The series n=1 (6n+4)³ is convergent. (A). According to the Remainder Estimate for the Integral Test, the error in the approximations, is 18-8al ≤ f(x) dx = (B). Find the smallest value of n such that the error in the approximation is less than 0.00004 11= 125

Sketch the graph of -x3 +7x2 -10x+2. Find the average rate of change of f(x) over the interval between a=2 and b=3. Repeat for b=2.5, 2.1, 1.9, 1.99. (Hint: Remember that Pascal’s Triangle can help a lot here with the Binomial Theorem.)

The population of petsons infectred by Covid-19 virus is knowu to increase at a rate proportional to the mmber of persons presently infected by the virus. After 5 days 1000( D) infected persons are olserved in the eity and after 25 days. 4000(D + 1) infected persons. Find i) an expression for the approximate mumber of infected persons in the city at any time t, and ii) the approximate number of persons initially infected in the city. Note: D = 9

Show that coth-1=1/2ln(1+x/x-1

The membership of The Fitness Center, which opened a few years ago, is approximated by the function N(t) = 100 * (4t + 64) ^ (3/2) (0 <= t <= 52) , where N(t) gives the number of members at the beginning of week . a). How fast was the membership increasing at the beginning of the 30 week? b). What was the membership when the center first opened? At the beginning of the 30th weck?

11 dx Determine whether is convergent or not. (3 – x)2/3

Differentiate the Maclaurin polynomial of degree 4 for f(x) = ex . Describe the relationship between the two series.

Consider p(x) = (x - 1.5001)(x-1.5)(x - 1.4999). Evaluate the formula = |p| \rp'(r)| at the root r= 1.5 of p. Interpret the value you obtained for K. If the error on the coefficients of p is 10-12, then, how large can the error Ar on the root be?

The number of deaths among members of the U.S. Navy in the first 3 months of the 1918 influenza epidemic can be modeled as 3,016 N(t) l + 119.25e-1.024t deaths where t is the number of weeks since the start of the epidemic, based on data for weeks 0 sts 13.t (a) Numerically estimate, to the nearest integer, the end behavior for N as t increases without bound. Show the numerical estimation table starting at t 1 and incrementing by adding 5 N(t) t oo 6 16 21 (b) Write an equation for the horizontal asymptote for N found in part (a). y (c) Write a sentence interpreting the result found in part (a) in context. deaths occurredSelect The model predicts that among members of the U.s. Navy as a result of influenza during the epidemic of 1918.

Suppose to solve for a root of f(x), i.e., f(x*) = 0, we use the iteration Xk+1 = ¢(xk) where o(x) and f(x) given functions with as many continuous derivatives as you require. Show that if |O'(x*)| < 1 then for |xo – x*| sufficiently small the iteration xk+1 = produces a sequence that converges to x*. Note that the iteration ø(x) is called a contraction mapping in the neighborhood of x* when |ø'(x*)| < 1. -