Answer:
The Taylor series of f(x) around the point a, can be written as:
Here we have:
f(x) = 4*cos(x)
a = 7*pi
then, let's calculate each part:
f(a) = 4*cos(7*pi) = -4
df/dx = -4*sin(x)
(df/dx)(a) = -4*sin(7*pi) = 0
(d^2f)/(dx^2) = -4*cos(x)
(d^2f)/(dx^2)(a) = -4*cos(7*pi) = 4
Here we already can see two things:
the odd derivatives will have a sin(x) function that is zero when evaluated in x = 7*pi, and we also can see that the sign will alternate between consecutive terms.
so we only will work with the even powers of the series:
f(x) = -4 + (1/2!)*4*(x - 7*pi)^2 - (1/4!)*4*(x - 7*pi)^4 + ....
So we can write it as:
f(x) = ∑fₙ
Such that the n-th term can written as:
Answer: 8 hrs and 3/4 of an hour (three quarters)
Step-by-step explanation:
the same logic such as a quarter of an hour
Step-by-step explanation:
Derivation using Product rule : -
To find the derivative of f(x) = sin 2x by the product rule, we have to express sin 2x as the product of two functions. Using the double angle formula of sin, sin 2x = 2 sin x cos x. Let us assume that u = 2 sin x and v = cos x. Then u' = 2 cos x and v' = -sin x. By product rule,
f '(x) = uv' + vu'
= (2 sin x) (- sin x) + (cos x) (2 cos x)
= 2 (cos2x - sin2x)
= 2 cos 2x
This is because, by the double angle formula of cos, cos 2x = cos2x - sin2x.
Thus, derivation of sin 2x has been found by using the product rule.
Answer: t= -0.799
This can also be written as t= -0.8
How to do it :
4.74t+ 5 = 13.5t + 12
first, subtract 4.74t from both sides
5= 8.76t + 12
next, subtract 12 from each side
-7 = 8.76t
next, divide 8.76 from each sides
-0.799 = t
Answer:
Select the one which meets the following characteristics.
Step-by-step explanation:
y = cos(2x)
Characteristics:
Mean line at y = 0
Amplitude = 1
Period = 360/2 = 180° or pi radians
i.e one complete cos cycle is 0 to 180, next is 180 to 360 and so on
Range : from -1 to 1
