What is 3 in a+ b- in C written as a single logarithmn?
1 answer:
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- First question:
Recall that and
for all
. So
For , we expect both
and
(i.e. the sine and cosine of any angle that lies in the first quadrant must be positive). By definition of absolute value,
if
.
So we have
making H the answer.
- Second question:
C is always true, because the inequality reduces to x > y.
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 - +
-
+ ...