Math Answers

Prove the limit by epsilon - delta definition lim (x^2+4)=13 when x tends to 3

Find domain and range of f(x)= 1/√(x^2-1)

Find domain and range of f(x)= 1/√(x-[x])

Find domain and range of f(x)= 1/(1-sinx)

If d2x/dt2+g(x-a)/b=0, (a, b, gbeing positive constants) and x = a′ and dx/dt=0 when t=0, show that x=a+(a'-a)cos {g underoot t/b}

Let X = {1,2,3}. Define a relation ∼ on P(X) by A ∼ B if A and B have the same number of elements.

Prove that ∼ is an equivalence relation and write down all equivalence classes of ∼.

At age 21 Julio begins saving ​$1 comma 250

each year until age 35 ​(15

​payments) in an ordinary annuity paying 5.7
​%
annual interest compounded yearly and then leaves his money in the account until age 65​ (30 years). His friend Max begins at age 41 saving ​$2 comma 500

per year in the same type of account until age 65​ (25 payments). How much does each have in his account at age​ 65?

Let X be a non-empty set, and let R be an equivalence relation on X. Let C be the set of all equivalence classes of R. So C={A⊆X such that A=[x] for some x ∈ X}.

Now, define f : X → C by the rule f(x) = [x] for all x ∈ X.

Suppose X = {1, 2, 3, 4, 5} and that R is an equivalence relation for which 1 R 3, 2 R 4 but 1 R̸ 2,1 R̸ 5,and 2 R̸ 5.

Write down the equivalence classes of R and draw a diagram to represent the function f.

Let X be a non-empty set, and let R be an equivalence relation on X. Let C be the set of all equivalence classes of R. So C={A⊆X such that A=[x] for some x ∈ X}.

Now, define f : X → C by the rule f(x) = [x] for all x ∈ X.

Prove that if x ∈ X, then there is one and only one equivalence class
which contains x.

Let X = {1,2,3}. Define a relation ∼ on P(X) by A ∼ B if A and B have the same number of elements.

Prove that ∼ is an equivalence relation. Write down all equivalence classes of ∼.