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:
yes
Step-by-step explanation:
because area of sphere equals =
so if we doubled the radius the surface area will be doubled
( y1 - y2 ) / ( x1 - x2 )
In this case, I calculated it to be 12/10, or 6/5
Next, we choose a point to use in our formula. I'll use point E since it does not have any negative signs.
The final slope-intercept equation is then:
y - 8 = 6/5 * ( x - 4 )
Each person received 3 doughnuts, do 6 times 4 which is 24 and divide that among 8, its 3
Answer:
Step-by-step explanation:
The given expression is
The tangent of -1 is defined, it's around -0.02.
The tangent is a trigonometric function with a period of 
, where each period is separated by a vertical asymptote which indicates that the function is not determined through all its domain, that's what the question refers to when it says "if is undefined, enter undefined".
However, at 
, the tangent is determined, that means, there's no asymptote on that coordinate, that's why it has a "determined value", which is -0.02 approximately.
