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Lecture

# 7.3 Curve Sketching .pdf

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School
Simon Fraser University
Department
Mathematics
Course
MATH 157
Professor
Chiaka Drake
Semester
Fall

Description
Chapter 7.3 Curve Sketching Limits and one-Sided Limits of Infinity: If f (x) becomes ______________ large in __________________ (positive or negative) as x approaches the number a from the left side, then the limit does _____ exist , but we can write lim f (x) or lim f (x) . Similarly for x a x a right side, lim f (x) or lim f (x) . x a x a Note 1: The line x a is a _____________ asymptote of the curve y f (x) if at least one of the following is true: xlia f (x) xia f (x) lxmaf (x) lim f (x) lim f (x) lim f (x) x a x a x a Example 2x,x 3 Q1: Given f (x) 4 , find the following limits, x 5 ,x 3 if they exist: a) xi5 f (x) b) lim f (x) x 5 c) lim f (x) x 5 3 RECALL – Horizontal Asymptotes: If xim f (x) L, then _______ is a horizontal asymptote . Similarly, if xlim f (x) M , then _______ is a horizontal asymptote . Curve Sketching Guidelines: I suggest you do the following steps in ____________ in order to sketch the graph of a function f . 1. Determine the __________, and where the function is ____________. 2. Find all ____________. Graph them, if any. 3. Determine if there are any ____________ asymptotes (x ,x ). Graph them, if any. 4. Determine if there are any ____________ asymptotes (x undefined place ). Graph them, if any. 5. Find f . 4 6. Find the ____________ numbers c ,c ,... 1f 2 and all x-values where f is ____________ u ,u ,...1 Us2 these numbers to make a ________ for f and f . 7. Apply the ____________ Test to determine intervals of ____________ and ____________. 8. Apply the ________ Derivative Test to determine ____________ and ____________ points. Graph them, if any. Add max, min mini-sketch: . 9. Find f . 10. Find the ____________ numbers c ,c ,... 1f 2 and all x-values where f is ____________ u ,u ,...1 Us2 these numbers to make a ________ for f and f. 11. Apply the ____________ Test to determine intervals of ____________ and ____________. 12. Find all ____________ points. Graph them, if any. Add inflection mini-sketch according to concavity table: . 13. Use both ________ to complete the sketch of the graph and don’t forget to ________ the graph f . 5 Examples Q2:
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