34) (t-4)+(-4t+1)
Answer: -3t-3
36) 3(x^3-3x^2)+2
Answer: 3x^3-9x^2+2
38) (3x-1)(x^3-2-2x)
Answer: 3x^4-x^3-6x^2-4x+2
Hello :
4cos60+3 tan pi/3= 4(1/2)+3(<span>√3)=2+3(1.71)= 7.13
because ; </span>cos60 = 1/2 and tan pi/3 =√3
-14.6, -1.295, 1.07, 24.6, 159
Hope that helps!
Given an ODE of the form

a regular singular point

is one such that

or

diverge as

, but the limits of

and

as

exist.
We have for

,

and as

, we have

and

, so indeed

is a regular singular point.
We then look for a series solution about the regular singular point

of the form

Substituting into the ODE gives




From this we find the indicial equation to be

Taking

, and in the

term above we find

. So we have

Since

, all coefficients with an odd index will also vanish.
So the first three terms of the series expansion of this solution are

with

,

, and

.