Find the remainder in the Taylor series centered at the point a for the following function. Then show that limn→[infinity]Rn(x)=0 for all x in the interval of convergence. f(x)=cos x, a= π/2

Step-by-step explanation:

From the given question; the objective is to show that :

for all x in the interval of convergence f(x)=cos x, a= π/2

Assuming for the convergence f the taylor's series , f happens to be the derivative on an open interval I with a . Then the Taylor series for the convergence of f , for all x in I , if and only if    

where;

is a remainder at x and c happens to be between x and a.

Given that:

a= π/2

Then; the above equation can be written as:

so c now happens to be the points between π/2 and x

If we recall; we know that:

(as a result of the value of n)

However, it is true that for all cases that  

Hence, the remainder terms is :

If   for all x and x is fixed, Then

answer: - (a)

(b) 88 seats

step-by-step explanation:

given: in an auditorium, there are 22 seats in the first row and 28 seats in the second row.

thus first term=

second term=

the number of seats in a row continues to increase by 6 with each additional row.

⇒d= 6

a) given formula :

b)   let the number of seats (n) = 12

substitute n=12 in the explicit rule formed in (a)

∴there are 88 seats in 12 rows.