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:
The 70 represents the number of people waiting to by tickets at the exactly moment when the ticket booth is opened.
Step-by-step explanation:
The 70 represents the number of people waiting to by tickets at the exactly moment when the ticket booth is opened.
You can see this by setting the x value to 0, it is, in the precise moment when the booth opened (as x cant be negative, because there is no negative time, you could also think of 70 as the number of people waiting before the booth opens).
Lateral Surface Area of a square pyramid (4 isosceles triangles): For the isosceles triangle Area = (1/2)Base x Height. Our base is side length a and for this calculation our height for the triangle is slant height s. With 4 sides we need to multiply by 4. (hope this will help)
So we are given the expression:
÷ 
When we divide fractions, we must flip the second term and change the sign to multiplication:
And then we multiply across:
Then we can break apart all of the like variables for simplification:
When we simplify variables through division, we subtract the exponent of the numerator from the exponent of the denominator. So we then have:
So then we multiply all of these simplified parts together:
So now we know that the simplified form of the initial expression is: 
.
Answer:Balloon payment:$84,646.62
Step-by-step explaination:
Monthly payment
Monthly principal and interest payment (PI). The monthly payment is calculated using a term up to 15 years.
Total interest paid:$22,374.55
Total regular payments:$51,227.93
Balloon payment:$84,646.62
