Use the Graphs of F and G Below to Evaluate $\lim _ { x \rightarrow - 2 } [ f ( x ) + g ( x ) ]$

question 46

Essay

Use the graphs of f and g below to evaluate each limit, if it exists. If it does not exist, explain why. (a) $\lim _ { x \rightarrow - 2 } [ f ( x ) + g ( x ) ]$ (b) $\lim _ { x \rightarrow 2 } \left[ \frac { g ( x ) } { f ( x ) } \right]$ (c) $\lim _ { x \rightarrow 1 } [ f ( x ) \cdot g ( x ) ]$ (d) $\lim _ { x \rightarrow 0 } \left[ ( x - 3 ) ^ { 2 } \cdot g ( x ) \right]$

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Definitions:

Flooding

A psychological exposure therapy technique for reducing phobias or anxiety disorders by exposing the patient to their fear at full intensity.

Behavior Therapy

A form of psychotherapy that focuses on changing undesirable behaviors through conditioning techniques, without necessarily addressing underlying psychological conditions.

Transference

In psychoanalysis, the process by which patients project feelings about important people in their lives onto the therapist.

Resistance

The opposition or counteracting force in various contexts, such as psychological resistance to change or physical resistance in electrical conductance.