(1) Suppose that (an)neN is a sequence of positive numbers that converges to a positive real number a. (a) Show that there exists an M such that an > for all n > M. (b) Prove that lim loge (an) = loge (a) using the definition of convergence. (You may use the inequality | loge (x) - loge(y)| ≤ for x, y > 0.) |x-y min{x,y}

Q: Solve for X in the equation, where -5 5 2 2 5 -3 A = and B = -4 0 4 1 3 2 2X = 2A – B X =

A:

Q: 1. Solve using substitution 2x + y = 14   3x - 2y = 7

A:

Q: b by factory Solve -2 2p²² + p ²²-1 1 = 0 D

A:

Q: Solve the following equation. 35x-4 = 6

A:

Q: X= 4+ 2+X

A:

Q: 4) Solve for x: 3x-24 16 - 3x-12 12 = 3

A:

Q: Solve the following equation. 32x+3 = 12 x= (Type an exact answer.)

A: We have to find the value of x

Q: Solve: х? — 7х — -12 O x = -3, 4 O x = – ¤ = — 4, 3 х —D — 4, — 3 %3D Ox = 3, 4

A: The given quadratic equation is: x2-7x=-12

Q: Differentiate - 3x 1 X+- X,

A:

Q: Solve for x: 11 + 5x+ 2 = 33

A: 11+5x+2=33

Q: V8x +33= x + 6

A:

Q: 5. Solve each of the following equations for x: a. 3x+7=9x+1 b. 16+3 64*-5 =

A: Use the exponent rules: 1). amn=am·n 2). If am=an then m=n.     (a). The given equation is:…

Q: 3. Solvex+17 = 35

A: Given the equation  x5 + 17 = 35 We need to solve it. Now, x5 + 17 = 35 implies that  x5 = 35 - 17…

Q: Solve the following equation. 35x + 2 = 24

A: