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1 answer:
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Option B: is the area of the compact disc.
Explanation:
The diameter of the compact disc is .
To determine the area of the compact disc, let us substitute the values in the area of the circle formula,
where
Substituting the value of d in , we get,
Thus, and
. Let us substitute these values in
, we get,
Simplifying, we have,
Multiplying, we get,
Thus, the area of the compact disc is
Hence, Option B is the correct answer.
Answer:
Step-by-step explanation:
As per the question,
let us consider f(x) = tan(x).
We know that <u>The Maclaurin series is given by:</u>
So, differentiate the given function 3 times in order to find f'(x), f''(x) and f'''(x).
Therefore,
f'(x) = sec²x
f''(x) = 2 × sec(x) × sec(x)tan(x)
= 2 × sec²(x) × tan(x)
f'''(x) = 2 × 2 sec²(x) tan(x) tan(x) + 2 sec²(x) × sec²(x)
= 4sec²(x) tan²(x) + 2sec⁴(x)
= 6 sec⁴x - 4 sec² x
We then substitute x with 0, and find the values
f(0) = tan 0 = 0
f'(0) = sec²0 = 1
f''(0) = 2 × sec²(0) × tan(0) = 0
f'''(0) = 6 sec⁴0- 4 sec² 0 = 2
By putting all the values in the Maclaurin series, we get
Therefore, the expansion of tan x at x = 0 is
.