Question

please help me on limits.

1.) lim x -> 2

sec(piex/6)

2.) Lim -> 0

[square root(2+x)- square root (2)]/ x

3.) lim -> 1

(lnx)/x

Answer 1

1) \(\large \lim_{x \rightarrow 2} sec(\frac{\pi x}{6}) = sec(\frac{2\pi}{6}) = sec(\frac{\pi}{3}) = \frac{1}{cos(\frac{\pi}{3})} =?\)

Answer 2

\[\large \lim_{x \rightarrow 0} \frac{\sqrt{2 + x} - \sqrt{2}}{x}\]

For this...have you learned L'Hospital yet?

Answer 3

for #2, you can multiply top and bottom by \(\LARGE \sqrt{2+x}+\sqrt{2}\) to rationalize the numerator

Answer 4

@johnweldon1993 no, I haven't.