Consider the integral integral from 1 to e startfraction 6 over x endfraction dx∫1e 6 xdx with nequals=44. a. find the trapezoid rule approximations to the integral using n and 2n subintervals. b. find the simpson's rule approximation to the integral using 2n subintervals. c. compute the absolute errors in the trapezoid rule and simpson's rule with 2n subintervals.

step-by-step explanation:

1. supplementary angles

2. acd and bcd

step-by-step explanation:

(a) common ratio in the given sequence is, 3

(b) push ups will do kendall do on the 20th week

step-by-step explanation:

geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio(r)

(a)

given the sequence: 6 , 18 , 54 , 162 ,

this sequence is geometric sequence where each term is 3 times the previous term.

therefore,

common ratio(r) = 3.

(b)

a formula for nth term of geometric sequence is given by;

,   where r is the common ratio between the successive terms and is the first term,

to find how many push ups will kendall do on the 20th week.

here. n = 20th term.

in the given sequence first term

then;

simplify:

therefore, push ups will do kendall do on the 20th week