Given That $\lim _ { x \rightarrow 3 } f ( x ) = 5 , \lim _ { x \rightarrow 3 } g ( x ) = 0 , \text { and } \lim _ { x \rightarrow 3 } h ( x ) = - 8 \text {, }$

question 83

Essay

Given that $\lim _ { x \rightarrow 3 } f ( x ) = 5 , \lim _ { x \rightarrow 3 } g ( x ) = 0 , \text { and } \lim _ { x \rightarrow 3 } h ( x ) = - 8 \text {, }$ find the following limits, if they exist. If a limit does not exist, explain why.(a) $\lim _ { x \rightarrow 3 } ( f ( x ) + h ( x ) )$ (b) $\lim _ { x \rightarrow 3 } x ^ { 2 } f ( x )$ (c) $\lim _ { x \rightarrow 3 } f ^ { 2 } ( x )$ (d) $\lim _ { x \rightarrow 3 } \frac { f ( x ) } { 2 h ( x ) }$ (e) $\lim _ { x \rightarrow 3 } \frac { g ( x ) } { f ( x ) }$ (f) $\lim _ { x \rightarrow 3 } \frac { f ( x ) } { g ( x ) }$ (g) $\lim _ { x \rightarrow 3 } \frac { 2 h ( x ) } { f ( x ) - h ( x ) }$ (h) $\lim _ { x \rightarrow 3 } \sqrt [ 3 ] { h ( x ) }$

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Definitions:

Dysfunctional Environment

A workplace or organizational setting that is characterized by conflict, poor leadership, and low morale, adversely affecting productivity and well-being.

Enlightened Workplace

is an organizational setting that prioritizes employee well-being, ethical practices, and a positive, inclusive culture.

McGregor's Prescriptions

Approach proposed by Douglas McGregor in management theory, advocating for leadership and motivational strategies based on the assumptions of Theory X and Theory Y.

Morale Problem

A situation in an organization where employee confidence, enthusiasm, and discipline are significantly diminished.