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Solve the following. Show the step-by-step solution. 1. Find the equation of the tangent line and normal line to the curve y = √x-3 and whose normal line is parallel to the line 6x + 3y -4 = 0. Sketch the graph.

Solve the following. Show the step-by-step solution. 1. Find the equation of the tangent line and normal line to the curve y = √x-3 and whose normal line is parallel to the line 6x + 3y -4 = 0. Sketch the graph.

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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Solve the following. Show the step-by-step solution. 1. Find the equation of the tangent line and normal line to the curve y = √x-3 and whose normal line is parallel to the line 6x + 3y -4 = 0. Sketch the graph. 2. The volume of a cube is increasing at the rate of 6 cm³/min. How fast is the surface area increasing when the length of an edge is 12 cm? (V= e³ and SA = 6e²) 3. Water is flowing into a vertical cylindrical tank at the rate of 24 cubic ft. /min. if the radius of the tank is 4 ft, how fast is the surface rising? (Hint: V = πr²h) 4. An object is moving along a horizontal line according to the position function s(t) = 2t³ - 21t² + 60t + 3, where t≥ 0. a. When is s increasing, when is it decreasing? b. When is v increasing, and when is it decreasing? c. Find the total distance traveled in the first 5 seconds of motion.
Transcribed Image Text:Solve the following. Show the step-by-step solution. 1. Find the equation of the tangent line and normal line to the curve y = √x-3 and whose normal line is parallel to the line 6x + 3y -4 = 0. Sketch the graph. 2. The volume of a cube is increasing at the rate of 6 cm³/min. How fast is the surface area increasing when the length of an edge is 12 cm? (V= e³ and SA = 6e²) 3. Water is flowing into a vertical cylindrical tank at the rate of 24 cubic ft. /min. if the radius of the tank is 4 ft, how fast is the surface rising? (Hint: V = πr²h) 4. An object is moving along a horizontal line according to the position function s(t) = 2t³ - 21t² + 60t + 3, where t≥ 0. a. When is s increasing, when is it decreasing? b. When is v increasing, and when is it decreasing? c. Find the total distance traveled in the first 5 seconds of motion.
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