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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-79402

Problems Calculus Number sequences Limit of a sequence, convergence Algebra Trigonometry Trigonometrical inequalities

15–16 4.0

Prove that the sequence $x_{n} = \sin (n^{2})$ does not tend to zero for $n$ that tends to infinity.