Nested Square roots Yue Kwok Choy Nested square roots problems are very interesting. In this article, we investigate some mathematical techniques applied to this topic that most senior secondary school students can understand. 1. 1+ 1+√1+⋯ (a) We put x= 1+ 1+√1+⋯ Then x =1+ 1+√1+⋯ √x −1= 1+ 1+⋯=x
Use patterns of transformation to sketch graphs of simple functions, or to write equations of simple functions based on their graphs. Compare important attributes of given functions. Give the domain of simple polynomial, rational, and square root functions. Recognize and perform operations on complex numbers. Solve quadratic equations.
Domain and range of rational functions. Domain and range of rational functions with holes. Graphing rational functions. Graphing rational functions with holes. Converting repeating decimals in to fractions. Decimal representation of rational numbers. Finding square root using long division. L.C.M method to solve time and work problems
These elementary functions include rational functions, exponential functions, basic polynomials, absolute values and the square root function. It is important to recognize the graphs of elementary functions, and to be able to graph them ourselves. This will be especially useful when doing transformations.
I. For each function below: a) Name the function (square root, cube root) b) Graph the parent function- you may use a table. c) Use what you know about transformations of graphs to describe the shift for each. d) Graph the function. (Think of the shift!) 1.) ( ) √ ( ) √ 2.)
Look below to see them all. They are mostly standard functions written as you might expect. You can also use "pi" and "e" as their respective constants. Please note: You should not use fractional exponents. For example, don't type "x^(1/3)" to compute the cube root of x. Instead, use "root(x,3)".
B = sqrt(X) returns the square root of each element of the array X. For the elements of X that are negative or complex, sqrt(X) produces complex results. The sqrt function’s domain includes negative and complex numbers, which can lead to unexpected results if used unintentionally.
If r is a vector of length 2, then square(r) creates the square with x and y coordinates ranging from r to r. unit.square creates the unit square \([0,1] \times [0,1]\). It is equivalent to square(1) or square() or owin(c(0,1),c(0,1)). These commands are included for convenience, and to improve the readability of some code.