Approximating Change www.mathxtc.com. Goto Calculus-Help.comCalculus-Help.com Revision: Differentiation by First Principles.

Slides:

Advertisements

Similar presentations

N.B. the material derivative, rate of change following the motion:

Advertisements

Tangent Planes and Linear Approximations

How do you find the volume of a cylinder?

Circle A is centered at (2,2) with a radius of 12 cm and Circle B is centered at (8,-2) with a diameter of 6 cm. Determine the translation and dilation.

If the diameter of a circle is 6 in, then what is its radius?

Lecture 14 Today Orthogonal coordinate systems 1.The Cartesian (rectangular) coordinate system 2.The cylindrical coordinate system 3.The spherical.

DO NOW Find the equation of the tangent line of y = 3sin2x at x = ∏

Circumference & Arc Length. Circumference The distance around a circle C = 2r or d.

The Circumference of a Circle diameter(d) Circumference (C) How many times does the diameter fit around the circumference? Choose your number. 11½22½33½4.

Circles: Area and Circumference. Definitions Circumference: Distance around the outside of a circle Area: How many squares it takes to cover a circle.

  investigate the relationship between the diameter and circumference of a circle.

Chapter 10 Lesson 1: Circles and Circumference Objective: Learn to find the circumference of circles.

Circles & Circumference Standard Math The circumference is the distance around a circle. Circumference Circumference is the perimeter of circles. Radius.

Circumference & Area of Circles Unit 5-3. Circumference Formula for Circumference: ** r is the radius ** ** 2r = d. d is the diameter. ** **Circumference.

Math Circumference of Circles & Area of Circles. Vocabulary A circle is the set of all points in a plane that are the same distance from a given point,

EOC Strategy - GEOMETRY Formulas. STRATEGY #1 CIRCLE FORMULAS & UNDERLINE VARIABLES If there is a formula:  -circle formula  -label info  -plug in.

Area of a Circular Sectors & Segments February 11, 2007.

Areas of Segments of Circles SWBAT: To find the areas of segments of circles.

7.7: Areas of Circles and Sectors

9.2 – The Area of a Triangle Essential Question: Explain the two ways to find the area of a triangle.

The area of the circle is about 227 m 2. COURSE 2 LESSON 8-4 Find the area of the circle to the nearest unit. = (8.5) 2 Substitute 8.5 for the radius.

A =  r 2 A =  x 8 2 A = cm 2 (1 dp) A =  r 2 A =  x A = cm 2 (1 dp) The Area of a Circle Find the area of the following circles.

Vocabulary: SECTOR of a circle: a region bounded by an arc of the circle and the two radii to the arc’s endpoints SEGMENT of a circle: a part of a circle.

 decimals/cc-7th-fracs-to-decimals/v/converting-fractions-to-decimals-example.

Circumference of a Circle

2.6 Related Rates I. Volume changes-implicit With change in volume, volume, radius, and height of the volume in a cone all depend upon the time of the.

1 of 84 SHAPE AND SPACE Circles. 2 of 84 The circumference of a circle Use π = 3.14 to find the circumference of this circle. C = πd 8 cm = 3.14 × 8 =

Mrs. Planavsky 4 th Grade.  Find the circumference of a circle  Find the measurement of a diameter of the circle.

Warm-Up Find the area: Circumference and Area Circles.

Working Backwards Finding Circumference From Area.

1.6 – Differentiation Techniques The Product and Quotient Rules.

13.4 Differentials “Mathematics possesses not only truth, but supreme beauty - a beauty cold and austere, like that of sculpture." -Bertrand Russell.

The Circle. The language of circles Circumference: The distance round the circle Circumference: The distance round the circle Diameter: the distance from.

Circumference Lesson #33. What is Circumference? The distance around the outside of a circle is called the circumference (essentially, it is the perimeter.

Revision Formulae: Diameter = 2 x Radius Area of Circle = πr 2 Circumference of circle = 2πr = πd π = 3.14 approximately.

Circumferences & Areas of Circles. Circle information Defn: Points on a plane that are equidistant from a given point (CENTER). Radius: From center to.

Arc Length Start with the formula for radian measure … … and multiply both sides by r to get … Arc length = radius times angle measure in radians.

Hannah D..  Radius is half the way across the circle  Diameter is the whole way across the circle.

Do now: Work out the circumferences and areas of these circles 10 cm 12 cm 9 cm 2 cm 1.5 cm.

Linearization and Newton’s Method. I. Linearization A.) Def. – If f is differentiable at x = a, then the approximating function is the LINEARIZATION of.

For any function f (x), the tangent is a close approximation of the function for some small distance from the tangent point. We call the equation of the.

© T Madas. Find the mean percentage mark of 37%, 42%, 68%, 55% and 39%. Find of Find 7% of 675. Find the area of a triangle with base of 1.25.

Slide 1 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Area, Volume, and Surface Area Section9.3.

Circles Formulas Circumference = π * diameter C = πd Area = π * r2

Warm-Up What is the distance between the two trees? If you wanted to meet a friend halfway, where would you meet.

Circles Shape and Space. Formula for the area of a circle We can find the area of a circle using the formula radius Area of a circle = πr 2 Area of a.

X = 3y = 4z = 8 2x Step 1X = 3 Step 22(3) 2 – 6 2 Step 4 2(9) – 6 2Step 3 18 – 12 =6.

The Circle. Examples (1) – (5) Determine the center and radius of the circle having the given equation. Identify four points of the circle.

9.6 Circles in the Coordinate Plane Date: ____________.

CIRCLES CIRCUMFERENCE & AREA. CIRCUMFERENCE C = ΠdorC = 2Πr 12cm.

By: Kay McInnis. Diameter DIAMETER is the distance across a circle passing through the center point.

SATMathVideos.Net If a circle of radius, r, is inscribed inside an equilateral triangle, what percentage of the area of the triangle is covered by the.

EQ: How do you find the circumference of a circle? Lesson 4-6 Circumference pp Vocabulary to watch out for this lesson: Circle Center Diameter.

Reminders on Circles ctd. radius Area Formula (iv) A =  r 2 Example 10cm r = 10 A =  r 2 = 3.14 X 10 X 10 = 314cm 2.

Recap: This circle has a diameter of 1. What is its circumference? 1.

Circles OCR Stage 6.

Half the circumference

Surface Area Circles. Area of Circles How could we find the area of a circle?

3.6 The Chain Rule Y= f(g(x)) Y’=f’(g(x)) g’(x). Chain rule Unlocks many derivatives.

Equation of a Circle. Equation Where the center of the circle is (h, k) and r is the radius.

Section 11.6: Areas of Regular Polygons Definitions – Given a regular polygon inscribed in a circle, the center and radius of the polygon is the center.

Circles Shape and Space. The value of π For any circle the circumference is always just over three times bigger than the radius. The exact number is called.

Do Now:. Circumference What is circumference? Circumference is the distance around a circle.

It’s the same for all circles! The Circumference of a Circle.

  Where the center of the circle is (h, k) and r is the radius. Equation.

5-5 Day 2 Linearization and differentials

How do you feel?

Revision: Circles Silent Intelligent Practice Teacher Your Turn

Presentation transcript:

Approximating Change

Goto Calculus-Help.comCalculus-Help.com Revision: Differentiation by First Principles

Example: Consider a circle of radius 10 cm. If the radius increases by 0.1 cm, approximately how much will the area change? very small change in A very small change in r (approximate change in area)

Compare to actual change: New area: Old area:

Example: If V=2x 3 use differentiation to find the approximate percentage change in V when x changes by 2% very small change in V very small change in x (when x changes by 2%, V changes by 6%)

Example: If V=2x 3 use differentiation to find the approximate percentage change in V when x changes by 2% (when x changes by 2%, V changes by 6%) A different method !!