Lesson 8 Nov 27 09
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The document discusses linear approximation and finding zeros using Newton's method. It provides the formula for calculating the equation of the tangent line near a given point using the value and derivative of the function at that point. As an example, it calculates the tangent line approximation of the function y = -4x^2 + 6x + 9 near x = 2. It also gives the general formula for performing one iteration of Newton's method to find zeros of a function.
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This document discusses using the shell method to calculate volumes of solids generated by revolving regions between functions around axes. It provides examples of revolving the function f(x)=x^2 around the x-axis and y-axis, and revolving the region between f(x)=0.5x^2-2x+4 and g(x)=4+4x-x^2 around both the x-axis and y-axis. Instructions are given to use the shell method to find each volume.
Lesson 08 Mar 23
Absolute value refers to the distance from zero on the number line. There are two values, -2 and 2, that have an absolute value of 2. Absolute value can never be negative because distance cannot be negative. The document provides examples of using absolute value to solve equations.
Lesson 07 Mar 20
This document discusses solving rational equations by finding the least common denominator, combining like terms, and then solving the resulting equation for the variable. It contains an exercise with questions 1, 6, and 7 about solving rational equations.
Vectors 03 Mar 20
This document provides instructions and problems for solving vector problems by drawing scale diagrams, adding vectors using the triangle method, and calculating distances and directions from starting points. Specifically, it asks the reader to: 1) draw scale diagrams of vectors for a person walking 13 blocks E15°S and a boat headed 300° at 45 km/h; 2) add the vectors using the triangle method; and 3) solve problems involving distances and directions for a man walking in different directions and a jogger moving north and east over time.
Lesson 06 Mar 19
An equation containing a radical is called a radical equation. This document refers to exercises 18 questions 1 through 5 and also questions 8 and 9 which involve solving or working with radical equations. The goal is to extract the key essential information about radical equations from the given document in 3 sentences or less.
Vectors 02 Mar 19
The document provides information about vector addition and trigonometric equations. It discusses drawing scale diagrams to represent vectors and their directions and magnitudes. Methods for adding vectors are described, including the triangle method used when vectors are tip-to-tail and the parallelogram method used when vectors are tail-to-tail. An example of each method is worked out to find the resultant vector.
Lesson 02 Appsof Integrals Mar19
The document contains instructions to find the volumes of solids generated by revolving regions bounded by graphs about axes. It gives the volume as 183.981 when revolving the region between the graphs y = 2x + 4 and y = ex about the x-axis. It also gives the volumes as 7/15 when revolving the region between y = x^2 + 1 and y = x + 1 about the x-axis and 4/5 when revolving the same region about the line y = -1.
Vectors 02 Mar 19
The document provides information about vector addition and trigonometric equations. It discusses drawing scale diagrams to represent vectors and their directions and magnitudes. Specific examples are given of adding vectors using the triangle method when vectors are tip-to-tail and the parallelogram method when they are tail-to-tail. Measurements from the scale diagrams along with a protractor can be used to find the resultant vector.
Vectors 01 Mar 18
The document discusses vectors and provides examples of identifying quantities as scalar or vector. It also discusses four notations for writing vectors using arrows, bearings, angle-direction-direction, and angle-direction of direction. Examples are given to demonstrate each notation. The document also discusses stating the direction of vectors in five ways and using diagrams of parallelograms to name vectors that are equal, opposite, collinear, or parallel but not equal to other vectors in the diagram.
Lesson 05 Mar 18
The document describes a problem where a rectangular piece of cardboard has a length longer than its width. Square pieces are cut from the corners and the sides are folded up to form a box with a volume of 450 cm3. The original length of the cardboard was 16 cm and the width was 11 cm.
Lesson 04 Mar 17
This document discusses methods for finding the roots of quadratic equations. It introduces the discriminant formula to determine the type of roots, and explains how to use the quadratic formula to find the exact values of the roots. It also shows how to write a quadratic equation given the sum and product of its roots, or given two integer roots.
Lesson 01 Appsof Integrals Mar17
The document discusses calculating the volume of solids of revolution using integrals. It provides the formula for finding the volume of a solid rotated about the x-axis between x=a and x=b using a cross-sectional area function A(x). It then works through an example of finding the volume of a right circular cone of height 4 and base radius 1, and confirms the result matches the standard volume formula for a cone.
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- 2. Linear Approximation Given y = x2 Find the equation of the tangent line near x = 2 y f(a) = f '(a) (x a)
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