Search & Filtering
Let x ∈ R such that
(2021 −2020/n)≤ x ≤( 2021 +2020/n)
for all positive integer n ≥ 10. Prove that x = 2021.
The annual profit for the firm depends upon the number of units produced. Specifically the function which describes the relationship between profit P (stated in dollars) and the number of units produced x is
P=-0.01x^2+5000x-25000
a) Determine the number of units x which will result in maximum profit.
b) What is the expected maximum profit?
Prove that |x+y+z|<=|x|+|y|+|z|
Differentiate: 2arcsin(y/2)+√(4-y^2)
Let n ∈ N. Prove that n^(1/k) is irrational unless n = m^k
for some m ∈ N.
Show that for every real number x > 0, there exists a real number y > 0 such that |2x + y| = 5
Show that there is real number x so that |x−1| = |x−2|.
Prove that the set A given by A:={2020/n +n² : n∈N} is unbounded above.
Use induction to prove that 1³+2³+...+(n−1)³ < n⁴/4 < 1³+2³+...+n³
Express the following function, F(x), as a composition of two functions, f and g. f(g(x)).
F(x)= x^2/(x^2+4)
Verify that f(g(x)) = F(x)
