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MATH 2250 (41)
Segars (3)
Lecture 1

MATH 2250 Lecture 1: MATH 2250 Part 1
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Department
Mathematics
Course
MATH 2250
Professor
Segars
Semester
Spring

Description
falling object Galileo's L. a IN y distance fallen in fee wher c at a elapsed time. a Aug speed on Co, Ia total distance A y -rata time AX DANg speed on t ELCI, SJ 0hs.eru ati on The speed Over Some interval is the slope of -tan lint Connect in line th two end poin of the inter X linn. flx DNE X- 0 lim ONE. X 20 falling object Galileo's L. a IN y distance fallen in fee wher c at a elapsed time. a Aug speed on Co, Ia total distance A y -rata time AX DANg speed on t ELCI, SJ 0hs.eru ati on The speed Over Some interval is the slope of -tan lint Connect in line th two end poin of the inter X linn. flx DNE X- 0 lim ONE. X 20Limit Theo cms 1) Limits of Polynomial s polynomial. Then 2) Limits of Rational Eunction s Ca mati o of patybomiais Let and be polynomials Then, Examples The problems denominato O For example, X20 m 13 NII must b 7 facto NOLDNE 20 Theorem 5 all x in Sam co-open interval f fux ex for containing c exce pt ssi 4 at x c and if lim Cx) exists and lime x Cxis 1 them one sided Limits fux) is the limit from vight sid onl linn NOTE-iim f exists if lim lim -fox) lina ILY 2 lim f.Lx DNE. lim f CAD DNE. Limit Theo cms 1) Limits of Polynomial s polynomial. Then 2) Limits of Rational Eunction s Ca mati o of patybomiais Let and be polynomials Then, Examples The problems denominato O For example, X20 m 13 NII must b 7 facto NOLDNE 20 Theorem 5 all x in Sam co-open interval f fux ex for containing c exce pt ssi 4 at x c and if lim Cx) exists and lime x Cxis 1 them one sided Limits fux) is the limit from vight sid onl linn NOTE-iim f exists if lim lim -fox) lina ILY 2 lim f.Lx DNE. lim f CAD DNE.lim Singh) 3 Csin h lim lim X n x Ca S X. sin 3X DNA greatest integer flkn 1x1 has a "Jump" discontinuity at euenJ infinit c disco minuity infinite discontin kumovable hole can be plugged With a single Def- A continuous function is a punct on that is continuous at ew point in its Ave these Can tinuous domain LI tan XL lim Singh) 3 Csin h lim lim X n x Ca S X. sin 3X DNA greatest integer flkn 1x1 has a "Jump" discontinuity at euenJ infinit c disco minuity infinite discontin kumovable hole can be plugged With a single Def- A continuous function is a punct on that is continuous at ew point in its Ave these Can tinuous domain LI tan XLFind the slape of the Cuvvc at paint P. Choose points close to x and ca cutate slope f secent line. Slope of Secent line is lim Csope secant ope tangent S Theorem a Composite Functions f fCx) is continuous at X c and qLx) is continuous at fcc) thcn gCfCx)) is continuous hcorcmu L0 Limits Continuous Functions ct g CX) be continuous at x b and let Continuous Extension to a Point Note FCA) ONE at x 3 2) lim fux So we can deri ve a nens function 2 when x is the continuo tension of f Lx) at Notice f is not defined at x x 2. im CX) So F 3 is the continuous extension 2.le Limits Involving Infinity M for Somc m means as X gets close to L. And, an for Le fCX Tho be as Close to Las T. wish by choosing enough Find the slape of the Cuvvc at paint P. Choose points close to x and ca cutate slope f secent line. Slope of Secent line is lim Csope secant ope tangent S Theorem a Composite Functions f fCx) is continuous at X c and qLx) is continuous at fcc) thcn
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