9514 1404 393
Answer:
c = -3; d = 5
Step-by-step explanation:
The function is differentiable if it is continuous and the derivative is continuous.
This function will be continuous if the limit as x approaches 3 from either side is the same. From the left, the limit is ...
5(3^2) +c = 45 +c
From the right, the limit is ...
d(3^2) -3 = 9d -3
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The derivative will be continuous if the limit as x approaches 3 from either side is the same. From the left, the limit is ...
f'(x) = 10x
= 10(3) = 30
From the right, the limit is ...
f'(x) = 2dx
= 2d(3) = 6d
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This gives us a pair of simultaneous equations in 'c' and 'd':
45 +c = 9d -3
6d = 30
The latter tells us d = 5. Then the former tells us ...
45 +c = 9(5) -3 ⇒ c = -3
The function is differentiable if c = -3 and d = 5.
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<em>Additional comment</em>
With these values, the function becomes ...
The area of a circle is:
A=πr^2, area=pi times the radius squared...
In this case the radius, r, is equal to 6mm so
A=π(6^2) mm^2
A=36π mm^2
So the area is 36π mm^2, where the units are square millimeters
You start with 5 baseball cards and purchase 10 cards every week until you have at most 45 cards.
10 cards every week = 10 w
Start with 5 baseball cards = + 5
At Most = ≥
that is an easy question, its 8.5