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# Calculus and Analysis

### Laplace Transform help

Example 1: Solve using Laplace Transform Answer: First, apply the Laplace Transform Knowing that , and we get After easy algebraic manipulations we get , which implies Next, we need to use the inverse Laplace. We have (see the table) For the second term we need to perform the partial dec

### Differientiate the function and tangent line

Please answer the attached problems and circle the answers. thanks 1. Differientiate g(x) = (7x - 5)/(5x + 1) + x^3 2. Find dy/dx, y = x^0.75 3. Differientiate the function y = sqrt(x^2 + 6) 4. Find an equation for the line that is tangent to the curve y = 4x^3 - 4x at the point (1, 0) 5. For the function, find t

### maximum value of theta angle

A missile is launched and travels along a path that can be represented by: A radar tracking station is located 2 km directly behind the launch pad. Placing the launch pad at the origin and the radar station at (-2, 0), find the largest angle of elevation required of the radar to track the missile. I included the equa

### Homework Help

Power supply P (in watts) in a satellite is given by: P=100e^0.005t where t is measured in days. find the time rate of change of power after 100 days.

### Conducting Various Probability Calculations

1. How many 8 letter arrangements can be made from the word RECYCLE? 2. In an experiment, a student is randomly selecting a letter from one of 4 boxes after selecting the first box at random. What is the probability the student will select the letter A? Box 1 has letters S,O,H Box 2 has letters S,O,H Box 3 has letters C,A,H

### Vectors in a plane

I need help figuring out how to solve the attached vector problem. Please solve and show how to solve for tension in each cable. A given weight (in pounds) is suspended by two cables. Find the tension in each cable.

### The equation for a hyperbola

How do you find an equation for a hyperbola. Need list of steps taken to find an equation for a hyperbola. Solve the following to reinforce my understanding: 1) Vertices (+or-4, 0) and passing thru (8,3) 2) Foci (0,+-9)Center, directrices y = +-4 3) Center (1,-3), vertices (-4,3) and (2,3), foci (-6, 3) and (4,3)

### Conic sections

Please provide steps needed to find equation of and ellipse with given information. Please include formulas used and detailed step-by-step solution. Thank you: 1. Foci (+or- 5, 0), major semiaxis 13 2. Center (0,0), vertical major axis 12, minor axis 8 3. Foci (0,+or-4), eccentrity 2/3

### Differential Calculus Problem

The function f(x) changes value when x changes from x0 to x0 + dx. Find the approximation error (trianglef -df) . Round your answer, if appropriate. f(x) = x^3, x0 = 3, dx = 0.02 a. 0.003608 b. 0.005412 c. 0.007216 d. 0.001804

### Differential Calculus for dV/dt or dr/dt

Solve the problem. Suppose that the radius r and volume V = r3 of a sphere are differentiable functions of t. Write an equation that relates dV/dt to dr/dt. a. dV/dt = 4/3 r^2dr/dt b. dV/dt = 4r dr/dt c. dV/dt = 3r^2dr/dt d. dV/dt = 4 r^2dr/dt

### Differentiate Introductory Calculus

1. Consider the function f(x)=(&#8722;5x^(2))+7x+15. a) For the given function f, the expression f(x+h)-f(x)/h can be simplified to the form Ax+Bh+C, where A, B and C are constants. Do it. Answer: f(x)=(&#8722;5x^2)+7x+15=____x+____h+____ b) Using the result of (a), find the derivative of f at x . Answer: f'(x)=______.

### Uniform and Pointwise Convergence

QUESTION 1 For each natural number n and each x in [0,1], define f_n(x)= x/(nx+1) Find the function f: [0,1] -> R to which the sequence {f_n} converges pointwise. Prove that the convergence is uniform. QUESTION 2 For each natural number n and each number x, define f_n(x)= (1-|x|^n)/(1+|x|^n) Find the function f: R -> R

### Simple quick intro calculus questions

1) Let f(x)= {-x+b, if x<-1 {5, if x=-1 {(-5/(x-b))+4, if x>-1 (and x=b) a) For what value(s) of b in f continuous at -1? b=________ b) For what value(s) of b does f have a removable discontinuity at -1? b=________ c) For what value(s) of b does f have an infinity discontinu

### Rate of Change

Suppose the amount of a mineral remaining in the bloodstream (in milligrams per cubic centimeter) "t" days after the initial injection is approximated by C(t)= (0.5)(6t+1)^(-0.5). Find the rate of change of the mineral level with respect to time for 0 days.

### Calculating the Volume of a Solid of Revolution

I have a general question regarding application of the general equation: volume= Pi * the integral of f(x)^2dx, from a to b This equation is used when revolving my function around y=0. what adjustment would I have to make to my equation to revolve my function around the line y=1 or any other line beside y=0?

### Implicit Function Theorem: Nonempty Open Set V

Determine whether the equation xyz + sin(x + y + z) = 0 can be solved for z in a nonempty, open set V containing the point (x, y, z) = (0, 0, 0). If it can, is the solution differentiable near the point (x, y) = (0, 0)? See the attached file. Solution to 11.6.2(a) is needed.

### Use the certain limit theorem to find the mean and standard

Use the certain limit theorem to find the mean and standard error of the mean of the indicated sampling distribution. Then sketch a graph of the sampling distribution. The per capita consumption of red meat by people in a country in a recent year was normally distributed, with a mean of 113 pounds and a standard deviation of 3

### L'hopital's Calculus Rule

I need help to find the indicated limit. I need to find the inderterminate form before applying the L'hopital's rule. on the first one. I need to find the derivative of the function for the next two. Please show work so I can understand better. Thanks

### Demand Equation: Cost, Revenue and Profit Calculations

A. Suppose a market research company finds that at a price of p = \$20, they would sell x = 42 tiles each month. If they lower the price to p = \$10, then more people would purchase the tile, and they can expect to sell x = 52 tiles in a month's time. Find the equation of the line for the demand equation. Write your answer in the

### Solving the differential equation.

I have this differential equation. y' = x^2*cos^2(y). I don't know if it's a separable differential equation or a first order differential equation. Please show me the steps in how to solve it. Thank you.

### Linear Functions

Answer the following questions and if required to do calculations please show your work: 1. What is a function? 2. What is a linear function? 3. What form does a linear function take? (I.e., What is the standard mathematical notation of a linear function?) 4. What is the formula for determining the slope of a li

### Determining Rate of Change: Example Problem

(a) Suppose the position of an object moving in a straight line is given by s(t)=5t^3 - t^2 +9. Find the instantaneous velocity when t=2. (b) Find the instantaneous rate of change for the function at the given value: f(x)= x^2 + 5x at x=2

### Interval Notation

1) Solve the following inequality. Write the answer in interval notation. X/X+3 ≤ -2/5(X-3) 2) Solve the inequality. 3 < |5X+3| < 5 3) a)Find an equation of the line, say y=mx+b, which passes through the point (-3,8) and is perpendicular to the line 3x+3y=33. y=? b)What is the shortest distance from the point (

### Calculus Elasticity

Elasticity Research has indicated that the demand for heroin is given by the function q=100p-0.17 a) Find E b) Is the demand for heroin elastic or inelastic? Solve this problem, show all steps used to solve the equation, and explain the answer to receive credit for the solution.

### Rate of Change of Number of Vehicles

The average number of vehicles waiting in a line to enter a parking ramp can be modeled by the function f(x) = (x2)/{(2(1-x)} where x is a quantity between 0 and 1 known as the traffic intensity. Find the rate of change of the number of vehicles in line with respect to the traffic intensity for the following values of the inte

### Evaluating integrals by parts: Example problems

Please see problems and show step by step solution in detail please. Evaluate the integral (using integration by parts): 1. t(lnt)^2 dt 2. x^3 (SQRT1-x^2) dx 3. sin(lnt)dt 4. ln(1+x^2)dx 5. x^2cos4x dx

### Put-Call Parity: One-Year European Call Option

Dynamic energy system stock is currently trading for \$33 per share. The stock pays no dividends. A one-year European put option on Dynamic with a strike price of \$35 is currently trading for \$2.10. If the risk-free interest rate is 10% per year, what is the price of a one-year European call option on Dynamic with a strike price

### Riemann integrable problem

Let f be continuous on [a,b] and suppose that f(x)>=0 for all x E [a,b]. Prove that if there exists a point c E [a,b] that f(c)>0, then b int a f> 0. Please refer to attached file for proper formatting.

### Parametric Curves...

For the parametric curve given by: x = e^(sqrt(t)) , y = t - ln(t^2) (a) find an equation of the tangent line to this curve at the point corresponding to t=1. (b) For what values of f is the tangent line vertical? (c) For what values of f is the tangent line horizontal?

### l'hopital and taylor series questions

Find lim┬(x→0+)⁡〖x^x 〗. (personal note: I think the approach is to use l'Hopital's rule) Prove that e is irrational. (hint: Suppose false, so that e = p/q where p,q ∈ N. Write e = e^1= P_n (1)+ R_n (1), multiple both sides by n! and deduce a contradiction when n ∈ N is sufficiently large). Expand the polynomia