Limits part 1?

**homeylova223** · June 26th 2011, 05:45 PM

Can anyone help me with these two limit without using l hospital rule which I do not know.

1. As x approaches zero

(x+2)^2-4/(x)

2. As x approaches -2

(x^3+8)/(x^2-4) This is what I did

x(x^2+8)/(x+2)(x-2) Can anyone help me continue.

**pickslides** · June 26th 2011, 05:47 PM

Originally Posted by homeylova223

Can anyone help me with these two limit without using l hospital rule which I do not know.

1. As x approaches zero

(x+2)^2-4/(x)

$\displaystyle \lim_{x\to 0} \frac{(x+2)^2-4}{x}$ or $\displaystyle \lim_{x\to 0} (x+2)^2-\frac{4}{x}$ ?

**pickslides** · June 26th 2011, 05:51 PM

Originally Posted by homeylova223

x(x^2+8)/(x+2)(x-2) Can anyone help me continue.

$\displaystyle x^3+8 \neq x(x^2+8)$ , do you know why?

Consider $\displaystyle a^3+b^3 = (a+b)(a^2-ab+b^2)$

**homeylova223** · June 26th 2011, 05:55 PM

Yes I see but how would I proceed?

**skeeter** · June 26th 2011, 06:07 PM

Originally Posted by homeylova223

Yes I see but how would I proceed?

factor $x^3+8$ correctly, then cancel the common factor in the numerator and denominator ... finally, sub in x = -2

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