Find the second Taylor polynomial P2(x) for the function f(x) = √4 + x about x0 = 0. Approximate √3.9 using P2(x). Find the absolute error and the relative error for the approximation (you can use your calculator to find the “exact” value for √3.9)

For f(x)=3x2 +4x+5 on the interval [-1, 1] estimate the area using 4 rectangles.  Do this with height of the rectangle be determined by the midpoint of the rectangle

please quickly

Suppose that in a certain biology lab experiment, the number of bacteria is related to the temperature 7 of the environment by the function N(T) = -27² + 250T - 4900 (40 ≤ T ≤ 90). Here, N(T) represents the number of bacteria present when the temperature is T °F. Also, suppose that t hr after the experiment begins, the temperature is given by T(t) = 10t + 40 (0 ≤ t ≤ 5). (a) Compute N[T(t)]. N[T(t)] = (b) How many bacteria are present when t = 0 hr? When t = 2 hr? When t = 5 hr? t = 0 hr bacteria bacteria t = 2 hr t = 5 hr bacteria

Few companies take the time to estimate the value of a good customer (and often spend little effort to keep one). Suppose that a customer at a restaurant spends, on average, R per visit and comes F times each year (for example, if a customer purchases once every two years, then 1 F-=-0.5. The restaurant realizes a gross profit margin of M (expressed as a fraction) on the average bil for food and drinks. In addition, the fraction of customers defecting (not returning) each year is D. Complete parts a and b. T a. Develop a mathematical model to compute V, the gross profit during a customer's Metime in doing business with the restaurant (this is often called the economic value of a customer). (Simplify your answer.) b. If the average purchase per visit is $50, the gross profit margin is 0.4 (that is, 40%), customers visit an average of six times each year and 30% of customers defect each year, what is the economic value of the customer? The economic value of the customer is $ (Round to…

Consider the following quadratic f(x) = x - 14x +4 with the roots a and B. Suppose the new quadratic g(x) = x² + px +q has the roots y = a+B and & =1+1. Find the coefficients p and q of the new quadratic correct to 2 decimal places. Select one: O p= 17.50, q = 51.00 O p= 14.50, q = 14.50 O not in the list O p= -10.50, q = 49.00

3- Verify the MVT with f (x) = √√7x, a=1 and b=16.

The upward velocity of an object is expressed as a function of time, which is recorded as follows t (detik) v (meter/detik) 10 22 15 36 20 57 22 10 Use a 2nd order polynomial approximation to get the acceleration value at t=17 seconds.