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Find the area A(R) of the region R described below.
1. R is the region bounded by y = 2x + 3, the x-axis and the line x=5 .
2. R is the region bounded by y=x^{2}+1 , the lines y=2 and y=5
3. R is the region bounded by x=y(8-y) and the y-axis.
4. R is the region bounded by y = x and y=x^{3} .
5. R is the region bounded by y=2-x^{2} and y=x^{2}-6
Show that β2π β«2π π₯ 2 sin8 (π π₯ )ππ₯| β€ 16π3 /3
Identify the domain of the following functions.
a) π(π₯) = sinβ1 (3π₯ β 1)
b) π(π₯) = [log(sinβ1 (βπ₯ 2 + 3π₯ + 2))]
c) π(π₯) = 1 β(π₯β2)2
d) π(π₯) = 1 π₯ββ(π₯+2)
e) π(π₯) = ln|π₯ + 3| β 5
A poster must have 32 square inches of printed matter with margins of 4 inches at the top, and 2 inches at each side. Find the dimensions of the whole poster if its area is MAXIMUM.
The approximating sine function for temperature in Fairbanks, Alaska is given as
π(π₯)=37sin(2π (π₯β100))+25 365
where π is temperature in degrees Fahrenheit and π₯ is the number of days counting from the beginning of the year. Use MATLAB to plot the function for one year. Find amplitude, period, horizontal shift, and vertical shift of the general sine function.
When two given functions, π(π₯) = π₯ 2 + 3 πππ π(π₯) = 2π₯ β 5, are divided with each other, a new third function is obtained. Find (π/π)(π₯) and identify its domain
When two given functions, π(π₯) = π₯ 2 + 3 πππ π(π₯) = 2π₯ β 5, are divided with each other, a new third function is obtained. Find (π/π)(π₯) and identify its domain
Given the function f(x)=-x^3/3+x^2-6x-2, discuss its relative maximum and minimum
points, the intervals where it is increasing and decreasing, the intervals of concavity, and the points of inflection. Construct a sketch of the graph of the function.
A poster must have 32 square inches of printed matter with margins of 4 inches at the top and bottom, and 2 inches at each side. Find the dimensions of the whole poster if its area is maximum.
incorporates variable hourly rate to encourage longer shifts. The company pays $10 for first
hour or any part of the first hour. Afterwards, company pays additional 2% per hour for each
hour or part of each additional hour. Write a piece-wise function that shows the salary as a
function of hours. Also sketch a graph of this function.
#339914 on Dec 2023