How would you find the absolute maximum and the absolute minimum over the interval of :

f(x)=x²+2.5x-6, -5 ≤ x ≤ 5

f(x)=12(1.5^x)+12(0.5^x), -3 ≤ x ≤ 5.1

1. All of the following regions are given in rectangular coordinates. Give a sketch of the region and convert to a coordinate system, which you believe would be the most convenient for integrating over the given region, and a brief explanation as to why you chose that coordinate system.

d) E = {(x, y, z) | − 2 ≤ x ≤ 2, − √ 4 − x^2 ≤ y ≤ √ 4 − x^2 , 2 − sqrt4 − x^2 − y^2 ≤ z ≤ 2 + sqrt4 − x^2 − y^2}

Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.)

cos²(θ) − cos(θ) − 12 = 0

The number of cell phone subscribers in the United States between the years 2000 and 2010 is approximated by the function N(t) = 385.474 1 + 2.521e−0.214t (0 ≤ t ≤ 10) where N(t) is measured in millions and t is measured in years, with t = 0 corresponding to the year 2000.† How many cell phone subscribers were there in the United States in 2000? (Round your answer to one decimal place.) million subscribers.

If the trend continued, how many subscribers were there in 2011? (Round your answer to one decimal place.) million subscribers

Use the power series method to solve the given initial-value problem. (Format your final answer as an elementary function.)

(x − 1)y'' − xy' + y = 0, y(0) = −4, y'(0) = 7

y =

f(x)=x4−8x2

a. Interval(s) of increase/decrease
b. Local maximum and minimum values as coordinates (x,y)
c. Intervals of concavity
d. Inflection points as coordinates (x,y)
e. Y-intercepts as coordinates
f. X-intercepts as coordinates

Is the interval [-4, 7) open, closed, half–open, or unbounded?

A rectangular box has a length of 1 in, width of 2 in, and height of 3 in. Find the cosine of the angle between the diagonal of the box and the diagonal of its base.

what is the volume of the parallelepiped by <-5; 2; 1>, <1; -1; -3> and
<-1; -1; -4>?

(a) 9 
(b) 10 
(c) 11 
(d) 12 
(e) None of the above

The set R^2 with addition and scalar multiplication defined by

(x1, y1) + (x2, y2) = (x1 + x2, y1 + y2)

c(x1, y1) = (cx1, y1)

is not a vector space. Determine which axiom fails and find a counterexample that shows that it fails.

Give the domains and ranges of the following functions. A) ln x, B) cos X, C) 10^x D) f(x)= 1/ x^2-12x-45 E) g(x)= sqrt(82-x).

Determine the following : a) what is the angle formed by an arc length of 3 radii?

b) what is the angle formed by an arc length of 1 radii?

c) what is the angle formed by an arc length of pi/2 radii?

d) what is the angle formed by an arc length of 4pi/3 radii?

Use the Midpoint Rule for triple integral to estimate the value of the integral. Divide B into eight sub-boxes of equal size. (Round your answer to three decimal places.)

B =

(x, y, z) | 0 ≤ x ≤ 4, 0 ≤ y ≤ 2, 0 ≤ z ≤ 1

The derivative of ln|x| is an odd function

is it true/false

In a class of 130 shs students,41 offers agricultural science ,62 offers business,and 31 offers visual arts .16 of these students offer both agricultural science and business only and 14 offers both business and visual arts only.Assuming none of the students offers all the three subjects ,illustrate the information on a venn diagram