Question

Please help with limits? Desperate!! x-->-1.

-2 when x
13 years ago

Answer 1

Here are the options!

Answer 2

a) lim f(x), x-->-1 from LEFT
b)lim f(x), x-->-1 from RIGHT
c) lim f(x), x--> 1

Answer 3

d)lim f(x), x--> 0 from LEFT
e) lim f(x), x-->0 from RIGHT
f) lim f(x), x--> 0

You have to find them for each of the above prob. PLEASE!!!

Answer 4

\[f(x) = \begin{cases}
-2 & \text{ if } x \le -1 \\
x-1 & \text{ if } -1 <x<0 \\
0 & \text{ if } 0 \le x \le 3
\end{cases}\] Limit of f(x) at x = a exists if and only if the limit of f(x) as x approaches a from the left = the limit of f(x) as x approaches a from the right.

(a) x --> -1 from left.
This means x < -1 and is approaching the value of -1. Given the definition of f(x), it is easy to see that for any x < -1, f(x) = -2
So, limit of f(x) as x-->-1 from Left = -2

(b) x--> -1 from right.
This means x > -1 and is approaching -1. For x > -1 (and small variations) the corresponding value of f(x) is x-1. So the limit as x --> -1 would be (-1) -1 = -2
So, limit of f(x) as x --> -1 from Right = -2

(c) Since the limit from the left = limit from the right,
limit of f(x) as x --> -1 = -2

Can you try (d),(e),(f) along similar lines?

Answer 5

I have been trying foreverrrr! Do u mind doing them @FoolAroundMath please?

Answer 6

I just need d, e, and f!

Answer 7

(d) Limit of f(x) at x --> 0 from LEFT.
This means that x is smaller than zero but quite close to zero.
x definitely is between -1 and 0 in this case, so the corresponding value of f(x) would be x-1
So, the limit in this case would be 0 -1 = -1

(e) Limit of f(x) at x--> 0 from RIGHT
This means that x > 0 but quite closeby (say for example 0.0001). x, in this case lies between 0 and 3 , thus the corresponding value of f(x) is 0.
Hence the limit is 0 as well

(f) Limit of f(x) at x = 0 from left = -1, from right = 0
As these two limits are not equal, limit of f(x) at x = 0 does not exist.