Question

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

Answer 1

oh and i cant use hospitals rule

Answer 2

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

Answer 3

are you sure it is +x^5?

Answer 4

yes

Answer 5

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

Answer 6

from - to +

Answer 7

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

Answer 8

\[(\sqrt{4+x^5}-2)(\sqrt{4+x^5}+2)=4+x^5-4=x^5\]

then cancel the \(x^5\) that is in the numerator and the denominator

Answer 9

then take limit

Answer 10

\[\lim_{x\to 0}\frac{\sqrt{4+x^5}-2}{x^5}\]

\[\lim_{x\to 0}\frac{\sqrt{4+x^5}-2}{x^5}\frac{\sqrt{4+x^5}+2}{\sqrt{4+x^5}+2}\]

\[\lim_{x\to 0}\frac{x^5}{x^5(\sqrt{4+x^5}+2)}\]

\[\lim_{x\to 0}\frac{1}{\sqrt{4+x^5}+2}\]

\[\lim_{x\to 0}\frac{1}{\sqrt{4}+2}=\frac{1}{4}\]

Answer 11

oh ok makes i see now thanks