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:
a= 12
b=-2
Step-by-step explanation:
12 x -2 = -24
12 - (-2) = 14
12 + (-2) = 10
After 3 hours, the faster car will be 75 miles ahead of the slower car.
Step-by-step explanation:
Given,
Speed of first car = 56 miles per hour
Speed of second car = 31 miles per hour
Let,
x be the number of hours.
Distance covered by first car = Speed * time = 56x
Distance covered by second car = 31x
According to given statement;
Difference between distance covered by both cars = 75 miles
Distance of faster car - Distance of slower car = 75 miles

Dividing both sides by 25

After 3 hours, the faster car will be 75 miles ahead of the slower car.
Keywords: subtraction, division
Learn more about subtraction at:
#LearnwithBrainly
4a + 6b = 10
2a - 4b = 12...multiply by -2
----------------
4a + 6b = 10
-4a + 8b = - 24 (result of multiplying by -2)
------------------add
14b = - 14
b = -14/14
b = -1
2a - 4b = 12
2a - 4(-1) = 12
2a + 4 = 12
2a = 12 - 4
2a = 8
a = 8/2
a = 4
so 12a = 12(4) = 48 <==
Answer:
option D 12 is correct..
in second question the student didn't multiply -3 with 4. that's the mistake he did.
hope it helps