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❶A limit is a number that a function approaches as the independent variable of the function approaches a given value.

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With this fact we can now do limits like the following example. Below is a graph of a continuous function that illustrates the Intermediate Value Theorem. Also, as the figure shows the function may take on the value at more than one place. It only says that it exists. These are important ideas to remember about the Intermediate Value Theorem. A nice use of the Intermediate Value Theorem is to prove the existence of roots of equations as the following example shows.

For the sake of completeness here is a graph showing the root that we just proved existed. Note that we used a computer program to actually find the root and that the Intermediate Value Theorem did not tell us what this value was. If it does, then we can use the Intermediate Value Theorem to prove that the function will take the given value. We now have a problem. Homework Help Integration Applications: Homework Help Differential Equations: Browse Browse by subject. Email us if you want to cancel for any reason.

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Password confirm does not match password. Unlimited access to all video lessons Lesson Transcripts Tech support. See all other plans. First Name Name is required. Last Name Name is required. Phone number is required. Phone number is invalid. Have a Coupon Code? You have not applied your coupon. Using Scientific Calculators in Calculus: Go to chapter Using Scientific Calculators in Calculus: Go to chapter Limits: Go to chapter Rate of Change: Calculating Derivatives and Derivative Rules: Go to chapter Calculating Derivatives and Derivative Rules: Go to chapter Applications of Derivatives: Area Under the Curve and Integrals: Go to chapter Area Under the Curve and Integrals: Integration and Integration Techniques: Go to chapter Integration and Integration Techniques: Go to chapter Integration Applications: Go to chapter Differential Equations: Earning College Credit Did you know… We have over college courses that prepare you to earn credit by exam that is accepted by over 1, colleges and universities.

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Limits and Continuity

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AP Calculus‎ > ‎AP Calculus Limits and Continuity‎ > ‎ AP Calculus Limits and Continuity Homework. Showing 19 items Assignment Day Solutions Assignment Number Video Solutions; Sort Intro to Limits Homework.

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In this section we will introduce the concept of continuity and how it relates to limits. We will also see the Intermediate Value Theorem in this section and how it can be used to determine if functions have solutions in a given interval. Reach infinity within a few seconds! Limits are the most fundamental ingredient of calculus. Learn how they are defined, how they are found (even under extreme conditions!), and how they relate to continuous functions.

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Free step-by-step solutions to Thomas' Calculus () - Slader. Free step-by-step solutions to Calculus () - Slader.