Mathematics Dictionary

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Elementary Calculus

Subjects

Read Symbol Defintion CA 00 | - Tips CA 01 | - Limit and Summation CA 02 | - Derivative of polynomial and rational functions CA 03 | - Derivative of trigonometric functions CA 04 | - Derivative of inverse trigonometric functions CA 05 | - Derivative of exponential family functions CA 06 | - Derivatice of logarithmic functions CA 07 | - Derivative of parametric equation CA 08 | - Integral : Anti-derivative and substitution rule CA 09 | - Arc Length and area bound by curve CA 10 | - Integral : Trigonometric function CA 11 | - Integral by part CA 12 | - Integral : Inverse trigonometric functions CA 13 | - Integral : Hyperbolic functions CA 14 | - Integral : Inverse Hyperbolic functions CA 15 | - Integral : Partial fraction CA 16 | - Integral : Rational and ir-rational functions CA 17 | - Integral : Area and Volume CA 18 | - Integral : Series CA 19 | - CA 20 | - Calculus Index CA 21 | - Graphs in caculus CA 22 | - Glossay CA 23 | - Home Work CA 24 | - References CA 25 | - Examples link to section numberReferences CA 26 | - Formula in Calculus CA 27 | - Examples with solutions

Answers

CA 01. Limit and Summation Topic | Limit of functions Example Lim[sin(x)/x] = 1 as x tends to zero Lim[tan(x)/x] = 1 as x tends to zero Go to Begin CA 02. Derivative of polynomial and rational functions Topic | Derivatives of polynomial and rational functions Example d/dx(x^3) = 3*x^2 d/dx(x^(-3)) = -3*x^(-4) d/dx(x^(1/2)) = (1/2)*x^(-1/2) Go to Begin CA 03. Derivative of trigonometrical functions Topic | Derivative of trigonometric functions Examples d/dx(sin(x) = cos(x) d/dx(tan(x) = sec(x)^2 Go to Begin CA 04. Derivatives of inverse trigonometric functionsNew Topic | Derivatives of inverse trigonometric functions. Examples d/dx(arcsin(x)) = 1/Sqr(x^2 - 1) d/dx(arctan(x)) = 1/(1 + x^2) Go to Begin CA 05. Derivative : Exponential family Topic | Derivative : Exponential family Example d/dx(exp(x)) = exp(x) d/dx(sinh(x)) = cosh(x) d/dx(cosh(x)) = sinh(x) Topic | Compare hyperbolic functions with trigonometry Go to Begin CA 06. Derivative : Logarithm family Topic | Derivative of logarithmic family functions Examples d/dx(ln(x)) = 1/x d/dx(arcsinh(x)) = 1/Sqr(1 + x^2) Go to Begin CA 07. Derivative : Parametric equation Topic | Derivative : Parametric equation Examples dy/dx = (dy/dt)/(dx/dt) dy'/dx = (dy'/dt)/(dx/dt) Go to Begin CA 08. Integral : Anti-derivative and substitution rule Topic | Integral : Anti-derivative and substitution rule Examples : Anti-differentiation Integral of x^n Integral of x^(-n) Integral of x^(1/n) Examples : Substitution rule Integral of x*Sqr(1 + x^2) Integral of x/(1 + x^2) Go to Begin CA 09. Arc length and area bound by curve Topic | Arc length Go to Begin CA 10. Integral : Trigonometric functions Topic | Integral : Trigonometric functions Examples Integral of tan(x) Integral of sec(x) Go to Begin CA 11. Integral by part Topic | Integral by part Examples Integral of ln(x) Integral of exp(x)*sin(x) Go to Begin CA 12. Integral : Inverse trigonometrical functions Topic | Integral : Inverse trigonometrical functions Example ∫arcsin(x)dx = +1/(x*Sqr(1-x^2) ∫arccos(x)dx = -1/(x*Sqr(1-x^2) ∫arctan(x)dx = +1/(1 + x^2) Go to Begin CA 13. Integral : Hyperbolic functions Topic | Hyperbolic functions Examples ∫sinh(x)dx = cosh(x) ∫cosh(x)dx = sinh(x) ∫tanh(x)dx = sech(x)^2 Go to Begin CA 14. Integral : Inverse hyperbolic functions Topic | Inverse hyperbolic functions Examples ∫arcsinh(x)dx = x*arcsinh(x) - Sqr(1 + x^2) ∫arccosh(x)dx = x*arccosh(x) - Sqr(x^2 - 1) Reference Go to Begin CA 15. Integral : Partial fraction Topic | Integral : Partial fraction Go to Begin CA 16. Partial fraction Topic | Integral : Rational and ir-rational functions Go to Begin CA 17. New Topic | - Go to Begin CA 18. - Topic | DeMovire's theory Example 1 : Solve x^5 - 1 = 0 Example 2 : Solve x^4 + x^3 + x^2 + x + 1 = 0 Go to Begin CA 19. - Topic | Go to Begin CA 20. Calculus Index Topic | Calculus Index How to find keyword ? Find the section number and topic number of keyword 1st number : Section number 2nd number : Topic number Remeber these two numbers Click Back to back subject page Click "Goto Begin" to top Click section number to enter the required section Click topic number Go to Begin CA 21. Graphs in calculus Topic | Graphs in calculus Contents Open the program and look Start application program Open the application program Select Run at current location (no download) Select Yes to Run Run the application program 03 04 Click Menu command Click section 03 in upper box Click program 04 The graph of y = (x^3 - 1)/(x^3 + 1) is given Change y-scale : -6 to 6 Click 6 at left side list of R-window Click Re-plot Click Menu to see other programs Go to Begin CA 22. Glossary Topic | Glossary Go to Begin CA 23. Home Work Questions by number sequence Topic | Math Home works Questions in algebra, geometry and trigonometry Questions by keywords in alphabetic order Topic | Math Home works Questions in algebra, geometry and trigonometry Go to Begin CA 24. References Topic | References Topics Mathematics on Internet Mathematics on PC computer Go to Begin Q25. Examples link to suction number Web-page Topic | Examples link to suction number How to use ? Search related example with keywords in alphabetic order Write down the question number. Example 02 10 Click back Go to Begin (On top) Click Section 02 to enter a new web-page of section 02 Click 10 to get program 02 10 Go to Begin Q26. Formula in Caculus Topic | Integral Table Q27. Examples with solutions Topic | Examples with solutions Go to Begin Q00. Tips Index and examples Lesson 20 : Index Lesson 21 : Application graphic programs Lesson 22 : Glossary Lesson 23 : Goto home works Lesson 24 : References Lesson 25 : Examples link to section numbers, e.g. 03 02 Lesson 26 : Formulae in calculus Lesson 27 : Select examples with solution (QA) Highlight tops (Update later) 1. Sketch using y' and y" in 02 10 2. Integral of y = 1/(a*x^2 + b*x + c) in xx xx Run Application graphic program (See Lesson 21) Step 1 : Run at current location (no download) Step 2 : Select Yes to run Notes 1. The application program is only for internet use (Update monthly) 2. Download only available upto end of the month Go to Begin

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