After login you will be able to create your own lists of problems.

Problems

Sort

Age

Difficulty

Found: 4

Problems Calculus Functions of one variable. Continuity Certain properties of a function and recurrence relations. Algebra Absolute value Inequalities containing absolute values Trigonometry Trigonometrical inequalities

15–16 4.0

Does there exist a function $f (x)$ defined for all $x \in R$ and for all $x, y \in R$ satisfying the inequality $| f (x + y) + \sin x + \sin y | < 2$ ?

Problem #PRU-111763

Problems Calculus Derivative Calculating a derivative Algebra Absolute value Inequalities containing absolute values Polynomials Quadratic polynomials

15–16 4.0

The quadratic trinomials $f (x)$ and $g (x)$ are such that $f^{'} (x) g^{'} (x) \geq | f (x) | + | g (x) |$ for all real $x$ . Prove that the product $f (x) g (x)$ is equal to the square of some trinomial.

Problem #PRU-86496

Problems Algebra Absolute value Inequalities containing absolute values

13–14 2.0

Solve the inequality: $| x + 2000 | < | x - 2001 |$ .

Problem #WSP-100023

Problems Algebra Absolute value Inequalities containing absolute values

10–14

Prove that $| x | \geq x$ . It may be helpful to compare each of $| 3 |$ , $| - 4.3 |$ and $| 0 |$ with $3$ , $- 4.3$ and $0$ respectively.