Question

Given the following function:
f(x) = { |3+x|/3+x if x < -3
x + K if -3 4

Determine the lim x-> 4+ f(x)

I am not sure how to approach this problem.

Answer 1

\[\lim_{x \rightarrow 4^+}f(x)=\lim_{x \rightarrow 4^+}(\frac{\sqrt{x}-2}{x-4})\]

Answer 2

you can factor the bottom

Answer 3

\[x-4=(\sqrt{x}-2)(\sqrt{x}+2)\]

Answer 4

any questions?
I looked at the part of function where x>4 because we wanted to look to the right of 4

Answer 5

so we would get 1/4 as a result?

Answer 6

yes \[\lim_{x \rightarrow 4}\frac{\sqrt{x}-2}{(\sqrt{x}-2)(\sqrt{x}+2)}=\lim_{x \rightarrow 4} \frac{1}{ \sqrt{x}+2}\]

Answer 7

1/(2+2) is 1/4

Answer 8

wow! thanks so much, this makes way more sense now.

Answer 9

great

Answer 10

Great profile picture! @Zarkon

Answer 11

lim f(x)

Answer 12

same answer as my prof wrote on the exam.. just didn't understand how he got it!

Answer 13

@No-data ty