find the limit

[spacewater]

Problem 1
lim ( when x is approaching 1 from the right \(\displaystyle f(x)\))
x->1+ f(x)
\(\displaystyle f(x) = \frac{\sqrt{2x+1}-\sqrt3}{x-1}\)
steps
\(\displaystyle f(x) = \frac{\sqrt{2x+1}-\sqrt3}{x-1} \cdot \frac {\sqrt{2x+1}+\sqrt3}{\sqrt{2x+1}+\sqrt3}\)
\(\displaystyle f(x) = \frac{2x+1-3}{(x-1)\sqrt{2x+1}+\sqrt3}\)
\(\displaystyle f(x) = \frac{2}{\sqrt{2x+1}+\sqrt3}\)

now I sub. 1+ to x and got
\(\displaystyle f(x) = \frac {2}{\sqrt3+\sqrt3}\)
\(\displaystyle f(x) = \frac {2}{\sqrt6} \cdot \frac{\sqrt6}{\sqrt6}\)
\(\displaystyle f(x) = \frac {2\sqrt6}{6} = \frac {\sqrt6}{3}\) for the final answer but the answer is different than what I have... can someone point out where I went wrong?

problem 2
\(\displaystyle f(x) = \frac{1-3\sqrt{x}}{x-1}\) (1 minus cuberoot of x over x minus 1)
I cant figure out how to form a^3 - b^3 for this problem...
(1 - ??)(1 + ?? + ??)

 

[BigGlenntheHeavy]

\(\displaystyle 1) \ \frac{2}{\sqrt3+\sqrt3} \ = \ \frac{2}{2\sqrt3} \ = \ \frac{1}{\sqrt3} \ = \ \frac{\sqrt3}{3}\)

\(\displaystyle Your \ algebra \ was \ wrong.\)

 

[spacewater]

Ah I c Thank you

can anybody give me a hint on problem 2?

 

[BigGlenntheHeavy]

\(\displaystyle Problem \ 2; \ The \ Marqui \ can, \ assuming \ you \ are \ finding \ the \ limit \ as \ x \ approaches \ 1.\)

\(\displaystyle Is \ this \ right? \ \lim_{x\to1}\frac{1-x^{1/3}}{x-1}\)

 

[spacewater]

yes, What do you mean by Marqui?

(1-x^1/???)(1+ab+b^2)
I still dont have a clue how to breakdown the fraction exponent?
whats the code for lim x->1 ?

 

[BigGlenntheHeavy]

\(\displaystyle Verily, \ you \ have \ no \ inkling \ of \ The \ Marqui \ Guillaume \ Francois \ Antoine \ De \ L'Hopital?\)