Question

Find the indicated limit, if it exists.

limit of f of x as x approaches 5 where f of x equals 5 minus x when x is less than 5, 8 when x equals 5, and x plus 3 when x is greater than 5

0
8
3
The limit does not exist.

Answer 1

@Nerdgirl

Answer 2

can you help me with this one too?

Answer 3

Hit me.

Answer 4

I'll certainly do my best.

Answer 5

thank you

Answer 6

You're welcome. What's the question?

Answer 7

i need to find the limit for the equation

Answer 8

lim f(x), f(x)= x-5 x<5
8 x=5
x+3 x>5

Answer 9

thats the equation

Answer 10

my teacher gave us notes on this, but i didn't understand the lesson very well

Answer 11

\[f(x)=\left\{\begin{array}{ll} 5-x & ,x<5 \\ 8 &, x=5 \\x+3 &,x>5 \end{array}\right.\]

Answer 12

yes thank you @Zarkon

Answer 13

hmm right \(\large { lim_{x\to 5}\ f(x)
\begin{cases}
5-x&x<5\\
8&x=5\\
x+3&x>5
\end{cases} }\)

Answer 14

yup

Answer 15

well... the issue is a matter of continuity
notice the 1st equation, the one on the "left side" of 5, what's its limit?
notice the 2nd, is just 8, so is a fixed value
notice the 3rd one, what's its limit

we know that when x = 5, f(x) = 8

so for the continuity to be maintained, the other 2 fellows, to the left and right side of 5
should give 8 also, so the line is continuous
and if it's so, then the "double-sided limit" does exist

Answer 16

so it doesn't exceed the limit?

Answer 17

Correct.

Answer 18

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yeap

Answer 19

@jdoe0001

Answer 20

but yes... the x+ 3 will give a limit of (5)+3 = 8
the 5-x will give a limit of 5-(5) = 0

those 2 fellows, the right-hand-side equation and the left-hand-side equation
do not meet at 8, thus the double-sided limit doesn't exist

Answer 21

ok thank you

Answer 22

yw