(a) The first four Hermite polynomials are 1,2t,−2+4t2, and −12t+8t3. These polynomials arise naturally in the study of certain important differential equations in mathematical physics. Show that the first four Hermite polynomials form a basis of P3.(b) The first four Laguerre polynomials are 1,1−t,2−4t+t2, and 6−18t+9t2−t3. Show that these four Laguerre polynomials form a basis of P3.

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2

207/8 is the right

answer:

your answer is: c. 196 7/8 in^3.

1. 3. can also be expressed as (22/7)

2. -4.5

3. 3.6

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