# Consider the following functio

Consider the following function.
h(x) = x−1⁄3 (x − 14)

A) Find the derivative of the function.
h ′(x) =?

B) Find the values of x such that h ′(x) = 0. (If an answer does not exist, enter DNE.)
x = ?

C) Find the values of x in the domain of h such that h ′(x) does not exist. (If an answer does not exist, enter DNE.)

x =?

D) Find the critical numbers of the function. (If an answer does not exist, enter DNE.)

x = ?

# Consider the following functio

Multiple Choice Question

Consider the following function. What is the purpose of the function f? Please do explain and describe in details all possible answers for this function given below.

int f(int n) {
if ((a >= b) && (c < b)) return b;
else if (a >= b) return f(a, c, b);
else return f(b, a, c);
}

a. To find the maximum number between a, b, and c.
b. To find the middle number between a, b, and c.
c. To find the minimum number between a, b, and c.
d. None of the other statements.

# Consider the following functio

1. Consider the following function. What is the purpose of the function f? Please do explain and describe in details all possible answers for this function given below.

int f(int n) {
if ((a >= b) && (c < b)) return b;
else if (a >= b) return f(a, c, b);
else return f(b, a, c);
}

1. To find the maximum number between a, b, and c.
2. To find the middle number between a, b, and c.
3. To find the minimum number between a, b, and c.
4. None of the other statements.
2. Suppose the letters a,b,c,d,e,f have probabilities of 1/2, 1/4, 1/8, 1/16, 1/32, 1/32 respectively. Which of the following is the Huffman code for the letter a,b,c,d,e,f? Please show how is the Huffman tree, so that you can determine one of the options below.
1. 0, 10, 110, 1110, 11110, 11111
2. 11, 10, 01, 001, 0001, 0000
3. 11, 10, 011, 010, 001, 000
4. 110, 100, 010, 000, 001, 111
3. An adjacency matrix of a graph is given below:

First, draw the graph defined by that adjacency matrix, and label the vertices of the graph with 1, 2, 3, …, 6 so that vertex i corresponds to row and column i.

Second, Give a coloring of the vertices (color the graph) that uses the minimum number of colors. Prove with explanations that your given coloring is the minimum coloring.

# Consider the following functio

Consider the following functions.

f(x)= 1/3x^2-3/4x

g(x)=1/2x+5/6

h(x)=1/4x^2-5/8x+2/5

Part a. Amarion wants to determine f(x)-g(x)-h(x) . His steps are shown below, but he made a mistake.
In which step did he make a mistake and what was the mistake?
Step 1:(1/3x^2-3/4x)-(1/2x+5/6)-(1/4x^2-5/8x+2/5)

Step 2: (1/3x^2-5/4x-5/6)-(1/4x^2-5/8x+2/5)

Step 3: 1/12x^2-15/8x-13/30

part b. because
a. he did not distribute the -1 to all terms
B. he did not get a common denominator for all the terms
C. he did not change the exponents when combining like terms

# Consider the following functio

Consider the following function.

f(x)= {4x+3, x ≤ −1

{x2-2, x > −1

a) Find the critical numbers of f. (Enter your answers as a comma-separated list.)

x = 0, -1

b) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)

increasing: (?, ?) ***the answer is NOT (0, ∞)

decreasing: (-1, 0)

c) Apply the First Derivative Test to identify the relative extremum. (If an answer does not exist, enter DNE.)

relative maximum (x, y) = (?, ?)

relative minimum (x, y) = (0, -2)

# Consider the following functio

Consider the following function main:
Int main()
{
int inStock[10][4];
int alpha [20];
int beta[20];
int gamma[4]= {11,13,15,17};
int delta [10] = {3,5,2,6,10,9,7,11,1,8};
}

a) Write the definition of the function setZero that initializes any one-dimentional array of type int to 0.
b) Write the definition of the function inputArray that prompts the user to input 20 numbers and stores the numbers into alpha.
c) Write the definition of the function doubleArray that initializes the elements of beta to two times the corresponding elements of alpha. Make sure that you prevent the function from modifying the elements of alpha.
d) Write the definition of the function copyGamma that sets the elements of the first row of inStock to gamma and the remaining rows of inStock to three times the previous row of inStock. Make sure that you prevent the function from modifying the elements of gamma.
e) Write the definitions of the function copyAlphaBeta that stores alpha into the first five rows of inStock and beta into the last five rows of inStock. Make sure that you prevent the function from modifying the elements of alpha and beta.
f) Write the definition of the function printArray that prints any one-dimensional array of type int. print 15 elements per line.
g) Write the definition of the function setInStock that prompts the user to input the elements for the first column of inStock. The function should then set the elements in the remaining columns to two times the corresponding elements in the previous column, minus the corresponding element in delta.
h) Write C++ statements that call each of the functions in parts a through g

i) Write a C++ program that tests the function main and the functions discussed in parts a through g. (Add additional functions, such as printing a two-dimensional array, as needed.)

please i need complete answers from question a) till i) in c++ programming language

# Consider the following functio

Consider the following functions for consumption and investment: C = 1,000 + (2/3)*(Y – T) and I = 1,200 – 100*r. Furthermore, Y = 8,000, G = 2500, T = 2,000.

1. Compute private, public, and national savings for this economy, and find the equilibrium real interest rate (r).
2. Assume that G declines by 500 units. How will it change your answers in part (a)?
3. What happens to the national savings, given everything else, if the public decides to consume less out of their disposable income (assume that the propensity of consume falls by 10 percent)?
4. Given your answer in part (c), what happens to investment and real interest rate?

# Consider the following functio

Consider the following function.

f(x)= {4x+3, x ≤ −1

{x2-2, x > −1

a) Find the critical numbers of f. (Enter your answers as a comma-separated list.)

x = ?

b) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)

increasing: (?, ?)

decreasing: (?, ?)

c) Apply the First Derivative Test to identify the relative extremum. (If an answer does not exist, enter DNE.)

relative maximum (x, y) = (?, ?)

relative minimum (x, y) = (?, ?)

# Consider the following functio

1. Consider the following function :

f(x)= (x– 3x +2)/(x2-1)

1. a) Find the limit of the function as x approaches -1, if it exists.
2. b) Find the limit of the function as x approaches +1, if it exists.
3. c) State whether the function is continuous over its domain. If it is not, name the values of x for which it is not continuous.
4. d) Use the quotient formula to determine the derivative of the function.
5. e) Can the function be simplified ? If so, simplify the function.
6. f) Graph the function. Show accurately any x and y intercepts and any asymptotes.
7.

# Consider the following functio

Consider the following function.

f(x) = |x + 8| − 9
(a) Find the critical numbers of f. (Enter your answers as a comma-separated list.)

x =

(b) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)

 increasing decreasing

(c) Apply the First Derivative Test to identify the relative extremum. (If an answer does not exist, enter DNE.)

relative maximum     (x, y)  =

relative minimum     (x, y)  =

# Consider the following functio

Consider the following function.
T: M2, 2 → R, T(A) = a − b − c − d,

where

A =

a b
c d
Find the following images for vectors

A1

a1 b1
c1 d1

and

A2

a2 b2
c2 d2

in

M2, 2

and the scalar c. (Give all answers in terms of

a1, b1, c1, d1, a2, b2, c2, d2, and c.)
T(A1)

=

T(A2)

=

T(A1) + T(A2)

=

T(A1 + A2)

=

cT(A1)

=

T(cA1)

=

Determine whether the function is a linear transformation.
linear transformation not a linear transformation

# Consider the following functio

Consider the following function: f (x) = (x − 4)(x + 2) / (x+4)(x+2

1.For what values of x is f(x) continuous? State your answer using interval notation

2.Find the following limits (if they exist)

a. lim f (x) x→ −4

b. lim f(x) x→ −2

3.Does f(x) have any vertical asymptotes? If yes, then write down the equation of the vertical asymptote(s)? Show working or give a reason for your answer.

4.Does f(x) have a horizontal asymptote? If yes, then write down the equation of the horizontal asymptote? Show working or give a reason for your answer.

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