MATHEMATICS HIGH SCHOOL

Find the indicated limit, if it exists. (2 points) 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

Answers

Answer 1

Answer:

It looks like we have

$f(x)=\begin{cases}5-x&\text{for }x<5\n8&\text{for }x=5\nx+3&\text{for }x>5\end{cases}$

and we want to find $\lim\limits_(x\to5)f(x)$ .

Since $x$ is approaching 5, we don't care about the value of $f(x)$ when $x=5$ .

We do care about how $f(x)$ behaves to either side of $x=5$ . If $x\to5$ from below, then $f(x)=5-x$ , so that

$\displaystyle\lim_(x\to5^-)f(x)=\lim_(x\to5)(5-x)=5-5=0$

On the other hand, if $x\to5$ from above, then $f(x)=x+3$ , so that

$\displaystyle\lim_(x\to5^+)f(x)=\lim_(x\to5)(x+3)=5+3=8$

The one-sided limits do not match, since 0 ≠ 8, so the limit does not exist.

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Does 4(x−8)+12=2(2x−9) have one solution, no solution, or infinitely many solutions?

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Answers

Answer: no solution

Step-by-step explanation:

The equation is given in the question is 4(x - 8) + 12 = 2(2x -9). Multiply x with 4 and 2 according to the equation. now, you can see this equation has no solution as the value of x cannot be determined.

A dry cleaner charges $5.00 to clean one item. He offers to clean a second item for $4.50, and a third for $4.00. If he continues to subtract $0.50 for each additional item, how much will it cost to clean six items? MARKING BRAINLEST IF HURRY

Answers

5+4.5+4+3.5+3+2.5 = 22.5

Answer:$2.50 to clean 6 items

Step-by-step explanation:

$5.00-0.5=$4.5= 2 items

$4.5-0.5=$4= 3 items

$4-0.5=$3.5= 4 items

$3.5-0.5=$3= 5 items

$3-0.5=$2.5= 6 items

Convert from feet to yards. 8,154feet=yards