Calculus Answers

The weekly sales (RS) at a big store x weeks after the end of an advertising campaign are given

by S(x)= 5000+

5000

X+5 Find the sale for the indicated week's limits

a) S(2),

b) lim S(x)

1) Find the following limit:  lim (x→0) ln(1 + (sin(2x))^2 )/ (1 − cos2(x)).

2) Determine type of the differential equation y`` − 2y` + y = sin x:

◦ partial differential equation.

◦ first order differential equation.

◦ linear differential equation with constant coefficients.

◦ linear nonhomogeneous differential equation.

◦ nonlinear homogeneous differential equation.

3) Write general solution of the differential equation x^(2) y'' + xy' + a^(2) y = 0:

◦ Ax^2 + Bx

◦ Ax^a + Bx^−a

◦ Ax^ia + Bx^−ia

◦ Ae^ax + Be^−ax

◦ Ae^iax + Be^−iax

◦ explicit algebraic form does not exist.

Find the general solution given y₁=x² is a particular solution of x^2y"-3xy'+4y=0.