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Q.1/Consider the following parametric functions y =1-cost and x =t -sint Find the following : dy a- dx b- The equation of the line that parallel to this function at (t =) 3 d²y c- The second derivative (- -) in their simplest form. dx

Q.1/Consider the following parametric functions y =1-cost and x =t -sint Find the following : dy a- dx b- The equation of the line that parallel to this function at (t =) 3 d²y c- The second derivative (- -) in their simplest form. dx

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Q.1/Consider the following parametric functions y =1- cost and x =t - sint Find the following : dy а- dx b- The equation of the line that parallel to this function at (t = d?y 5) in their simplest form. dx c- The second derivative ( Q.2// Identify and graph the following functions: 4у -Зх 3D 12 b-y =x? - 4x +3 c- y =x - 2|-1 d-x'+y2-4y =5 a- x +2-2<x <-1) e- y ={ x2 -13x <1 2-x 1<x <2 Q.3// Find the inverse function f'(x) of the following, then graph them: a- y =f (x)=2x -4 b- y =f (x)= Vx +2 Q.4// Find the following limits: +12 - 4 -5x +6 2x 2 -5x +6 Vx a- Lim cos x b- Lim c- Lim d- Lim x - 2 x'-8 3x-8 dy ) By definition of derivative : dx Q.5// Find ( a- f (x) = 2x +1 b- f (x) = x - 2 d'y +9y 0} dx Q.6// consider ( y =4cos3x + 2sin 3x ), show that { . 2 d'y d'y then show that : dx 2 dy -25 Q.7// consider { 5x-6y =10}, find and 2 dx dx 18y
Transcribed Image Text:Q.1/Consider the following parametric functions y =1- cost and x =t - sint Find the following : dy а- dx b- The equation of the line that parallel to this function at (t = d?y 5) in their simplest form. dx c- The second derivative ( Q.2// Identify and graph the following functions: 4у -Зх 3D 12 b-y =x? - 4x +3 c- y =x - 2|-1 d-x'+y2-4y =5 a- x +2-2<x <-1) e- y ={ x2 -13x <1 2-x 1<x <2 Q.3// Find the inverse function f'(x) of the following, then graph them: a- y =f (x)=2x -4 b- y =f (x)= Vx +2 Q.4// Find the following limits: +12 - 4 -5x +6 2x 2 -5x +6 Vx a- Lim cos x b- Lim c- Lim d- Lim x - 2 x'-8 3x-8 dy ) By definition of derivative : dx Q.5// Find ( a- f (x) = 2x +1 b- f (x) = x - 2 d'y +9y 0} dx Q.6// consider ( y =4cos3x + 2sin 3x ), show that { . 2 d'y d'y then show that : dx 2 dy -25 Q.7// consider { 5x-6y =10}, find and 2 dx dx 18y
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