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:
-1
Step-by-step explanation:
(0, 0) and (3, 3)
To find slope:
3-0/3-0 = 3/3 = 1
Since it's looking for the perpendicular slope, you just do the opposite of 1.
Which is -1.
Answer:
14 rides
Step-by-step explanation:
16 = 0.79x + 4.5
11.5 = 0.79x
x = 14.55 or 14
rounding down because it can't go over $16.
0.79(14) + 4.5 = $15.56
Answer:
8x+30=334
Step-by-step explanation:
X= the amount of cups he got and 30 is the initial fee so he only has to pay that once