Math Problem Statement

Use the graph to find the indicated limits.

Step 1 of 3 :

Find limx→2−f(x).

x−10 −5 5 10 y−10 −5 5 10 Cartesian Coordinate PlaneThe horizontal axis is labeled with x. The horizontal axis contains 21 grid lines, starts at -10, and ends at 10; and the axis is labeled with the values: -10, -5, 5, 10.The vertical axis is labeled with y. The vertical axis contains 21 grid lines, starts at -10, and ends at 10; and the axis is labeled with the values: -10, -5, 5, 10.Piecewise GraphThe graph is made up of a set of different curves, defined over the 2 regions,for the curves: Left Curve and Right Curve.Region 1The region of the coordinate plane containing horizontal values to the left of the value 2 units right of the origin and all vertical values.Left CurveA solid curve is drawn with the equation f(x)=34x−2+4.Left Curve AsymptoteA dashed vertical line segment is drawn 2 units right of the vertical axis.Region 2The region of the coordinate plane containing horizontal values to the right of the value 2 units right of the origin and all vertical values.Right CurveA solid curve is drawn with the equation f(x)=12(x−2)⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√2+3to the right of the endpoint Right Curve Endpoint.Right Curve EndpointAn open circle drawn 2 units right of and 3 units above the origin.

Answer

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Solution

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Math Problem Analysis

Mathematical Concepts

Limits
Piecewise Functions
Left-Hand Limit

Formulas

f(x) = (3 / (4x - 2)) + 4

Theorems

Limit Theorem
Continuity and Discontinuity Theorems

Suitable Grade Level

Grades 11-12