A differentiable function f has the property that f(x + y) = f(x) + f(y) 1 − f(x)f(y) holds for all x, y in the domain of f. It
is known also that lim x→ 0 f(x) = 0, lim x →0 f(x) x = 5. (i) Use the definition of the derivative of f to determine f ′ (x) in terms of f(x).
1 answer:
Answer:
f'(x) = 5[1 + f²(x)]
Step-by-step explanation:
By definition, f'(x) = lim h => 0 {[f(x + h) - f(x)]/h}
This was used, together with the given limits:
lim x => 0 f(x) = 0
lim x => 0 f(x)/x = 5,
to determine the derivative of the given function:
f(x + y) = [f(x) + f(y)]/[1 - f(x)f(y)].
The workings are shown in the attachments.
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Answer:
B. $840
Step-by-step explanation:
Given that
Rate of simple interest = 3.5%
Principal amount = $12,000
Time = 2 year
To find:
Interest earned = ?
Solution:
Formula for Simple Interest is given as:
Where P is the principal amount
R is the annual Rate of interest
T is the time for which principal was invested.
Here, we are given that:
P = $12,000
R = 3.5%
T = 2 years
Putting all the values in the formula:
So, answer is:
B. $840