Use Euler's method with each of the following step sizes to estimate the value of y(0.8), where y is the solution of the initial-value problem: y' = y, y(0) = 5.

(i)    h = 0.8

y(0.8) = 9

(ii) h = 0.4

y(0.8) = 9.8

(iii)    

h = 0.2

y(0.8) = ?

The error in Euler's method is the difference between the exact value and the approximate value. Find the errors made in part (a) in using Euler's method to estimate the true value of y(0.8), namely 5e^0.8.

(Round your answers to four decimal places.)

1. solve the initial value problem.

(t^(2)+1)y'+2ty=tant , y(0)=2

2.find the solution to this initial value problem.

yy'=e^x+x , y(0)=y_0

y_0 is a nonzero constant.

The exponent rules are needed in order to perform operations on polynomials. In your own words:
Explain what a polynomial is and identify the different parts of a polynomial
Explain the different labels used to categorize polynomials
Explain how addition and subtraction of polynomials is accomplished
When multiplying polynomials, we are taking every term of one polynomial and multiplying them by every term of the second polynomial, then collecting like terms- explain how foil helps us to accomplish this, and what category of polynomials foil applies to
There are two special case products where the product takes on special patterns- explain these two cases and when they occur
For each of the two special cases, illustrate your explanation with an appropriate exercise from the text (note the pg. and exercise number in your post), showing how the multiplication is performed using the special pattern formula, then also showing the same result using foil.

Using a scalar surface integral, compute the surface area of the portion of the unit
sphere that is above the cone z = sqrt(x^2+y^2)

Factor the following:

a) f(x)=x^5+5x^4-21x^3-137x^2-88x+240, knowing that f(5)=0 and f(-3)=0.

b) f(x)=x^3+8x^2+5x-50

c)f(x)=-x^4-4x^3+19x^2+46x-120, knowing that (x+5) and (x-2) are factors.

Consider the function and the value of a.

f(x) =

, a = 9. (a) Use m_tan = lim h→0

to find the slope of the tangent line m_tan = f '(a).

m_tan =  

(b)Find the equation of the tangent line to f at x = a.

(Let x be the independent variable and y be the dependent variable.)

Evaluate the integral. (Use C for the constant of integration.)

(x^2-1)/(sqrt(25+x^2)*dx

Evaluate the integral. (Use C for the constant of integration.)

dx/sqrt(9x^2-16)^3

Evaluate the integral. (Use C for the constant of integration.)

3/(x(x+2)(3x-1))*dx

?" + 3?′ + 2? = ????, ?(0) = 0, ?′(0) = 2

1) Please solve using an annihilator

2) Please solve using the Method of Variation of Parameters

Thank you.

A bicycle shop sells two styles of a road bike, 10-speed and 14-speed. During the month of September, the management expects to sell exactly 45 road bikes. The monthly profit is given by P(x,y)=−(1/9)x^2−5y^2−(1/9)xy+10x+65y−100, where x is the number of 10-speed road bikes sold and y is the number of 14-speed road bikes sold. How many of each type should be sold to maximize the profit in September?

Instructions: For each solid described, set up, BUT DO NOT EVALUATE, a single definite integral that represents the exact volume of the solid. You must give explicit functions as your integrands, and specify limits in each case. You do not need to evaluate the resulting integral.

1. The solid generated by rotating the region enclosed by the curves y = x^2 and y = x about the line x-axis.