Find the indicated limit, if it exists. (2 points) limit of f of x as x approaches 2 where f of x equals x plus 3 when x is less than 2 and f of x equals 3 minus x when x is greater than or equal to 2.

1. the limit does not exist.

2. 1

3. 2

4. 5

carrieaj08   ·   10.01.2020 10:31
ANSWER(S)
answered: nicky123415
27.06.2019 11:40

answer: you need the equation in the question so i can answer it

step-by-step explanation:

26.06.2019 17:30

the answer is 10.

step-by-step explanation:

12 + ( n / 2 ) - 4

12 + ( 4 / 2 ) - 4

12 + 2 - 4

14 - 4

10

answered: Dracopaul03
25.06.2019 23:00

ruth is 6 years old

step-by-step explanation:

6 + 24 = 30,   so 6/30 = .2  

if you do 1/5 it also equals .2, so that is the answer.

03.08.2020 23:06

The correct option is 1.

Step-by-step explanation:

The given function is

f(x)=\begin{cases}x+3 & \text{ if } x

We need to find the lim_{x\rightarrow 2}f(x).

The limit of a function exist if the left hand limit is equal to the right hand limit.

L=lim_{x\rightarrow a^-}f(x)=lim_{x\rightarrow a^+}f(x)

Left hand limit:

LHL=lim_{x\rightarrow 2^-}f(x)

LHL=lim_{x\rightarrow 2^-}x+3

Apply limit.

LHL=2+3=5

Right hand limit:

RHL=lim_{x\rightarrow 2^+}f(x)

RHL=lim_{x\rightarrow 2^+}3-x

Apply limit.

RHL=3-2=1

5\neq 1

Since LHL≠RHL, therefore the limit does not exist. Option 1 is correct.

answered: cindyc1103
03.08.2020 23:06

Option 1.

The limit does not exist.

Step-by-step explanation:

The function is  

f(x) = \left \{{{x+3\ \ \ if\ \ \ x

We seek to find

\lim_{x \to 2}f(x)

Then we must find the limits on the right of 2 (2 ^+) and on the left of 2 (2 ^ -)

If both limits exist and are equal then the \lim_{x \to 2}f(x) exists, if both limits are different or do not exist then the \lim_{x \to 2}f(x) does not exist.  

Limit on the left of 2

\lim_{x \to 2^-}x+3 = (2) +3 =5\\\\ \lim_{x \to 2^-}x+3 =5

Limit on the rigth of 2

\lim_{x \to 2^+}3-x = 3-(2) = 1\\\\ \lim_{x \to 2^+}3-x =1

Note that both limits give different results. The limit of f(x) when x tends to 2 on the left is equal to 5, and the limit of f(x) when x tends to 2 on the rigth is equal to 1.

Then the \lim_{x \to 2}f(x) does not exist.

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