + (3 + 3) = 63 + 12 = 75

What's the wrong with the first One ?

Please help.