New User Special Price Expires in

Let's log you in.

Sign in with Facebook


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


Create a StudySoup account

Be part of our community, it's free to join!

Sign up with Facebook


Create your account
By creating an account you agree to StudySoup's terms and conditions and privacy policy

Already have a StudySoup account? Login here

Calc for BusLife Sciences

by: Alvena McDermott

Calc for BusLife Sciences MATH 1314

Marketplace > University of Houston > Mathmatics > MATH 1314 > Calc for BusLife Sciences
Alvena McDermott
GPA 3.69

Mary Flagg

Almost Ready


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

Purchase these notes here, or revisit this page.

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

Preview These Notes for FREE

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

Unlock Preview
Unlock Preview

Preview these materials now for free

Why put in your email? Get access to more of this material and other relevant free materials for your school

View Preview

About this Document

Mary Flagg
Class Notes
25 ?




Popular in Course

Popular in Mathmatics

This 11 page Class Notes was uploaded by Alvena McDermott on Saturday September 19, 2015. The Class Notes belongs to MATH 1314 at University of Houston taught by Mary Flagg in Fall. Since its upload, it has received 22 views. For similar materials see /class/208403/math-1314-university-of-houston in Mathmatics at University of Houston.


Reviews for Calc for BusLife Sciences


Report this Material


What is Karma?


Karma is the currency of StudySoup.

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

Date Created: 09/19/15
Math 1314 Lesson 1 Limits What is calculus The body of mathematics that we call calculus resulted from the investigation of two basic questions by mathematicians in the 18 centuIy 1 How can we nd the line tangent to a curve at a given point on the curve 2 How can we nd the area ofa region bounded by an arbitraIy curve The investigation of each ofthese questions relies on the process of nding a limit so we ll start by informally de ning a limit and follow that by learning techniques for nding limits Limits Finding a limit amounts to answering the following question What is happening to the y Value of a function as the xValue approaches a speci c target number If the y Value is approaching a speci c number then we can state the limit of the function as x gets close to the target number Example 1 I I I I I I I I I I I I I I I I I I I I I I I I I t 9 8 7 6 S 4 3 2 1 2 3 4 5 6 397 8 9 1 It does not matter Whether or not the x value every reaches the target number It might or it might not Example 2 When can a limit fail to exist We will look at two cases Where a limit fails to exist note there are more but some are beyond the scope of this course Case 1 The y value approaches one number from numbers smaller than the target number and it approaches a second number from numbers larger than the target number Case 2 At the target number for the x value the graph of the function has a vertical asymptote 79724757574472 3455729 For either of these two cases we would say that the limit as x approaches the target number does not exist Definition We say that a function f has limit L as x approaches the target number a written lim f x L ifthe value x can be made as close to the numberL as we please by taking x suf ciently close to but not equal to a Note that L is a single real number Evaluating Limits There are several methods for evaluating limits We will discuss these three 1 substituting 2 factoring and reducing 3 nding limits at in nity To use the rst two of these methods we will need to apply several properties of limits Properties of limits Suppose lim fx L and limgx M Then liiralfx39 fx L for any real number r cfx fx CL for any real number c 13mm gx 13mm 933m L M lxijfallfXgxl lim fx1imgxl 1M xgta xgta bUJN lim fx lim fx fa i providedM 0 Ha gx 11mgx M V39 We ll use these properties to evaluate limits Substitution Example 3 Evaluate lim3x2 4x 5 Xgt2 2x 1 Example 4 Evaluate lim Xgt0 3 Example 5 Evaluate lim 3x2 xgt4 k What do you do when subst1tut10n g1ves you a value 1n the form 6 where k 15 any nonzero real number 2 5 Example 6 Evaluate 11m x H3 x3 Indeterminate Forms 0 What do you do when subst1tutlon glves you the value 6 This is called an indeterminate form It means that you are not done with the problem You must try another method for evaluating the limit See if you can factor the function If you can you may be able to reduce the fraction and then substitute x2 4x 5 Example 7 Evaluate lim 2 H1 x 1 x2 5x6 Example 8 Evaluate lim xgt2 x 2 So far we have looked at problems Where the target number is a speci c real number Sometimes we are interested in nding out What happens to our function as x increases or decreases Without bound Limits at In nity Example 9 Consider the function f x 2 22x 1 What happens to x as we let the value x of x get larger and larger We say that a function x has the limitL as x increases Without bound or as x approaches in nity Written lim f x L if x can be made arbitrarily close toL by taking x large enough We say that a function x has the limitL as x decreases Without bound or as x approaches negative in nity Written lim f x L if x can be made arbitrauly close to L by taking x to be negative and suf ciently large in absolute value We can also nd a limit at in nity by looking at the graph of a function 2x77 Example 10 Evaluate lim We can also find limits at in nity algebraically or by recognizing the end behavior of a polynomial function Example 11 Evaluate lim4x3 7x 5 Limits at in nity problems often involve rational expressions fractions The technique we can use to evaluate limits at infinity is to divide every term in the numerator and the denominator of the rational expression by xquot where n is the highest power of x present in the denominator of the expression Then we can apply this theorem 1 n 0 and lim 1 0 provided is defined Theorem Suppose n gt 0 Then lim 1 n Hoe x x xn After applying this limit we can determine what the answer should be YOUMUST KNOW THIS PROCEDURE 2 2 5 1 Example 12 Evaluate limxz x H 3x 2x 7 Often students prefer to just learn some rules for nding limits at in nity The highest power of the variable in a polynomial is called the degree of the polynomial We can compare the degree of the numerator with the degree of the denominator and come up with some generalizations o If the degree of the numerator is smaller than the degree of the denominator then lim fx 0 Hoe gx o If the degree of the numerator is the same as the degree of the denominator then you can nd lim by making a fraction from the leading coef cients of the Hoe g x numerator and denominator and then reducing to lowest terms 0 If the degree of the numerator is larger than the degree of the denominator then it s best to work the problem by dividing each term by the highest power of x in the denominator and simplifying You can then decide if the function approaches 00 or oo depending on the relative powers and the coef cients The notation lim f x 00 indicates that as the value of x increases the value of the xgt o function increases without bound This limit does not eXist but the 00 notation is more descriptive so we will use it 2x4 5x4 Example 13 Evaluate lim 2 H x xl 5 2 3 4 Example 14 Evaluate llme x H 4x 2x 8 4 5 Example 15 Evaluate limzx H x 9x 9 From this lesson you should be able to State the two basic problems of the calculus De ne limit indeterminate form Find a limit as x approaches a target number from a graph off State when a limit fails to exist k Evaluate 11m1ts where subst1tution gives 6 k 72 0 Evaluate limits by substitution or by factoring Evaluate limits at in nity


Buy Material

Are you sure you want to buy this material for

25 Karma

Buy Material

BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.


You're already Subscribed!

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."

Jim McGreen Ohio University

"Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."


"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


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


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:

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

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.