Question

help on a limit problem?

Answer 1

\[\lim \rightarrow \infty \cos ( \frac{ 5x }{ x^2+7 } +\frac{ \pi }{ 3 })\]

Answer 2

do you know the following equals:
\[\lim_{x \rightarrow \infty} \frac{5x}{x^2-7}\]

Answer 3

and whatever -7 or +7
either way this limit is?

Answer 4

is the limit to that 0??

Answer 5

yes the particular limit I asked about is 0
\[\lim_{x \rightarrow \infty}\cos(\frac{5x}{x^2+7}+\frac{\pi}{3} ) \\ =\lim_{u \rightarrow 0}\cos(u+\frac{\pi}{3})\]

Answer 6

do you know how to evaluate your limit now?

Answer 7

so is that 1?

Answer 8

well you can find that limit by direct substitution now

Answer 9

cos(0+pi/3)
is that 1?

Answer 10

no thats 1/2 ...

Answer 11

yep :)

Answer 12

wow thank you so much!

Answer 13

np