Evaluate the following limits algebraically:
lim x - 0 1/3+x - 1/3/x
lim x - infintity 7x^3 + 5x/(8x^9 + x^6 + 4)^ 1/3

Question

Evaluate the following limits algebraically: 
lim x -> 0 1/3+x - 1/3/x 
lim x -> infintity 7x^3 + 5x/(8x^9 + x^6 + 4)^ 1/3

mathmath333 · Answer

is it?

$\huge\tt \color{black}{\lim_{x\to0}\frac{1}{3+x}-\frac{1}{\frac{3}{x}}}$

anonymous · Answer

no i should have used parenthesis lim x -> (1/3+x - 1/3) / x

mathmath333 · Answer

$\large\tt \color{black}{\lim_{x\to0}\dfrac{\dfrac{1}{3+x}-\dfrac{1}{3}}{x}}$


$\large\tt \color{black}{\lim_{x\to0}\dfrac{1}{x}\times(\dfrac{1}{3+x}-\dfrac{1}{3})}$



$\large\tt \color{black}{\lim_{x\to0}\dfrac{1}{x}\times(\dfrac{3}{3(3+x)}-\dfrac{(x+3)}{3(x+3)})}$



$\large\tt \color{black}{\lim_{x\to0}\dfrac{1}{x}\times(\dfrac{3-x-3}{3(3+x)})}$



$\large\tt \color{black}{\lim_{x\to0}\dfrac{1}{x}\times\dfrac{-x}{3(3+x)}}$



$\large\tt \color{black}{\lim_{x\to0}\dfrac{-1}{3(3+x)}}$



$\large\tt \color{black}{=\dfrac{-1}{3(3+0)}}$


$\large\tt \color{black}{=\dfrac{-1}{9}}$

mathmath333 · Answer

this one is correct

anonymous · Answer

thank you so much!!

mathmath333 · Answer

yw