(a) Consider the piecewise function -x+1, if f(x) ={x-1, 5-x, if x<1 if 1

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter11: Rational And Irrational Numbers
Section: Chapter Questions
Problem 23CLR
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(a) Consider the piecewise function
-x+1, if
f(x) ={x-1,
5-x, if
x<1
if 1<x<2
x22
(i) Find lim f(x) if it exists.
(ii) Show that ƒ(x) is continuous at x= 2.
(iii) Sketch the graph of f(x).
dy
(b) Use the techniques of differentiation to find
dx
(i) 3e* = xy +x² + y²
2.r
(ii) y=
(r² -4)
(c) Find the slope of the tangent line at the indicated point
y +y = x at (1,3)
Write an equation of the tangent linc.
Transcribed Image Text:(a) Consider the piecewise function -x+1, if f(x) ={x-1, 5-x, if x<1 if 1<x<2 x22 (i) Find lim f(x) if it exists. (ii) Show that ƒ(x) is continuous at x= 2. (iii) Sketch the graph of f(x). dy (b) Use the techniques of differentiation to find dx (i) 3e* = xy +x² + y² 2.r (ii) y= (r² -4) (c) Find the slope of the tangent line at the indicated point y +y = x at (1,3) Write an equation of the tangent linc.
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