Rectangular (i) x=r cos 0 Polar Conversion Formulas (ii) y=r sin (iii) x² + y² = r² (a) Use implicit differentiation to find the slope and inclination of the tangent lines to the graph of the cardioid: (x² + y² + y)² = x² + y² at the points P = (1,0) and Q = (-1,0). (b) Use the conversion formulas (i), (ii) and (iii) noted above to rewrite the equation for the cardioid from part (a) in terms of only r and as: r = 1 - sin 0. (c) Sketch a careful graph which displays the cardioid and its tangent lines at P and Q.
Rectangular (i) x=r cos 0 Polar Conversion Formulas (ii) y=r sin (iii) x² + y² = r² (a) Use implicit differentiation to find the slope and inclination of the tangent lines to the graph of the cardioid: (x² + y² + y)² = x² + y² at the points P = (1,0) and Q = (-1,0). (b) Use the conversion formulas (i), (ii) and (iii) noted above to rewrite the equation for the cardioid from part (a) in terms of only r and as: r = 1 - sin 0. (c) Sketch a careful graph which displays the cardioid and its tangent lines at P and Q.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.2: Derivatives Of Products And Quotients
Problem 37E
Related questions
Question
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Step 1: Introduction
VIEWStep 2: Determine the slope and inclination of the tangent line
VIEWStep 3: Determine the slope and inclination of the tangent line at the point P
VIEWStep 4: Determine the slope and inclination of the tangent line at the point Q
VIEWStep 5: Rewrite the equation of cardioid
VIEWStep 6: Graph
VIEWSolution
VIEWTrending now
This is a popular solution!
Step by step
Solved in 7 steps with 2 images
Recommended textbooks for you
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,