×

### Let's log you in.

or

Don't have a StudySoup account? Create one here!

×

or

22

0

13

# Class Note for MATH 1431 with Professor He at UH

Marketplace > University of Houston > Class Note for MATH 1431 with Professor He at UH

No professor available

These notes were just uploaded, and will be ready to view shortly.

Either way, we'll remind you when they're ready :)

Get a free preview of these Notes, just enter your email below.

×
Unlock Preview

COURSE
PROF.
No professor available
TYPE
Class Notes
PAGES
13
WORDS
KARMA
25 ?

## Popular in Department

This 13 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 22 views.

×

## Reviews for Class Note for MATH 1431 with Professor He at UH

×

×

### What is Karma?

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 02/06/15
Lecture 5Section 31 The Derivative Jiwen He 1 Review 11 Info Homework and Quizzes Homework 2 amp 3 o Homework 2 is due today in lab 0 Homework 3 is due September 16th in lab Online Quizzes o Quizzes 1 and 2 have expired 0 Quiz 3 is posted and due on this Friday before 1159 PM 0 Quiz 4 is posted and due 919 Weekly Written Quizzes in Lab 0 Quizzes will be given every week on Thursday in lab beginning THIS WEEK 0 The weekly written quizzes form is posted on the course homepage You must print out this form and BRING it to class every Thursday Daily Grades 0 Daily grades start Today 0 The daily grades form is posted on the course homepage You must print out this form and BRING it to class every day Quiz 1 Quiz 1 902 1 hrn x gt1 13 1 a 1 b 2 C 1 d None of these Quiz 2 Quiz 2 Classify the discontinuity at 36 1 for 902 1 a Jump b In nite C Removable d None of these 12 The Pinching Theorem The Pinching Theorem 2 Theorem 1 Let p gt 0 Suppose that for all 36 such that 0 lt 30 0 lt p M90 S ft S WE If lirn L and lirn 930 2 L than lirn L lihe Pincihing Theorem Continuity of Sine and Cosine eorem lim sinx 0 lim cosx 1 r gt0 r gt0 lim sinx sin 0 lim cosx cos c ZU N LC N 0 lt lsinxl lt lxl l d 3w i 7 Isin xl m L 1 B r J he Pinclrgng Theorem I rigonometric Limits eorem sinx 1 cosx 11m 1 11m r gt0 L r gt0 IL O 1 tan x Proof Use Geometric argument to get sinz coszlt lt1 7 then apply the pinching theorem MiBErgkiggnometric Limits lim 1 i sinm z m for m near 0 070 Sinz Theorem 5 1 7 cosz 1 1 11m 7 7 gt cosz z 1 7 7m2 for z near 0 170 2 2 2 Theorem 6 For my number 04 7 O sin om 1 7 cos om hm 17 11m 07 9270 04m 9270 04 om 1 7 cos 04 1 hm 17 11m 2 7 170 Sin om x70 04 2 Quiz 3 Quiz 3 What day is today a Monday b Wednesday C Friday d None of these 13 The IntermediateValue Theorem The IntermediateValue Theorem Theorem 7 If f is continuous on ab and K is any number between fa and fb then there is at least one number 0 in the interual ab such that f0 K M M fb fb J K K l x 39a t i The IntermediateValue Theorem Roots of Equation Theorem 8 ff is continuous on a b and falt0ltfba 07 fblt0ltfa then the equation fac 0 has at least a root in a b The IntermediateValue Theorem Solution of Inequality Solve the inequality x3 x2 6xgt0 Solution 2 0 U 3 00 Solution of Inequality Solve the inequality 30 332x 1x 42 S 0 000 O l39 0 II gtlt Solution 312 14 The ExtremeValue Theorem The ExtremeValue Theorem Theorem 9 A function f continuous on a bounded closed cub takes on both a mascimum ualue M and a minimum ualue m 2 Section 31 The Derivative 2 1 The Derivative Secant Lines vs Tangent Lines RV r C X C X De nition 10 The slope of the graph at the point e is given by hmf M f h gtO h 7 provided the limit exists Derivative and Differentiation 3 A fc P C gtltv De nition 11 A function f is di ei entiable at e if hmf M f exists h gtO h If this limit exists it is called the derivative of f at e and is denoted by f 22 Derivative as Function Derivative as Function De nition 12 The derivative of a function f is the function f With value at v given by h jw hmf fa h gtO h 7 provided the limit exists To di ei entiate a function f is to nd its derivative Examples 13 gtltv E pb ggvmas Function More Examples 1 fxE7 square root function Examples 15 tangent HIi t Line Functions For a line function fx mx b the derivative f x m Examples 16 1 06 7 f 1 y 2 2 Examples 17 23 Nondifferentiability Nondi erentiability Discontinuity A function f is not di erentiable at C if flt0h flt0gt h lim does not exist h gtO Jump discontinuity at 0 as v gt 0 f gt 00 as v gt 0 f gt 0 y 10 In nite discontinuity at 0 as a gt 0 f x gt 00 as a gt 0 f 1 gt 00 y slope i x2 tangent HID t Nondifferentiability Corner Points A function f is not differentiable at e if fC h fC h lim does not exist h gtO Corner point at 0 as a gt 0 f x gt 1 as a gt 0 f x gt 1 ylk 2 2 2 2 Corner point at 1 as a gt 1 f 1 gt 2 as 1 gt 17 f 1gt 11 y 1 gtltv no derivative at 1 Nondifferentiability Vertical tangents A function f is not di e39r entz able at c if hm fc h fc h does not exist h gtO vertical tangent at 0 as x gt 0 f x gt 00 y R fx x13 vertical tangent at 2 as x gt 2 f gt 00 311 k gx 2 x15 12 Nondifferentiability Vertical Cusps A function f is not di erentiable at c if hm fc h fc h gtO 2 does not exist vertical cusp at O as 6 gt 0 f 6 gt 00 as 6 gt 0 f 6 gt 00 J A RV fx 923 vertical cusp at 1 as 6 gt 1 f 6 gt 00 as 6 gt 1 f 6 gt 00 J A 1 2 39 Xv gm2 a 1w5 13

×

×

### BOOM! Enjoy Your Free Notes!

×

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

Bentley McCaw University of Florida

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

Jennifer McGill UCSF Med School

#### "Selling my MCAT study guides and notes has been a great source of side revenue while I'm in school. Some months I'm making over \$500! Plus, it makes me happy knowing that I'm helping future med students with their MCAT."

Steve Martinelli UC Los Angeles

Forbes

#### "Their 'Elite Notetakers' are making over \$1,200/month in sales by creating high quality content that helps their classmates in a time of need."

Become an Elite Notetaker and start selling your notes online!
×

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com