## anonymous 4 years ago hey guys i need help solving this limit problem, i know the answer is .25 but i dont know how to show that algebraically i will upload the equation

1. anonymous

2. anonymous

oh and i cant use hospitals rule

3. Zarkon

multiply top and bottom by $\sqrt{4+x^5}+2$

4. anonymous

are you sure it is +x^5?

5. Zarkon

yes

6. Zarkon

the only sign change you need in the one in front of the 2

7. Zarkon

from - to +

8. anonymous

well that leaves me with 0/0 which is indeterminate form which is bad

9. Zarkon

$(\sqrt{4+x^5}-2)(\sqrt{4+x^5}+2)=4+x^5-4=x^5$ then cancel the $$x^5$$ that is in the numerator and the denominator

10. Zarkon

then take limit

11. Zarkon

$\lim_{x\to 0}\frac{\sqrt{4+x^5}-2}{x^5}$ $\lim_{x\to 0}\frac{\sqrt{4+x^5}-2}{x^5}\frac{\sqrt{4+x^5}+2}{\sqrt{4+x^5}+2}$ $\lim_{x\to 0}\frac{x^5}{x^5(\sqrt{4+x^5}+2)}$ $\lim_{x\to 0}\frac{1}{\sqrt{4+x^5}+2}$ $\lim_{x\to 0}\frac{1}{\sqrt{4}+2}=\frac{1}{4}$

12. anonymous

oh ok makes i see now thanks