2x + 13 h(x) x - 4 x2 – x - 12 (a) At what x-values is the function h(r) discontinuous? For each point of discontinuity, classify it as either a removable, jump, or infinite discontinuity. Fully justify your answers by showing (without a graph) it meets the criteria for the claimed discontinuity type. (b) Show that h(x) = x² for some x in the interval (0, 2]. %3D
2x + 13 h(x) x - 4 x2 – x - 12 (a) At what x-values is the function h(r) discontinuous? For each point of discontinuity, classify it as either a removable, jump, or infinite discontinuity. Fully justify your answers by showing (without a graph) it meets the criteria for the claimed discontinuity type. (b) Show that h(x) = x² for some x in the interval (0, 2]. %3D
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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Consider the function attached below. May you help me learn how to solve A and B?
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Step 1 First part (a)
Rational functions are discontinuous for the values of x, where they are not defined.
Note that since, the rational function, is real valued function, so, the denominator of any fraction must be non-zero.
Thus, the function is discontinuous when which gives , to be the only discontinuities.
Removable Discontinuity: If the continuity can be removed by simple algebraic methods.
Note that .
So, after algebraic manipulation there is no discontinuity at , hence, it is a removable discontinuity.
Infinite Discontinuity: If either of the right hand limit and left hand limit at the point of discontinuity are infinite.
Note that
So, the discontinuity at is infinite discontinuity.
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