# Few calc limit questions need help!

1. Oct 11, 2012

### venom2121

few calc limit questions!! need help!

1. The problem statement, all variables and given/known data

limit x-> -1 of cubed rt (3x-5/25x-2)

i think the answer is 2/3 but i cant work it up

lim x->0 √(3x+2) - √2
x

r(x)= |3x| A) lim x->0 of r(x) question 2 B) r(0)
x

3. The attempt at a solution

2. Oct 11, 2012

### venom2121

Re: few calc limit questions!! need help!

these werent formatted right. the middle one the x is underneath the top term as well as for the absolute (|3x|)/x

also, i tried to multiply the middle one by its conjugate √(3x+2) - √2

i wind up getting (3x)/(x (√(3x+2) - √2) ) i think thats the right track but im not sure

3. Oct 11, 2012

### tiny-tim

welcome to pf!

hi venom2121! welcome to pf!

(btw, never reply to your own first post , use the EDIT button instead … then you'll stay on the No-replies list! )
but it isn't 0/0, so what's the difficulty?

just put x = -1 !
use a binomial expansion (and √(3x+2) = √x√(3 + 2/x))
try drawing a graph

4. Oct 11, 2012

### venom2121

Re: few calc limit questions!! need help!

the cubed rt problem the answer is supposed to be 2/3 DERP ok had a brain fart haha got that now..

im still confused about the binomial expansion.

and as far as the absolute value one im not sure. i see that the y values max out at -3 and 3 and as it goes to zero the y values stay at 3 until zero. so is that the limit? would that mean that r(0)=0? also how would you figure this out without graphing?

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Last edited: Oct 11, 2012
5. Oct 11, 2012

### tiny-tim

can't you do the binomial expansion of (1 + x)1/2 ?
not following you
i wouldn't!

6. Oct 11, 2012

### Ray Vickson

Re: few calc limit questions!! need help!

Your "cube-root" problem, as written, is
$$\lim_{x \rightarrow -1} \sqrt[3]{\left( 3x - \frac{5}{25x} - 2\right)} = -\frac{\sqrt[3]{600}}{5},$$
but perhaps you meant
$$\lim_{x \rightarrow -1} \sqrt[3]{\left( \frac{3x-5}{25x - 2}\right)}.$$
In that case you should have used brackets, and written cube rt ((3x-5)/(25x-2)).

RGV