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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 3E

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Directions: Use the definition of continuity to determine whetherfis contimuous at e. Identify the type
of discontimuity whenever there is one.
1. Given:
f-6x-6, x=1
ste) = {*-
Condition 1
Condition 2
Condition 3
23-24.
25-26
27-30. What kind of discontinuity? Why

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If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?
Determine if the statemment is true or false. If the statement is false, then correct it and make it true. If the function f increases on the interval -,x1 and decreases on the interval x1,, then fx1 is a local minimum value.
Show that the function “f” is discontinuous at x=0. Is it a removable discontinuity? Sketch “f” neatly Show all the steps for the continuity test
Find the values of a and b that make f continuous at all points in its domain. For a complete solution, it is recommended to make explicit reference to the definition of continuity at a point in your work.
1. For what value of k is the function h(x) continuous on the whole real line? HINT:Use definition of continuity. h(x) = {2x + kx2, x < 2} {x3 - kx, x ≥ 2}
Use the definition of continuity, along with the One- sided continuity theorem, to determine whether the following function is continous at x=4. Also discuss whether the function is left-continuous and/ or right-continous at 4. f(x)={3 if x=4 {|3x-12|/x-4 if x not equal to 4 Refering to graph or a table of value will earn zero credit.
Identify the type of discontinuity at x= 0.a) Removable Discontinuity b) Essential infinite Discontinuity c) Essential Jump Discontinuity
Prove, using the definition of continuity from the topological point of view, that the constant function f(x)=5 (with x∈R with the usual topology) is continuous. Why is it continuous even though the inverse image of a closed in R (the point y=5) is R? Please be as clear as possible with the last question. Thank you
Let h(x) = {x^2 +3, x<2 {5, x=2 {1/x-2, x>2 Determine the continuity of h(x) at/over the following point/interval. Classify the discontinuity if h(x) is discontinuous at the given point. Provide concise justifications for your answers a. x= 2 b. (0,2] c. (2,∞)
Solve using a theorem or definition for uniform continuity.
3. Prove fx=3x-5 is continuous at x=-1 using the definition of continuity where , f: R → R and R has the usual metric, dRx,y=| x-y |
5. Use the continuity test to verify which of the following functions are continuous at specified points. 6. Find the vertical and/or horizontal asymptotes of the following functions

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