For the given functions f and g, find: (a) the composition of (f o g) (4) Â (b) (g o f) (2) Â (c)( f o f)(1) Â (d) (g o g) (0) f(x) = x3/2; g(x) = 2 / x + 1 Â *note: x3/2 is actually a square root number but I couldn't figure out how to make the numbers small.
For the given functions f and g, find: (a) Â the composition of (f o g) (4) (b) (g o f) (2) Â (c)( f o f) (1) Â (d) (g o g) (0) f(x) = 2x; g(x) = 3xsquared + 1
For the given functions f and g, find the following functions and state the domain of each. (a) f + g  (b)f - g  (c)f x g  (d) f / g f(x)= square root of x + 1;  g(x) = 2 / x
For the given functions f and g, find the following functions and state the domain of each. (a) f + g  (b)f - g  (c)f x g  (d) f / g f(x) = 2xsquared + 3; g(x) = 4xcubed + 1
Sketch the graph of each function. Â Be sure to label three points on the graph. If f(x) = integral (2x), find: (a) f(1.2) Â (b) f(1.6) Â (c) f(-1.8)
Please help me with #4, #10, and #16. I am having trouble woth these. Please show your work so that I may better understand the process.
Solve: x3 - 2x2+x=-5(x-1)2.
Let m be the smallest positive integer such that @^m=E for all @eS_n. Show that m=lcm(2,3,4,5,...,n).
What is the additive principle? Please provide simple examples.
Assume that the sum and product of two roots of a quadratic equation are 5 and 6, respectively. Find two roots.
I am asked to verify Fubini's Theorem for an integral evaluated over an equilateral triangle. I am asked to fully discuss the reasons for the limits of integration in my solution. See attached file for full problem description.
Factor: 9q^2-72q+750.
Test the following for divisibility by 2,3,4,5,6,8,9,and 10. (No calculator, explain your thinking). i. 6 543 210 b. What is the smallest whole number that is divisible by 2,3,4,5,6,8,9 and 10.
Simplify each of the following expressions further and identify the number property(ies) used in each. 1. 2 x (15+8)= (2 x 15)+ (2 x 8)= 2. 5/2 x (3/4 x 2/5)= (5/2 x 2/5)x 3/4=
Show by induction that: a) Sum(n^2/[(2n-1)*(2n+1)],n=1..) = n(n+1)/[2*(2n+1)] b) Sum( r/(r-1)!, r=1..n) = 1-1/(n+1)! c) n^3+3n^2-10n is divisible by 3 d) 4^(2n+1) + 3^(n+2) is divisible by 13 See attached file for full problem description.
Please see the attached file for the fully formatted problems. Find the following: a) The coefficient of x in the expansion of b) The coeffiecient of in the expansion of c) The coefficient of in the expansion of d) The coefficient of in the expansion of is equal to the coefficient of in the
Three numbers are in arithmetic progression. The sum of the three numbers is 30 and the sum of their squares is 398. What are the three numbers? b) An arithmetic series is such that its first term is a and its third term is b. The sum of the first n terms is Sn . Find S4 in terms of a and b. Given that S4, S5 , S7 are cons
Find the following. (Questions held on attachment) Find the following: a) The coefficient of x in the expansion of b) The coeffiecient of x^3yz^4 in the expansion of c) The coefficient of x^3 in the expansion of d) The coefficient of x^5 in the expansion of is equal to the coefficient of x^4 in the
Prove by induction where n is a positive integer. (The questions are attached).
Solve this equation: 3x²- 5x -1 = 0.
Please see the attached file for full problem description.
Find the value of x: log_3 7.2 = x
Find a new dependent variable such that the equation becomes linear in that variable. Then solve the equation: 1/(y^2 + 1) y' + 2/x tan^-1 y =2/x
First determine if the equation is exact. If it is exact, find the general solution, or at least a relation that defines the solutions implicitly: [cos(x^2 + y) - 3xy^2]y' + 2x cos(x^2 + y) - y^3=0
Solve for either the general solution or relation. xy' - y = x(1 + e^(-y/x)).
If the perimeter of a rectangle is 10 inches, and one side is one inch longer than the other, how long are the sides? Can you show me the steps to take to work out this and similar problems.
Diagonals in a Rectangle. In the case of a 2 X 2 rectangle, or a 3 X 5 rectangle, we can simply count. However, can we make a decision about a 100 X 167 or a 3600 X 288 rectangle? In general, given an N X K rectangle, how many grid squares are crossed by its diagonal?
Find the equation of a line passing through (1,-3) and parallel to x+y=2.
Find the equation of a line L which passes through the point (1,4) and is perpendicular to the line: 6x + 3y=12.
The endpoints of the diameter of a circle are P=(-3,2) and Q=(5,-6) Find: (i) the center of the circle (ii) The radius of the circle (iii) the equation of the circle.