MATH116 Lecture Notes - Lecture 17: Regular Polygon, Opata Language, Maryland Route 2

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cyanimpala400

9 Dec 2015

School

University of Waterloo

Department

Mathematics

Course

MATH116

Professor

Fiona Dunbar

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Document Summary

Practice solutions 9: use di erentials (or a linearization) to estimate the value of 3. Solution: here it should be clear that we want to use x = 125 as our point of tangency. x we have (for general x) Doing this with the function f (x) = 3 f (x) = f (125) + y. Therefore, when trying to approximate 3 (x 125) 150 = f (150) we have f (150) 5 + 1 + x3 taken over the interval: approximate the area under the curve of the function y = [0, 1], by dividing the interval into 5 equal parts, and making rectangles touching the curve at sample points in the interval. We have x = 1 x4 = 0. 8, and x5 = 1. 5, and xi = 0 + i x = i: that is, x0 = 0, x1 = 0. 2, x2 = 0. 4, x3 = 0. 6, (a) the area using left endpoints is:

Related Questions

Let P denote the vector space of all polynomials and f'(x)denote the derivative of all numbers in P. State true or false tothe following:

1. T: R^2 --> R^3 defined by T(x,y)=(?^2x,0, y/2) is a linear transformation

2. T: R^2 --> R^3 defined by T(x,y)=(x+y, x-y, xy) is alinear transformation

3. T: R^2 --> R^3 defined by T(x,y)=(1,0,0) is a lineartransformation

4. T: R^2 --> R^3 defined by T(x,y)= (y, x, y) is a lineartransformation

5. T: R^2 --> R^3 defined by T(x,y)= (x, x^2, x^3) is alinear transformation

6. T: R^2 --> R^3 defined by T(x,y)= (2x+3y, 3x+4y, 4x+5y) isa linear transformation

7. T: P --> P defined by T(f(x))= f(0) +f'(0)x + f''(0)x^2 isa linear transformation

8. T: P --> P defined by T(f(x))= f(1) + f'(2) + f''(3)x^2 isa linear transformation

9. T: P --> P defined by T(f(x))= f(x-3) is alinear transformation

10. T: P --> P defined by T(f(x))= f(x)-3 is a lineartransformation

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4. (16 pts) Let f be a differentiable one-to-one function with domain (0,6) with the particular values of f and f' given in the table below, and let f-1 be the inverse function of f. Let g be the function given by the graph below. x f(x) f'(x) --- 23 = g(x) Find the value or write "not defined". Show your work! (a) lim 5(x) – 8(5) x+5 X-5 (b) [6'«x+2)(x) at x = 3 (c) [p-(x)) at x = 2 (0( vecm) at x = 2

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MATH116 Lecture Notes - Lecture 17: Regular Polygon, Opata Language, Maryland Route 2

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