PPT-Sec 5: Vertical Asymptotes & the Intermediate Value Theorem

Definition of a Vertical Asymptote If fx approaches as x approaches c from the left or right then the line x c is a vertical asymptote Vertical Asymptotes can be determined by finding where there is . he year Design Value s based on the average of a 3 year period which includes the selected year plus the two prior years Also displayed is the following informat on for each year the umber of Complete Quarters for that year the 99 th Percentil samp Then there exists a number in ab such that The idea behind the Intermediate Value Theorem is When we have two points af and bf connected by a continuous curve The curve is the function which is Continuous on the interval ab and is a numb Continuity, IVT & Bisection Method. A function is . continuous at a point . c. . if and only if . . a. is defined . b. exists. c. the two are equal; i.e. . AII.7 e . 2009. Objectives:. Find the Vertical Asymptotes. Find the Horizontal Asymptotes. Rational . Functions . A rational function can have more than one . vertical asymptote. , but it can have at most one . RevIEw. precalculus. y = (x+2). 2. y = (x-2). 2 . -1. y = -(x+1). 2 . + 3. 4) . The number of horsepower . H. required to overcome wind drag on a certain car is approximated by . H(s) = 0.002s. 2. + 0.05s - 0.029 , 0 < s < 100. Standard Form:. Transverse axis (axis that vertices lie on): Horizontal . Center (. h,k. ). Slopes of asymptotes: . a comes first!.  . Standard Form:. Transverse axis (axis that vertices lie on): Vertical . Rolle’s. theorem. Exploration:. Sketch a rectangular coordinate plane on a piece of paper.. Label the points (1, 3) and (5, 3).. Draw the graph of a differentiable function that starts at (1, 3) and ends at (5, 3).. A bit more practice in Section 4.7b. Analysis of the Inverse Sine Function. 1. –1. D:. R:. Continuous. Increasing. Symmetry: Origin (odd . func. .). Bounded. Abs. Max. of at . x. = 1. Abs. Min. of at . A brief journey into Section . 4.5a. Analysis of the Tangent Function. by. Domain: All . reals. except odd. multiples of. Range:. Continuous on its domain. Increasing on each interval in. i. ts domain. Divergence. In calculus, the divergence is used to measure the magnitude of a vector field’s source or sink at a given point. Thus it represents the volume density of the outward flux of a vector field . . Peter Liljedahl. Students are not . thinking!. Teachers are planning . their teaching . on the assumption that students either cannot or will not think. . begin with good problems . use vertical non-permanent surfaces. 3.2. Calculus AP/Dual, Revised ©2017. viet.dang@humbleisd. .net. . . 6/23/2018 3:32 PM. §3.2: Mean Value Theorem. 1. Activity. Draw a curve . on a separate sheet of paper within a defined closed interval . Writing Rational Functions Honors Algebra II Keeper Think Backwards!!! Example: Write a rational function f that has a vertical asymptote at , a horizontal asymptote and a zero at .   Example: Write a rational function g with vertical asymptotes at ADDRESS 1 2 3 TRUTH IN LENDING DISCLOSURESCREDIT APPLICATION