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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 ...
Answer: The expression will be
Step-by-step explanation: Frank has to pay $50 as the registration fee. This amount is compulsory to be paid
Step 1: Dues for $12 months
Let the due to be paid every month be $x, so dues to be paid for 12 months will be 12x
Step 2: Expression for the average monthly cost for x-month will be
Expression:
Total cost = 50 + 12x
Expression: