Question

use \(\lim_{x \rightarrow 0}f(x)=3 \) and (\lim_{x \rightarrow 0}g(x)=\frac{2}{3} \) to solve the following:

\[\large a. \lim_{x \rightarrow 0}[4f(x)] \]\[\large b. \lim_{x \rightarrow 0}f(x)g(x)\]\[large c. \lim_{x \rightarrow 0}[g(x)]^2 \]

Answer 1

\[\large b. \lim_{x \rightarrow 0} [f(x)g(x)] \]\[\large \ c. \lim_{x \rightarrow 0}[g(x)]^2 \]

Answer 2

:)

Answer 3

12
2
4/9

Answer 4

Just use basic limit properties :)
For a constant c,
\[\lim_{x \rightarrow a} c(f) = c \lim_{x \rightarrow a} (f)\]\[\lim_{x \rightarrow a} f(x) g(x) = \lim_{x \rightarrow a} f(x) \times \lim_{x \rightarrow a} g(x)\]

Answer 5

the second parameter is \[\lim_{x \rightarrow 0}g(x)=\frac{2}{3} \]

Answer 6

For the first one, I meant \[\lim_{x \rightarrow a} c f (x) = c \lim_{x \rightarrow a} f (x)\]

Answer 7

btw this question is from Anna so please explain it to her understanding lol... it was only posted by me cos attachments wasn't possible... apparently it's a bug :P she's taking pre calculus so fairly new to the subject :)

Answer 8

:-D

Answer 9

nah,guys Im fine))) just give me answers:)

Answer 10

It's better that you understand the concepts though =)

Answer 11

Anna we don't feed answers here :) u need to understand, that's the fundamental purpose for this site... to help :) that would make as homework machines but that shouldn't be... try to understand it yourself :)

Answer 12

ok

Answer 13

For the first one,\[\large a. \lim_{x \rightarrow 0}[4f(x)]\]four is just a constant, so we can put it outside the limit\[4 \lim_{x \rightarrow 0}f(x)\] You are already given that \[\lim_{x \rightarrow 0}f(x) = 3\] so plug that in.\[4 \lim_{x \rightarrow 0}f(x) = 4 * 3 = 12\]

Answer 14

I will be typing 2 more of her questions as new questions and after those i believe she should be able to handle the rest :)

Answer 15

For the second,\[\lim_{x \rightarrow 0} [f(x)g(x)] = \lim_{x \rightarrow 0} f(x) \times \lim_{x \rightarrow 0} g(x) = 3 * \frac {2}{3}\]

Answer 16

For the third, just use the same rule for # 2. split up (g(x))^2 into g(x) * g(x).

Answer 17

ok