Consider the error in using the approximation e−x≈1−x on the interval [−1,1]. (a) reasoning informally, on what interval is this approximation an overestimate? 1 an underestimate? (for each, give your answer as an interval or list of intervals, e. g., to specify the intervals −0.25≤x< 0.5 and 0.75

is a classic approximation, true for small x.

The next term in the polynomial expansion will be where k is a positive number. So our estimate 1-x is definitely an underestimate on both sides of x=0.

Since for negative xs the exponential rises exponentially and the line only linearly, the exponential exceeds the line for all negative x. For positive x, the line quickly goes negative while the exponential is always positive.

So, there's no interval for which our approximation is an overestimate.

the answer is 40.

proof:

(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