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Projected learning outcomes: Attempt to interpret and understand the definition of a limit This will give the main idea behind the mathematical proof of the limit of in Equation 1, as the continuity of functions of the form f(x) = frequently, further illustrating that there are will use in this course as well 0. We will refer back to this fact proof) behind the "facts" we directly) mx + 6 for m (i.e we will not have time to cover every such reason logical reasons а (even though Problems 1. Adapt the work on the first example from Supplemental Lecture 2 to show by the definition of the limit that for any real numbers a, b, m with m / 0, we have that lim (mx (1) та + b. х—а Hint: First state what you wish to accomplish by interpretting the meaning of Equation (1). Then use your interpretation and the guidance from the supplemental lecture notes to find positive function 5(e) which works. Recall that, when multiplying inequality by a number, you keep track of whether this number is positive or negative (since such an operation will preserve or reverse the inequality, respectively) а dividing both sides of or an Lucture Supplament 2 We ux he rigorous detiaitim of a lmit a few ean.pls Exnafla' Ue definim of imtto shou thatli 2x = 2. x1 We st find 04 /x-i1<5Ce) guarau tes 2 x -2

Projected learning outcomes: Attempt to interpret and understand the definition of a limit This will give the main idea behind the mathematical proof of the limit of in Equation 1, as the continuity of functions of the form f(x) = frequently, further illustrating that there are will use in this course as well 0. We will refer back to this fact proof) behind the "facts" we directly) mx + 6 for m (i.e we will not have time to cover every such reason logical reasons а (even though Problems 1. Adapt the work on the first example from Supplemental Lecture 2 to show by the definition of the limit that for any real numbers a, b, m with m / 0, we have that lim (mx (1) та + b. х—а Hint: First state what you wish to accomplish by interpretting the meaning of Equation (1). Then use your interpretation and the guidance from the supplemental lecture notes to find positive function 5(e) which works. Recall that, when multiplying inequality by a number, you keep track of whether this number is positive or negative (since such an operation will preserve or reverse the inequality, respectively) а dividing both sides of or an Lucture Supplament 2 We ux he rigorous detiaitim of a lmit a few ean.pls Exnafla' Ue definim of imtto shou thatli 2x = 2. x1 We st find 04 /x-i1<5Ce) guarau tes 2 x -2

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Example number 1 on the second image is where 'Example' appears first followed by the example.

Projected learning outcomes: Attempt to interpret and understand the definition of a limit This will give the main idea behind the mathematical proof of the limit of in Equation 1, as the continuity of functions of the form f(x) = frequently, further illustrating that there are will use in this course as well 0. We will refer back to this fact proof) behind the "facts" we directly) mx + 6 for m (i.e we will not have time to cover every such reason logical reasons а (even though Problems 1. Adapt the work on the first example from Supplemental Lecture 2 to show by the definition of the limit that for any real numbers a, b, m with m / 0, we have that lim (mx (1) та + b. х—а Hint: First state what you wish to accomplish by interpretting the meaning of Equation (1). Then use your interpretation and the guidance from the supplemental lecture notes to find positive function 5(e) which works. Recall that, when multiplying inequality by a number, you keep track of whether this number is positive or negative (since such an operation will preserve or reverse the inequality, respectively) а dividing both sides of or an
Transcribed Image Text:Projected learning outcomes: Attempt to interpret and understand the definition of a limit This will give the main idea behind the mathematical proof of the limit of in Equation 1, as the continuity of functions of the form f(x) = frequently, further illustrating that there are will use in this course as well 0. We will refer back to this fact proof) behind the "facts" we directly) mx + 6 for m (i.e we will not have time to cover every such reason logical reasons а (even though Problems 1. Adapt the work on the first example from Supplemental Lecture 2 to show by the definition of the limit that for any real numbers a, b, m with m / 0, we have that lim (mx (1) та + b. х—а Hint: First state what you wish to accomplish by interpretting the meaning of Equation (1). Then use your interpretation and the guidance from the supplemental lecture notes to find positive function 5(e) which works. Recall that, when multiplying inequality by a number, you keep track of whether this number is positive or negative (since such an operation will preserve or reverse the inequality, respectively) а dividing both sides of or an
Lucture Supplament 2 We ux he rigorous detiaitim of a lmit a few ean.pls Exnafla' Ue definim of imtto shou thatli 2x = 2. x1 We st find 04 /x-i1<5Ce) guarau tes 2 x -2<E positive fnetion E that Phnt Frmunty to bid a quess r5 we worle acewods First ne consider that 2x-21=2(x-) = 121-I-1 2-l< 1 w 2x-1, Sioe 20 ued to Since 270 we may divida 2 while pradring both sides of this e inquality JK-1 take 5)= Thus we 0 k-1< what that tt fallows tt when 2-21=12(a-)= 12l- 2«1x-|522 =E. Sine 20 Tolt As a ol e hawe Pamare Fov asns 5- prots are preated in fhe opporife ordkr Haveer, at thic leel pertminivg to mutlernatical logic, mere Concerred we Cfe fmhion Ce widh weras Plene beadrare at there is are addifiona dresks to be made to rewrite this as a proof
Transcribed Image Text:Lucture Supplament 2 We ux he rigorous detiaitim of a lmit a few ean.pls Exnafla' Ue definim of imtto shou thatli 2x = 2. x1 We st find 04 /x-i1<5Ce) guarau tes 2 x -2<E positive fnetion E that Phnt Frmunty to bid a quess r5 we worle acewods First ne consider that 2x-21=2(x-) = 121-I-1 2-l< 1 w 2x-1, Sioe 20 ued to Since 270 we may divida 2 while pradring both sides of this e inquality JK-1 take 5)= Thus we 0 k-1< what that tt fallows tt when 2-21=12(a-)= 12l- 2«1x-|522 =E. Sine 20 Tolt As a ol e hawe Pamare Fov asns 5- prots are preated in fhe opporife ordkr Haveer, at thic leel pertminivg to mutlernatical logic, mere Concerred we Cfe fmhion Ce widh weras Plene beadrare at there is are addifiona dresks to be made to rewrite this as a proof
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