Evaluate 3x^2-1 when x=2
2 answers:
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Answer:
Cos x = 1 - +
-
+ ...
Step-by-step explanation:
We use Taylor series expansion to answer this question.
We have to find the expansion of cos x at x = 0
f(x) = cos x, f'(x) = -sin x, f''(x) = -cos x, f'''(x) = sin x, f''''(x) = cos x
Now we evaluate them at x = 0.
f(0) = 1, f'(0) = 0, f''(0) = -1, f'''(0) = 0, f''''(0) = 1
Now, by Taylor series expansion we have
f(x) = f(a) + f'(a)(x-a) + +
+
+ ...
Putting a = 0 and all the values from above in the expansion, we get,
Cos x = 1 - +
-
+ ...
Answer:
2/5
Step-by-step explanation:
Given Marcellus drank 1/4 gallon of the limeade and Marcy drank 1/8 gallon of the limeade
Given that only 5/8 portion of the pitcher contains limeade
Total amount drunk = amount drunk by Marcellus + amount drunk by Marcy
Total amount drunk = =
The amount of Limeade remained = The amount initially - the amount drunk
The amount remained = =
Fractional part = amount remained / amount initially = =