Question

Evaluate the limit:
limx→∞ (4x+5)/3

Answer 1

What do you get?

Answer 2

@geerky42 I honestly have no idea since there is no x on the bottom

Answer 3

What happened to the value of \(\dfrac{4x+5}{3}\) as x getting bigger and bigger?

Answer 4

@geerky42 is it moving closer to 0?

Answer 5

really? What made you think that?

Answer 6

hard to explain. Am I wrong? What's right? is it moving away from 0?

Answer 7

\(x→∞\) basically mean x getting closer and closer to infinity.

So we have \(\displaystyle \lim_{x→∞}\dfrac{4x+5}{3}\), which mean the value of \(\dfrac{4x+5}{3}\) as x approaches to \(\infty\)

Answer 8

say x is start at 0. f(x) is 5/3, right?

at x=1, f(x) = 9/3 = 3
at x=2, f(x) = 13/3
at x=3, f(x) = 17/3

Note how numerator grows?

Answer 9

Correct go on

Answer 10

ok, what happen to f(x) when x is becoming infinity?

Answer 11

if we keeping going on:

x=5, ...
x=6, ...
\(\vdots\)

Answer 12

it becomes infinity?

Answer 13

Gotcha

Answer 14

So \(\displaystyle \lim_{x\rightarrow \infty}\dfrac{4x+5}{3} = \infty\)

Answer 15

thank you very much!!!

Answer 16

welcome