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# Graphs and Functions

### Finding Values that Make a Function Differentiable Everywhere

Let f(x) ={ x^2 x &#8804;2 {mx + b, x > 2 Find the values of m, b that make f differentiable (everywhere). See the attached file.

### Stirling's Approximations and Growth Rate of Functions

Function A Function B (n^2) ! n^n is A=O(B) ? Yes/No is A=o(B) ? Yes/No is A=Big Omega(B) ? Yes/No is A=Small Omega(B) ? Yes/No is A=Theta(b) ? Yes/No.

### 20 Problems : Solving equations, graphing equations, finding domains, simplyfing and determine the inverse of f using switch and solve strategy

Please see the attached file for the fully formatted problems. Includes: Solving equations, graphing equations, finding domains, simplyfing, determine the inverse of f using the switch and solve strategy. Thanks for your help!

### Point Estimation in Statistics

22. Let X denote the proportion of alloted time that a randomly selected student spends working on a certain aptitude test. Suppose the pdf of X is ... a. Use method of moments to obtain an estimator ... b. Obtain the maximum likelihood esitmator ... Please see attachment for complete question. Thank you!

### Solve and Graph Equations

SOLVE (roots): 3X^2 - 3X - 5 GRAPH: 3X^2 - 3X - 5

### Functions and Graphs : Heart Disease, Cancer and AIDS - Trends and Real World Implications

You have been invited to present statistical information at a conference. To prepare, you must perform the following tasks: 1. Search the Internet and the Cybrary to find the number of deaths in the United States due to each of the following medical conditions in each of these years; 1985, 1990, 1995, and 2002.: o heart dis

### Find Y-Intercept and the Slope Given the Equation of a Line

Determine the y-intercept and the slope from the following equation: 6x - 9y = 24.

A square picture is mounted in a frame 1 cm wide. The area of the picture is 2/3 of the total area. Find the length of a side of the picture.

### lines where the x-coordinate is the same as the y-coordinate.

The coordinates of the x-intercept are the same as the coordinates of the y-intercept on the graph of the line whose equation is what?

### Find the Equation of a Vertical Line Passing Through a Point

What is the equation of a vertical line passing thorugh (-1,2) ?

### Function solutions

2. Given the polynomial f(x) = 2x 3 -5x2-4x+3, find the solutions if the function is completed as a) f(x) =0 b) f(x+2)=0 d) f(2x) = 0

### Functions and Graphs : Heart Disease, Cancer and AIDS - Trends and Real World Implications

I need the following info: Find the number of deaths in the United States due to each of the following medical conditions in each of these years; 1985, 1990, 1995, and 2002. Heart disease Cancer AIDS Plot The data for each disease as points in a rectangular coordinate system. Using a smooth line, connect your dat

### Prove A Variation of Fermat's Theorem

There always exists a real number n such that a^n = b^n + c^n , where a, b and c are any integers. The problem is not Fermat's Last Theorem, but a variation of it with real exponents.

### Functions and Graphs : Heart Disease, Cancer and AIDS - Trends and Real World Implications

I am presenting this information as a speaker to present statistical information at a conference. To prepare, this information is important: Finding the number of deaths in the United States due to each of the following medical conditions in each of these years; 1985, 1990, 1995, and 2002.: Heart disease Cancer AID

### Functions: Onto and One-to-one, Bijections and Functions

Please help with the following problems on graphs and functions. Provide step by step calculations. 1. Assuming A,B not equal to no solution, define m1:AxB->A and m2:AxB-> as follows: m1(x,y)=x and m2(x,y)=y. If f: A->B, show that a) f onto=>m2 |f is onto b)f one-to-one=>m2 f is one-to-one 2. Assuming f: A->B and g:

### Given a graph of a trigonometric function find period, amplitude, phase shift and equation.

The figure below shows the graph of a sine function - y is a function of &#952;, with &#952; measured in degrees. For this function state: a. its Period b. its Amplitude c. its Phase Shift from the sine function y = sin2x d. the Equation of the Function Answer in degrees also please Please see attached.

### Functions and Graphs: Trends and Real World Implications

Plot your data for each disease as points in a rectangular coordinate system. Year...................1985..........1990..........1995......2002 Heart Disease 771,169 720,058 684,462 162,672 Cancer 461,563 505,322 554,643 557,271 AIDS * 8,000 25,188 39,979 14,095 - Use individu

### Completing the Square to Find Radius and Center of a Circle; Slope and Intercept; Equation of Tangent Line and Time and Velocity of Falling Object

Complete the square to find the center and the radius of the circle x^2+y^2- 4x+2y+3=0 Find the slope and the y-intercept of: 3x+y= -2 Find the equation of the line tangent to f(t)=2/3t^2 The height s (in feet) at time t (in seconds) of a silver dollar dropped from the top of the Washington Monument is s= -16t^2+5

### Function Inverse

Let f(x)=3x-5. Find f^-1(x). Show all steps.

### Composition of Two Functions 'f o g'

Let f(x)=x^2-2 and g(x)=4/x. Find (g o f)(-8). Show all steps

### Limit and Slope of Tangent Line, Midpoint and Trapezoidal Rule

Use the limit definition to find the slope of the tangent line, f(x)= X^2+2X+1 Use the midpoint rule to approximate the area of the function f(x)=-2x+3 from [0,1] when n=4. Compare this approximation to the actual area by integration to the approximate area using the trapezoid rule. Sketch the and find its average rate

### Average Value of a Function on an Interval

Find the average value of the function f(x)=x^2 + 1 on the interval [0,4].

### Plotting a Surface Function

Consider the function u(x,t) = sin(4 pi x) e^(-pi t). Plot using a graphical tool and explain what you observe. Please see the attached file for the fully formatted problems.

### Statistics

What is the "causal relationship" between independent and dependent variable?

See attached

### Find the equation of a line given two points.

Find the slope-intercept form of the linear equations that go through the following points: (-1,6) and (1,2) also through points (5,3) and (-2,3).

### Find the slope-intercept form of the equation.

Find the slope-intercept form of the equation for the line perpendicular to y=-2/5x+4 that goes through the point (1,4).

### Sequence of Functions and Mean Value Theorem

Let a<b. Let f_n: [a,b] -> R be a sequence of functions such that, for each n in N ( N set of natural numbers),f_n is differentiable on (a,b). Suppose that for all n in N, Sup on [a,b] of | f'_n(x) | < or = to M, where M is in R. ( Sup is supremum = least upper bound) Prove that for all n in N and all x, y in [a,b], one has

### Uniformly Cauchy Sequence of Continuous Functions

Let f_n : [0,1] -> R be a sequence of continuous functions such that for each n in N (natural numbers), f_n is differentiable on (0,1). Suppose that f_n(0) converges to some number, denoted f(0), and also suppose that the sequence (f'_n) converges uniformly on (0,1) to some function g: (0,1) -> R. Prove that the sequence (f_n) c

### Diffusion Equation : Energy Decreasing as a Function of Time

3. Suppose that u(x. t) satisfies the diffusion equation ut = kuxx for 0 < x < L and t > 0, and the Robin boundary conditions ux(0, t) ? aou(0, t) = 0 and ux(L, t) + aLu(L, t) = 0 where k, L, a0 and aL are all positive constants. Show that ... is a decreasing function of t. Please see the attached file for the fully for