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# Graphs and Functions

### Uniform convergence of functions

1.Show that if a>0, then the convergence of the function nx/(1+n^2 x^2) is uniform on the interval [a,infinity), but is not uniform on the interval [0,infinity). 2. Show that if b is greater than 0 and less than 1, then the convergence of the function x^n/(1+x^n) is uniform on the interval [0,b] but is not uniform on the interv

### Formulas and Graphs

A breeding group of beavers introduced into a protected area. After t years the number of beavers in the area is modeled by the function N(t) = _____54__________ 0.35+0.68t (note: this t by 0.68 should be an exponent,couldn't make one here.) 1. How many beavers were initially introduced? 2. Estimate

### Construct a Scattergram

A social worker was interested in exploring whether there was a relationship between the severity of her clients' alcohol abuse problems and the degree to which they were depressed. (All scores in this exercise are fictitious, invented for the purpose of the exercise). Ten clients had been given the Michigan Alcoholism Screening

### Solving for volume

A 10 oz. soft drink sells for 50 cents. A 16 oz sell for 68 cents. The price is determined from the volume v of the cup by a linear equation. What is the equation and what would the cost of a 20-oz drink?

### Finding y as a function of t

1. Find y as a function of t if y'' - 3y' - 18y = 0, y(0) = 6, y(1) = 8. Remark: The initial conditions involve values at two points. 2. Find y as a function of t if 3y'' + 28y = 0, y(0) = 8, y'(0) = 5. Note: This particular problem can not handle complex numbers, so write your answer in terms of sines and cos

### Linear Functions: Market price, Cost equation

1. A company sells it's products in a market where the market price, p, is linked to the quantity sold, q, by the linear equation p=120-2q. a) Calculate the market price if the company sells 50 units. What is the revenue equation and the revenue if company sells 50 units? The company incurs fixed costs of \$400 and an addit

### Finding Marginal Cost: Example Question

If the cost function for a commodity is: C(x) = (1/90)x^3 + 4x^2 + 4x + 10 dollars Find the marginal cost at x= 3 units and tell what this predicts about the cost of producing 1 additional unit and 2 additional units.

### What is the slope of the line?

Please see attached file. What is the slope of the line: 3x - y = 6 A. -1 B. 1/2 C. 3 D. 2 What is the slope of the line: 2y + 8x = 26 A. 1/4 B. 2 C. -4 D. 8 What is the slope of the line: 14y - 2x = 28 A. 2 B. 7 C. 1/7 D. -2

### Calculate distance between 2 points !

Calculate distance between 2 points ! 1. P1 = (-1, -5) P2 = (-7, -13) 2. P1 = (-4, -3) P2 = (3, -4) 3. P1 = (-2, -5) P2 = (2, -7) 4. P1 = (0, 0) P2 = (9, 7) 5. P1 = (0, 6) P2 = (-2, 6) 6. P1 = (0, -4) P2 = (3, -4)

### Plotting a graph and then find the function value.

The electrical resistance R (in ohms) of a resistor is measured at different temperatures T (in Celsius). The results are in the following table. Plot the graph of R=f(T), and use the graph to find f(22). T (Celsius) 0 5 10 15 20 25 R (Ohms) 600 620 635 640 650 670

### Exponential and reciprocal functions

1. Identify an exponential function. Give an example of this function related to the business environment. Assignment Notes Discussion Question 1: If we look at the formula to calculate the dollar amount of a \$1 we put into savings today, we see that it is fv = pv*((1+i)^n). The variables are fv = future value, pv = pre

### Use an Excel Spreadsheet and the FV function for following

A. The future value of a \$2,000 annuity for 30 yrs at 8% compound annually. b. The future value of a \$2,000 annuity for 30 years at 8% compound semiannually. c. The future value of a \$2,000 annuity for 30 years at 8% compound quarterly. d. How much extra interest is earned onthe annuity above simply by chnaging the compoun

### Standard form of the equation of the circle and graph.

Write the standard form of the equation of the circle and graph: 1. With r = 3 and tangent both axes in Q1. 2. With C (-1, -3) and passing through (-2, 0). 3. With points (2, 5) and (6, -1) as ends of a diameter. 4. With C (0, 0) and touching the line 3x + 4y = 10.

### Functions and their graphs

1. f(x)= 2x+5 if -3 <= X <0 -3 if x=0 -5x if x>0 a. Find the domain of each function. b. Locate any intercepts. c. Graph each function d.Based on the graph find the range. e. Is f continuous on its domain? 2. If f(x)= int(x/2) Find, (a) f(1.2) (b) f(1.

### Excel help: Pleas help with attached problem.

(a)Use an excel spreadsheet with the data provided activity time (sec) 4022 38.6 3424 77.0 2613 113.8 2158 152.6 1590 188.9 1337 228.6 940 269.7 prepare a graph of activity vs. seconds. Use a trend line to produce the best exponential line through the points. (b) Use the excel spreadsheet again wi

### Functions and their graphs

1. f(x)=X3-3X2+5 (-1,3) I need to find local Maxima and Local Minima for this Question. Also determine where the function is increasing and where it is decreasing. round answer to two decimal places. 2. g(x)= X2+1 (a) Find the average rate of change from -1 to 2. (b) Find an equation of the secant line containing

### Linear Programming: Maximize

Consider the following linear programming problem Max 8X + 7Y s.t. 15X + 5Y < 75 10X + 6Y < 60 X + Y < 8 X, Y &#61619; 0 a. Use a graph to show each constraint and the feasible region. b. Identify the optimal solution point on your graph. What are the values of X and Y

### Considering the Various Functions

Consider the function f(x) = 3x^2-5x+7 (a) What is f(4)? (b) What is f(a+2)? (c) What is f(x+h)? (d) What is f(x+h)-f(x)? (e) What is (f(x+h) â?" f(x))/h? (f) What is lim as h approaches 0 of (f(x+h) â?" f(x))/h? (g) What is f prime of (x).

### Write a C program which implements 2-D Newton's method to find the minimum of the Rosenbrock function, starting from the point (-2,2).

The Rosenbrock function f(x,y) = (1 - x)^2 + 100(y - x^2)^2 is a well known test function for optimization methods. Write a C program which implements 2-D Newton's method to find the minimum of the Rosenbrock function, starting from the point (-2,2). The functions E1(x,y) and E2(x,y) and their x and y partial derivativ

### Assessing Rouche's Theorem

Use Rouche's Theorem to determine the number of zeros, counting multiplicities, of the polynomials inside the given regions. a) z^4 + 3z^3 + 6 inside the circle |z| = 2 b) 2z^5 - 6z^2 + z + 1 in the annulus 1 <= |z| < 2 Thanks

### Graph the function f(x) over the given interval.

Graph the function f(x) over the given interval. Partition the interval into 4 subintervals of equal length. Then add to your sketch the rectangles associated with the Riemann sum (attached), using the indicated point in the kth subinterval for ck. f(x) = x2 - 3, [0, 8], midpoint (Graph is also attached) Answer Options:

### Geometry problems with area and volume

1. Find the area of the triangle. 2. There is a shaded triangular prism 6in x 8in x 11in with a rectangle solid 3in x 4in x 11in not shaded. Find the volume of the shaded area. 3. Given the graph, name an edge that is a bridge, if any. 4. Find the area in meters of a trapezoid with a height of 4 m and bases of 8 m and

### Interpreting Function's Graph: Example Problems

Please see attached for function's graph. 1. Given the information on the graph, answer the following questions: i. Explain why f represents the graph of a function. ii. Use the graph to find a reasonable estimate of f (- 2). iii. What is the domain of f? iv. What is the range of f? 2. Given f(x) = 8x - 2 and g(x) =

### Graphing non-linear inequalities

What is the purpose of a dashed line when graphing a non-linear inequality? Give examples of graphs with and without dashed lines.

### Description of Average Value

Use a finite sum to find the average value of the function on the given interval by partitioning the interval and evaluating the function at the midpoints of the subintervals. Show all work! f(x) = 5 + sin (Pi)x on [0, 2] divided into 4 subintervals

### Graphing Line Containing Pairs

I'm having a problem graphing. Please help! 1. Find the slope of the line containing the given pair of points. If the slope is undefined, state so... 2. Find the intercepts for the equation... 3. Determine the x- and y-intercepts of the given equation. Show your work. Then plot the intercepts, and graph the line... 4. Determ

### MAT101 - College Mathematics (Exponential & Logarithmic Functions) SLP

Take the current amount you have in your checking or savings account. Suppose you have a choice of keeping your money for five years in a savings account with a 2% interest rate, or in a five year certificate of deposit with and interest rate of 4.5%. Calculate how much interest you would earn with each option over five years

### MAT101 - College Mathematics (Graphs & Functions)

Need help to describe in words the graph of each of these curves below. Include in the description of the shape, along with other possible relevant information such as length, width, and center points. a. Y = 3X^2 b. (X-1)^2 + (Y-8)^2 = 16 c. (X+2)^2 + (Y-4)^2 = 36 d. Y = X^2 + X Need assisting in finding the

### Increase in number of micrograms of epinephrine

Estimate the answer from the table or graph. The following graph shows the number of micrograms of Epinephrine in a person's bloodstream after being injected from 2 minutes to 5 minutes. [see attachment] Estimate the increase in the number of micrograms of Epinephrine in a person's bloodstream from 2.5 minutes to