In Exercises 7 - 14 , determine the limit by substitution. Support graphically. lim x →2 √( x +

step 1 Exercise 14 asks you to determine the limit by substitution and to support it graphically. So th

In Exercises 7 - 14 , determine the limit by substitution....

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Key Concepts

Limit of a Function

A limit describes the behavior of a function as the input approaches a particular value. It is a fundamental concept in calculus that helps in understanding how functions behave near points of interest, even if the function is not defined at that point.

Direct Substitution

Direct substitution is a method for evaluating limits by simply replacing the variable with the value it is approaching. This method works when the function is continuous at the point of interest, meaning there are no discontinuities or undefined operations.

Continuity

Continuity is a property of functions where a function has no breaks, jumps, or holes at a point, and the limit of the function as it approaches that point equals the value of the function at that point. This is a key factor in determining if direct substitution is applicable.

Graphical Analysis

Graphical analysis involves using visual representations like graphs to understand the behavior of a function. It is used to confirm the results of limit calculations by showing that the function approaches a specific value as the input nears a given point.

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