Math Answers

-Find the derivative of f(x) = 8x2 + 11x at x = 7.

-Find the derivative of f(x) = 3x + 8 at x = 4.

-Find the derivative of f(x) = 5 divided by x at x = -1.

-Find the derivative of f(x) = negative 7 divided by x at x = -3.

Prove that for all integers n with 1≤n≤10,n^2 −n+11 is prime.

Prove that for all positive integers n
3^n +7^n −2 is divisible by 8

Let X = {0, 1, 2}. Consider the power set P(X). Recall that P(X) = {A such that A ⊆ X}.
Determine if each statement is true or false. (a) X ∈ P(X).
(b) ∅∈P(X)
(c) X ⊆ P(X).
(d) {0,2}∈P(X) (e) {0,2,1} ∈ X (f) {0}⊆X
(g) {{0}} ⊆ P(X)

Define the relation R as
R = {(a, b)|a, b ∈ Z, 4 divides a − b}. Show that R is reflexive, transitive and symmetric.

Prove that 3n2 − n + 10 is an even integer for all integers n. (Hint: Prove the statement
true when n is odd, then prove it is true when n is even.)

Write down the contrapositive of the statement “If 3n2 + 4 is even then n is even.” Then prove the statement for all integers n.

Prove that
A − (B ∪ C) = (A − B) ∩ (A − C),

Prove that for all sets A and B,
A ∪ B^c = B^c ∪ (A ∩ B).

Prove that
A − (B ∪ C) = (A − B) ∩ (A − C),
for sets A, B and C.