1. ## Limits Help

1.) lim as x--> infinity (x - cube root of x)

2.) lim as x-->0+ ln(2x)

Anyone know how to solve these limit equations? Thanks.

2. Originally Posted by sleepiiee
1.) lim as x--> infinity (x - cube root of x)

2.) lim as x-->0+ ln(2x)

Anyone know how to solve these limit equations? Thanks.
1.) x gets bigger a lot faster than cube root of x .......

2.) Do you know what the graph of y = ln(2x) looks like .....?

3. $\displaystyle x - x^{\frac{1}{3}} = x^{\frac{1}{3}}(x^{\frac{2}{3}} - 1)$

$\displaystyle \lim_{x \to \infty} x^{\frac{1}{3}}(x^{\frac{2}{3}} - 1)$

$\displaystyle \lim_{x \to \infty} x^{\frac{1}{3}} \cdot \lim_{x \to \infty} (x^{\frac{2}{3}} - 1)$

finish up

$\displaystyle \lim_{x \to 0^+} \ln(2x)$

$\displaystyle \lim_{x \to 0^+} (\ln{x} + \ln{2})$

$\displaystyle \lim_{x \to 0^+} \ln{x} + \lim_{x \to 0^+} \ln{2}$

finish up

4. I got the first one thanks. Still don't understand what to do next with the 2nd problem

5. From the right hand side ln(2x) goes to negative infinity as it approaches 0