Advanced Calculus: power series, the pointwise and uniform convergence of sequences of functions, and the uniform limit of continuous continuous function

The question is in attached file.

Expanded Notation

Write each of the follwing sums in decimal form. a. 5(1/10)2+ 7(10)+ 3(1/10)5 (supposed to be exponent 2 and 5) b. 8(1/10)+ 3(10)3+ 9(1/10)2 (should be exp 3 and 2) c. 5(1/10)3+ 2(1/10)2+ (1/10)6 (should be exp 3,2,6)

arithematic equations

show that there are exactly four distinct sets of integers which satisfy the equations:

Cryptology

decipher the following CFQGE KAZEMF ZMAGVMC NMO VYSV which was obtained by a formula of the type y=kx (mod 26)

Decoding a message encoded in a columnar transposition cipher.

Use columnar transposition cipher with keyword: Greek (keep e's in order), to decode the following message: VOESA IVENE MRTNL EANGE WTNIM HTMEE ADLTR NISHO DWOEH

Factoring

Factor the following: a. 81a4- 16b4 (should be exponent 4) b. 12x2+ x- 35 (should be exponent 2)

equations.

Simplify the following expressions: a. 3x-2/2x2+x-3 Divide by 9x-6/2x-2 b.(108)1/2- (48)1/2+ (192)1/2 (should be exponent 1/2) c. (20x3+3x2-4x+5)/(4x2+3x-7) (should be exponent 3 and 2,2).

Business Mathematics/problem solving

Joe's Sporting Goods store sold 25 cans of tennis balls last Friday some at $3.00 each, and the rest at $2.00 each. If the store's sales for the tennis balls totaled $60.00, how many cans of each were sold?

Business Math

Determine if the point (-5, 4/5) falls on the line passing through the points (-2,-1) and (3,-4).

Business Math

Solve for x,y,z in: 3x-y-z= -1/2 2x+y+4z=0 4x+3y+5z=6