Mathematics

Book Calculus by Thomas/Finney, 9th Edition, Page 275 Differential Calculus to Integral Calculus. This is where we stop asking “how fast is it changing?” and start asking “how much have we accumulated?” Indefinite Integrals The chapter kicks off with a simple question: If I give you the answer (the derivative), can you tell me the ... Read More

Book Calculus by Thomas/Finney, 9th Edition, Page 248 Linearization: Approximating functions https://math.stackexchange.com/questions/1385936/approximating-sqrt1-frac1n-by-1-frac12n#:~:text=The%20function%20f(%20x)=%20%E2%88%9A%201+%20x,%E2%88%9A%201+%20x%20for%20x%20%E2%89%A5%200. Differentials Differential Estimate of Change:In calculus, estimating change with differentials is a method from calculus used to approximate how much a function’s output changes when the input changes by a small amount. Instead of calculating the exact change (which can be difficult and ... Read More

Book Calculus by Thomas/Finney, 9th Edition, Page 233 Example problem: Find 2 positive numbers whose sum is 20 and their product is as large as possible.

Book Calculus by Thomas/Finney, 9th Edition, Page 220 Definitions of limits: There are various properties of limits: For more pages 220 – 232, Book Calculus by Thomas/Finney, 9th Edition.

Book Calculus by Thomas/Finney, 9th Edition, Page 205 Function’s critical points, local extreme values. How to test for local extreme values. At left and right endpoints? Graphing

Book calculus by Thomas/Finney, 9th Edition, Page 189 Derivatives can be used to analyze the behaviour of functions and solve practical optimization problems. Max-Min Theorem relates to existence of max and min value for a function $f4$ that is continous at every point of closed interval I. Absoluted maxima and minima on a closed interval ... Read More

Book Calculus by Thomas/Finney, 9th Edition, Page 109 Derivates is one of the most important concept in calculus. It measures the rate at which a function changes. It is defined actually as the limit of secant slopes which is the slope of curve at a point. Derivative of the funtion $f$ with respect to variable ... Read More

Book Calculus by Thomas/Finney, 9th Edition; Page 51 Limit: One of the main concept that differentiates calculus with algebra and trigonometry (page 51). Core concepts: limit, limits to describe how different functions changes or varies (continuously or erratically), how limits can be used to define tangent lines to the graph of the functions, derivative of ... Read More

Book: Calculus by Thomas/Finney. 9th Edition Radian is a unit of measurment. In calculus, angle is measured in radian. (Navigation and astronomy uses degrees for angles) – page 35 Radian measure $\theta$ is given by $\frac{s}{r}$ wher $s$ is arc length AB and $r$ is the radius. Six basic trigonometric functions. Some other functions. For ... Read More