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1. Let C be the curve described by the equation x³ + 3x²y-xy² = 3. dy dz (b) C contains the point (-1,1). Find the two other points at which C intersects the line y = 1. Note: your final answers should be in the form (x, 1). (c) Find the equations of the lines tangent to C at each of the three points in part (b). (a) Find

1. Let C be the curve described by the equation x³ + 3x²y-xy² = 3. dy dz (b) C contains the point (-1,1). Find the two other points at which C intersects the line y = 1. Note: your final answers should be in the form (x, 1). (c) Find the equations of the lines tangent to C at each of the three points in part (b). (a) Find

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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1. Let C' be the curve described by the equation ³ + 3x²y - xy² = 3. dy da (b) C contains the point (-1,1). Find the two other points at which C intersects the line y = 1. Note: your final answers should be in the form (x, 1). (c) Find the equations of the lines tangent to C at each of the three points in part (b). (a) Find 2. Find the indicated derivatives. dy (a) y = π 3 (cos(x) + 2)", dx ds (b) 2st2 + cos(3s +t)=√s-1, dt 3. When asked to determine the derivative for the function f(t) = (csc² (t))", one student provided the following solution: f' (t) = π (csc² (t))" (2-csc(t)) (-csc(t) cot(t)) (a) What error(s) did the student make while attempting to find f'? Identify the error(s) and provide an explanation that you would use to correct the student's thinking. That is, your explanation should help the student avoid making the same mistake on future problems. (b) Determine the correct derivative for the function f(t) = (csc² (t))**.
Transcribed Image Text:1. Let C' be the curve described by the equation ³ + 3x²y - xy² = 3. dy da (b) C contains the point (-1,1). Find the two other points at which C intersects the line y = 1. Note: your final answers should be in the form (x, 1). (c) Find the equations of the lines tangent to C at each of the three points in part (b). (a) Find 2. Find the indicated derivatives. dy (a) y = π 3 (cos(x) + 2)", dx ds (b) 2st2 + cos(3s +t)=√s-1, dt 3. When asked to determine the derivative for the function f(t) = (csc² (t))", one student provided the following solution: f' (t) = π (csc² (t))" (2-csc(t)) (-csc(t) cot(t)) (a) What error(s) did the student make while attempting to find f'? Identify the error(s) and provide an explanation that you would use to correct the student's thinking. That is, your explanation should help the student avoid making the same mistake on future problems. (b) Determine the correct derivative for the function f(t) = (csc² (t))**.
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