Solve the first-order linear recurrence T(n) = 8T(n-1) +4", T(0) = 9 by finding an explicit closed formula for T(n) and enter your answer in the box below. T(n) =

Q: - (3) Show that for a, b € R we have a + b + |a − b] = 2 max{|a|, |b|}.

A: Solution:

Q: Show that an = 1/2n + 1 is decreasing.

A: Given: an=12n+1 Substitute 1 for n in the equation an=12n+1. a1=12(1)+1=13=0.333

Q: = Solvex (t) = Ax(t) where A 3 -2 [1] [8] = 4 and (0)

A:

Q: d The constant term of (x¹ - 3)º e The last term of 2 G- 3

A: It is related to binomial expansion : 1: the constant term of (x⁴ - 3)⁹ 2: the last term of ( -2x² -…

Q: If f(1) = 9 and f(n) = -3f(n – 1) – n then find the value of f(5).

A: Given ,  f(1) = 9  &  f(n) = -3 f(n - 1) - n  We have to find f(5)  Put , n = 2

Q: A particular road is used by N drivers each day. Each driver obtains a benefit v from the journey…

A:

Q: find the general solution to Ut – 2Ux = 0 |

A:

Q: Evaluate S(3) if S(r) = 4xr².

A: Given query is to find the value of S(3).

Q: 2. Show that (2x + i)(2x– i) = 4x +1 %3D |

A: Prove the equation

Q: (1,k,-1)x(-k,-4,2)=(2,1,5). Find k.

A: In vector calculus, the cross product of two vectors results in a third vector that is perpendicular…

Q: Find (f + g)(x) if f(æ) = V16a4 and 9(2) = 3a? – 3a – 5. %3D (f + 9)(x) = 0² + 3 + 5 O (f + 9)(x) =…

A: