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Calculus.org - THE CALCULUS PAGE .

Calculus.org - THE CALCULUS PAGE .
Related:  Calculus and Analysis

Exponential and Logarithmic functions Exponential functions Definition Take a > 0 and not equal to 1 . Then, the function defined by f : R -> R : x -> ax is called an exponential function with base a. Graph and properties Let f(x) = an exponential function with a > 1. From the graphs we see that The domain is R The range is the set of strictly positive real numbers The function is continuous in its domain The function is increasing if a > 1 and decreasing if 0 < a < 1 The x-axis is a horizontal asymptote Examples: y = 3x ; y = 0.5x ; y = 100.2x-1 Logarithmic functions Definition and basic properties Take a > 0 and not equal to 1 . are either increasing or decreasing, the inverse functions are defined. loga(x) log10(x) is written as log(x) So, From this we see that the domain of the logarithmic function is the set of strictly positive real numbers, and the range is R. log2(8) = 3 ; log3(sqrt(3)) = 0.5 ; log(0.01) = -2 From the definition it follows immediately that Example: log(102x+1) = 2x+1 Graph log2(x) ; log(2x+4) ; log0.5(x) Thus,

Math S1101 - Calculus I - Syllabus Alice Rizzardo Fall 2009 We'll cover the theory and applications of differential calculus and get a glimpse into the world of integral calculus and the fundamental theorem of calculus, an amazing result that connects differential and integral calculus in a surprising and very useful way. Contact information You can contact me by email at rizzardo@math.columbia.edu . Class Schedule Monday and Wednesday, 4:10-5:25 pm Room 417 Required text James Stewart, Calculus (Early Transcendentals), 6th edition published by Thomson Brooks/Cole. Important Dates Midterm I: October 7 Midterm II: November 16 Final Exam: projected Monday, Dec 21 4:10-7:00 pm Details Workload: There is much to be done in a relatively short period of time, so please try to keep up. Homework: I will assign homework during most class meetings. To receive full credit for a solution, it is not enough for you to simply write down the correct answer. You can come to office hours for help or just ask questions after class.

THE CALCULUS PAGE PROBLEMS LIST Problems and Solutions Developed by : D. A. Kouba And brought to you by : Beginning Differential Calculus : Problems on the limit of a function as x approaches a fixed constant limit of a function as x approaches plus or minus infinity limit of a function using the precise epsilon/delta definition of limit limit of a function using l'Hopital's rule ... Beginning Integral Calculus : Problems using summation notation Problems on the limit definition of a definite integral Problems on u-substitution Problems on integrating exponential functions Problems on integrating trigonometric functions Problems on integration by parts Problems on integrating certain rational functions, resulting in logarithmic or inverse tangent functions Problems on integrating certain rational functions by partial fractions Problems on power substitution Problems on integration by trigonometric substitution ... Sequences and Infinite Series :

7 Tech Upgrades to the Old-School Science Class Long gone are the days of science fair poster boards and paper quizzes, at least not exclusively. Technological breakthroughs have flooded into classrooms, changing the face of K-12 education. From smart boards to smartphones, these digital trends have become useful educational tools in the teaching process. With new apps and interactive sites, science class, in particular, has received a few upgrades. 1. Anatomy teachers loved that life-sized plastic skeleton model hanging in the back of the classroom. In the touch of a button, you can hide or fade certain bones, view different angles, pin notes on the 3D model and read descriptions of each bone. 2. Remember those old school tri-fold poster boards you used at the science fair? With video-sharing sites like YouTube and blogging platforms like Glogster, students no longer need scissors and glue to craft a project. 3. We've always known the standard 18-column Periodic Table of Elements to be organized in a grid-like format. 4. 5. 6. 7.

Karl&#039;s Calculus Tutor - Box 6.0: Exponential and Log Identities Adding the Exponents: If b is any positive real number then bx by = bx+y for all x and y. This is the single most important identity concerning logs and exponents. Since ex is only a special case of an exponential function, it is also true that ex ey = ex+y Multiplying the Exponents: If b is any positive real number then (bx)y = bxy for all x and y. (ex)y = exy Converting to roots to exponents: The nth root of x is the same as x1/n for all positive x. _ √x = x1/2 In addition: __ √ex = ex/2 Converting to ex form: If b is any positive real number then bx = ex ln(b) for all x. xx = ex ln(x) or if you have f(x)x: f(x)x = ex ln(f(x)) or if you have xf(x): xf(x) = ef(x) ln(x) or if you have f(x)g(x): f(x)g(x) = eg(x) ln(f(x)) As an example, suppose you had (x2 + 1)1/x. e(1/x) ln(x2 + 1) ex is its own derivative: The derivative of ex is ex. ex is always positive: You can put in any x, positive or negative, and ex will always be greater than zero. logb(xy) = logb(x) + logb(y) This includes k logb(x) = logb(xk) and

MDTP - Online Diagnostic Test MDTP on-line multiple-choice tests were designed to help individual students review their readiness for some mathematics courses and may be useful in preparing for some mathematical placement tests used by some California colleges and universities. Each on-line test includes a diagnostic scoring report to help students identify strengths and weaknesses in some topic areas. These 40 question multiple-choice tests should be taken without a calculator. MDTP has two on-line tests available for student use to help them prepare for Precalculus and Calculus level mathematics courses. There is no fee for taking these tests. On-line Mathematical Analysis Readiness Test (MR) The MR test should be taken prior to courses typically called trigonometry, precalculus, or math analysis. On-line Calculus Readiness Test (CR) The CR test should be taken prior to a Calculus course.

The AP Calculus BC Exam Exam Content In 1956, 386 students took what was then known as the AP Mathematics Exam. By 1969, still under the heading of AP Mathematics, it had become Calculus AB and Calculus BC. The Calculus BC exam covers the same differential and integral calculus topics that are included in the Calculus AB exam, plus additional topics in differential and integral calculus, and polynomial approximations and series. This is material that would be included in a two-semester calculus sequence at the college level. If students take the BC exam, they cannot take the AB exam in the same year because the exams share some questions. Multiple-Choice Questions For sample multiple-choice questions, refer to the Course Description. AP Calculus Course Description, Effective Fall 2012 (.pdf/2.28MB) AP Calculus Multiple-Choice Question Index: 1997, 1998 and 2003 AP Calculus Exams(.xls/144KB) Free-Response Questions Below are free-response questions from past AP Calculus BC Exams. 2013: Free-Response Questions

Etusivu | Polku Homework and Study Help - Free help with your algebra, biology, environmental science, American government, US history, physics and religion homework Can I take a course at HippoCampus for credit? How do I enroll in a course at HippoCampus? Are there any fees to take your courses? How do I make a comment or ask a question? How do I get individual help with my homework assignment? What are the preferred texts? How can I use HippoCampus in my classroom? How can I use HippoCampus in my home school? Can I use the resources you have available for my homeschoolers? Do you know of any wet lab resources to accompany HippoCampus content? Is there a script, app, or something that can be used to track student use of HippoCampus? Can I share my HippoCampus content with my fellow teachers? Can I download the video? Can I change the size of the video window? Why won't the Environmental Science animations play? What if my page scroll bars or "submit" button are not showing? I can't find closed captioning. Where does the content from your site come from? There is an error in the multimedia presentation. How do I report a course errata item? No. AP Course Ledger

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