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To evaluate the right-hand limit ($\lim_{x \to c^+} f(x)$), trace the graph starting from x-values greater than c and moving leftward toward c. Observe the height (y-value) that the curve approaches.

Conditions: Evaluating the limit from the right side (inputs strictly greater than c).; The graph shows a clear trend toward a finite y-level.

To evaluate the right-hand limit ($\lim_{x \to c^+} f(x)$), trace the graph starting from x-values greater than c and moving leftward toward c. Observe the height (y-value) that the curve approaches.

Conditions: Evaluating the limit from the right side (inputs strictly greater than c).; The graph shows a clear trend toward a finite y-level.

To find the left-hand limit as x approaches a value c (denoted $\lim_{x \to c^-} f(x)$), observe the behavior of the function's curve strictly for input values less than c, moving towards c. If the y-values grow without bound in either the positive or negative direction, the finite real limit does not exist.

Conditions: The function has a vertical asymptote or discontinuity at $x=c$.; You are evaluating the limit from the left side (inputs strictly less than c).

To find the left-hand limit as x approaches a value c (denoted $\lim_{x \to c^-} f(x)$), observe the behavior of the function's curve strictly for input values less than c, moving towards c. If the y-values grow without bound in either the positive or negative direction, the finite real limit does not exist.

Conditions: The function has a vertical asymptote or discontinuity at $x=c$.; You are evaluating the limit from the left side (inputs strictly less than c).