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[DOCX File]www.lcps.org
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Intermediate Value Theorem. EX 1] Show that has a root in [0,1]. Mean Value Theorem. EX 2] If is continuous on [a,b] and differentiable on (a,b), the Mean Value Theorem guarantees a point between and . such that… b) d) none of these. Rolle’s Theorem. EX 3] Let on the interval [0,3]. If Rolle’s Theorem applies, find the value
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[DOC File]CALCULUS
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• Understanding continuity in terms of limits• Geometric understanding of graphs of continuous functions (Intermediate Value Theorem and Extreme Value Theorem)Concept of the derivative • Derivative presented graphically, numerically and analytically• Derivative interpreted as an instantaneous rate of change• Derivative defined as the ...
intermediate value theorem calculus

Chapter 1: Limits and Their Properties
Intermediate Value Theorem Extreme Value Theorem. Rolle’s Theorem Mean Value Theorem for Derivatives & Definite Integrals. FUNDAMENTAL THEOREM OF CALCULUS. Be sure you remember the 2nd part is called the Total Change Theorem. Also, in your justifications, if a problem says it is differentiable at x = a, then the function is continuous at x = a.
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[DOC File]AP Calculus: Midterm Review
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Theorem 8: The Intermediate Value Theorem for Continuous Functions. A function that is continuous on a closed interval [a, b] takes on every value between f(a) and f(b). Example: Let with corresponding table of values: x -4 -3 -2 -1 0 1 2 f(x) -139 72 41 2 -3 -4 17 Use the intermediate value theorem to show that f has three zeros in the ...
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[DOC File]Intermediate Value Theorem: Given real numbers a …
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Whether the theorem holds or not, sketch the curve and the line y = k. _____ 13. Use the Intermediate Value Theorem to show that takes on the value 9 for some x in [1, 2]. _____ On problems 14 – 15, use the Intermediate Value Theorem to show that there is …
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[DOC File]AP BC Calculus First Semester Exam Review Guide
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6. (10 points) Use the Intermediate Value Theorem to show there is a real root of on (1.5, 2). 7. (10 points) a. Use the definition of derivative at a point to find the derivative of at . b. Find the equation of the tangent line to the curve at x = 2. 8. (10 points) The graph below includes the functions , and . Explain which is which. 9.
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[DOC File]If the values of a function can be made as close as …
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Ex: Find the value of a that will make f continuous at x = 2 if . AP Calculus Notes: Limits – 6. Intermediate Value Theorem. Ex: You go for a hike in the Adirondack Mountains. At 8:00 AM you are at 1500’ elevation; at noon you are at 3500’ elevation. Between 8:00 AM and noon, can you say for sure if you were ever at an elevation of. a ...
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Intermediate Value Theorem Problems
Now verify the1 unit integral interval that the zeros are in using the Intermediate Value Theorem. Use the Intermediate Value Theorem to find the 1 unit integral interval for each of the indicated number of zeros. One zero: Four zeros: Given : What is a value guaranteed to be between f(2) and f(3). What is another value guaranteed to be there?
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[DOC File]CALCULUS BC
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Determine if the Intermediate Value Theorem holds for the given value of k . If the theorem holds, find a number c such that f (c) = k. If the theorem does not hold, given the reason. Sketch the curve and the line y = k. TURN--->>> C. C. C. Title: CALCULUS Author: Nancy W. Stephenson Last modified by:
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[DOC File]AP Calculus Notes: Limits
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• Intermediate Value Theorem • Infinite limits • Using limits to find the asymptotes of a function . Chapter 2: Differentiation (2-2.5 weeks, 1 test, daily quizzes) • Understanding of the derivative: graphically, numerically, and analytically • Approximating rates of change from graphs and tables of data
intermediate value theorem calculus

Intermediate value theorem calc