1. determine id the functions f1(x)=0, f2(x)=0, f3(x)=e^x are linear independent on the interval (-infinity, infinity)
2.for the ode y''-4y=0,
a) verify if y1=cosh2x, y2=sinh2x form a fundamental set of the solutions of y''-4y=0
b) form the general soulution of the ode y''-4y=0
3. a) verify if y(subscript)p=3e^2x is a particular solution of the ode y''-6y'+5y=-9e^2x
b) verify if y(subscript)p=x^2+3x is a particular solution of the ode y''-6y'+5y=5x^2+3x-16
c) find a particular solution of the ode y''-6y'+5y=10x^2+6x-32+9e^2x
d) verify y=c1e^x+c2e^5x is the gerneral solution of the homogeneous ode y''-6y'+5y=0
e)form the general solution of the nonhomogeneous ode y''-6y'+5y=10x^2+6x-32+9e^2x

answer: on graphs, the open and closed circles, or vertical asymptotes drawn as dashed lines us identify discontinuities.

as before, graphs and tables allow us to estimate at best.

when working with formulas, getting zero in the denominator indicates a point of discontinuity.

when working with piecewise-defined functions, check for discontinuities at the transition points where one piece ends and the next begins.

step-by-step explanation:

a

step-by-step explanation:

constant of proportionality = 3 and the equation is c = 3p.

step-by-step explanation:

c = kp   where c = amount of caffeine in mg., p = oz of pepsi and k is the constant of proportionality.

substituting the values given:

24 = 8k

k = 3.

the same value of k will be obtained if we substitute the other given values.