Suppose one wants a taylor polynomial approximation for f(x) = ln(4 − 2x) around x0 = 0 over the interval [−1, 1]. using the error bounding method from class (alternatively from the textbook as in the previous problem), what is the minimum order taylor polynomial that guarantees the error will never exceed ε = 0.1 anywhere in the interval? what is the corresponding taylor polynomial? what are the actual errors at x = −1, x = 0 and x = 1?

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step-by-step explanation:

what is the figure? attach a picture.

(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