limit x-> -1 of cubed rt (3x-5/25x-2)
not sure how to go about this at all
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
limit x-> -1 of cubed rt (3x-5/25x-2)
not sure how to go about this at all
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
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
The first one you can just plug in -1 for x:
$\displaystyle \lim_{x \rightarrow -1} \sqrt[3]{ \frac{3x-5}{25x-2}}=\sqrt[3]{ \frac{3(-1)-5}{25(-1)-2}}$
The second one you were almost there:
$\displaystyle \lim_{x \rightarrow 0} \frac {\sqrt{3x+2} - \sqrt{2}}{x}=\lim_{x \rightarrow 0} \frac {(\sqrt{3x+2} - \sqrt{2})(\sqrt{3x+2} + \sqrt{2})}{x(\sqrt{3x+2} + \sqrt{2})}=\lim_{x \rightarrow 0} \frac{3x}{x(\sqrt{3x+2} + \sqrt{2})}$
So....... can it be simplified any further?
For the third one, you look at the limit as x approaches 0 from the right and from the left. If they're the same, that's the limit, and if they're different, the limit doesn't exist. So what is |3x| in terms of x when x<0 and what is it when x>0? Remember x is negative in the x<0 case.
$\displaystyle \lim_{x \rightarrow 0}\frac{|3x|}{x}$
Of course r(0) is undefined.
- Hollywood