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:

Research Methods

Systematic approaches to conducting scientific investigations, including both qualitative and quantitative techniques.

Scientific Investigation

A methodical approach to research where scientists formulate hypotheses, collect and analyze data to draw conclusions.

Data Collection

The systematic approach to gathering and measuring information from varied sources to get a complete and accurate picture of an area of interest.

Operational Definition

A clear, precise criteria for defining a term specifically within the context of an experiment or study.