G (1 point) Let f(x)=ecos(x) and I=∫2π0f(x)dx. (a) Use M10 to approximate I to six decimal places. M10= (b) Use the fact that |f′′(x)|≤e on [0,2π] to obtain an upper bound on the absolute error |EM| of the approximation from (a). Make sure your answer is correct to six decimal places. |EM|≤ (c) Use S10 to approximate I to six decimal places. S10= (d) Use the fact that |f(4)(x)|≤4e on [0,2π] to obtain an upper bound on the absolute error |ES| of the approximation from (c). Make sure your answer is correct to six decimal places. |ES|≤ (e) Use a CAS to approximate I to six decimal places. I≈ (f) Which of the two approximations M10 and S10 is better? A. S10 B. Both are equally good approxiamtions. C. M10 (g) Using the information given in part (d) and the appropriate error formula from your textbook, how large do we have to choose n to ensure that the approximation Sn is accurate to within 0.0001? (Your answer must be a whole number.) n =

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺