question 8

Essay

$$\text { Show that the function } f ( x ) = ( x + 2 ) \log \left( x ^ { 2 } + 1 \right) + \log \left( x ^ { 3 } + 1 \right) \text { is } O ( x \log x ) \text {. }$$

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Definitions:

Cramming

A study technique involving intense memorization and learning in a short period, usually right before an examination.

Learning and Memory

The processes by which new information is encoded, stored, and retrieved, essential for adapting and responding to new experiences.

Ebbinghaus

Hermann Ebbinghaus was a German psychologist known for his pioneering work on memory, particularly the discovery of the forgetting curve, which describes the rate at which information is lost over time if there is no attempt to retain it.

Working Memory

A cognitive system responsible for temporarily holding information available for processing, critical for reasoning and the guidance of decision-making and behavior.