Step-by-step explanation:
The Taylor series expansion is:
Tₙ(x) = ∑ f⁽ⁿ⁾(a) (x − a)ⁿ / n!
f(x) = 1/x, a = 4, and n = 3.
First, find the derivatives.
f⁽⁰⁾(4) = 1/4
f⁽¹⁾(4) = -1/(4)² = -1/16
f⁽²⁾(4) = 2/(4)³ = 1/32
f⁽³⁾(4) = -6/(4)⁴ = -3/128
Therefore:
T₃(x) = 1/4 (x − 4)⁰ / 0! − 1/16 (x − 4)¹ / 1! + 1/32 (x − 4)² / 2! − 3/128 (x − 4)³ / 3!
T₃(x) = 1/4 − 1/16 (x − 4) + 1/64 (x − 4)² − 1/256 (x − 4)³
f(x) = 1/x has a vertical asymptote at x=0 and a horizontal asymptote at y=0. So we can eliminate the top left option. That leaves the other three options, where f(x) is the blue line.
Now we have to determine which green line is T₃(x). The simplest way is to notice that f(x) and T₃(x) intersect at x=4 (which makes sense, since T₃(x) is the Taylor series centered at x=4).
The bottom right graph is the only correct option.
Answer:
Yes, the student is correct
Step-by-step explanation:
Given
Required
Does it represent the x intercept
At the x intercept, the value of x is 0.
So, the function 
becomes 
can be compared to
Hence, the student is correct
It would be 384.58, or 384.57909
Answer:
525267262525226
Step-by-step explanation:
594944+757548484-848484%
Answer:
A and C
Step-by-step explanation:
Given
2cos²x - 2 = 0 ( add 2 to both sides )
2cos²x = 2 ( divide both sides by 2 )
cos²x = 1 ( take the square root of both sides )
cos x = ± 
= ± 1
cos x = 1 ⇒ x = 
(1) = 0°
cos x = - 1 ⇒ x = (- 1) = 180°
