Answer:

Step-by-step explanation:
So we have the function:

And we want to find the derivative using the limit process.
The definition of a derivative as a limit is:

Therefore, our derivative would be:

First of all, let's factor out a 4 from the numerator and place it in front of our limit:

Place the 4 in front:

Now, let's multiply everything by (√(x+h)(√(x))) to get rid of the fractions in the denominator. Therefore:

Distribute:

Simplify: For the first term on the left, the √(x+h) cancels. For the term on the right, the (√(x)) cancel. Thus:

Now, multiply both sides by the conjugate of the numerator. In other words, multiply by (√x + √(x+h)). Thus:

The numerator will use the difference of two squares. Thus:

Simplify the numerator:

Both the numerator and denominator have a h. Cancel them:

Now, substitute 0 for h. So:

Simplify:

(√x)(√x) is just x. (√x)+(√x) is just 2(√x). Therefore:

Multiply across:

Reduce. Change √x to x^(1/2). So:

Add the exponents:

And we're done!

Answer:
18 jars can be filled completely.
Step-by-step explanation:
7L=7000ml
1 jar contain 375 ml
375ml can be filled in 1 jar
375ml=1 jar
1 ml = 1/375 jar
7000 ml = 7000× 1/375 jar
7000ml= 18.67 jar
hence 18 jars can be filled completely.
Answer:
89 seats are not being used
Step-by-step explanation:
You subtract the seats being used by teachers
342 - 75 =267
Change 2/3 into a percentage = 66.6%
Find 66.6% of 267= 177.8 (I rounded up to 178)
Then subtract 177.8/178 from 267 to find the amount of seats not being used.
The amount of seats not being used would come down to 89 seats.
I hope this helps!
9514 1404 393
Answer:
r = ±√47
Step-by-step explanation:
-7r^2 = -329 . . . . given
r^2 = 47 . . . . . divide both sides by -7 (multiplication property of equality)
r = ±√47 . . . . square root both sides (square root property of equality)