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a) ii. ii. The curve c has equation 3 1- x² Write down the equations of the asymptotes of curve C. Find the coordinates of the point where curve C crosses the y- axis and, without using calculus, show that there is a minimum at this point. Sketch curve C (this must not be done on graph paper). Show clearly the asymptotes and the coordinates of the point where the curve crosses the y -axis. #

a) ii. ii. The curve c has equation 3 1- x² Write down the equations of the asymptotes of curve C. Find the coordinates of the point where curve C crosses the y- axis and, without using calculus, show that there is a minimum at this point. Sketch curve C (this must not be done on graph paper). Show clearly the asymptotes and the coordinates of the point where the curve crosses the y -axis. #

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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11. M. b) i. The curve C has equation y= 1 3 x Write down the equations of the asymptotes of curve C. Find the coordinates of the point where curve C crosses the y-axis and, without using calculus, show that there is a minimum at this point. Sketch curve C (this must not be done on graph paper). Show clearly the asymptotes and the coordinates of the point where the curve crosses they – axis. Use the identity cosh²x – sinh²x = 1 to show that 1 = cosech²x. coth²x Solve the equation 6 coth²x - 5 cosech x = 5. Give your answers in terms of natural logarithms and in exact form.
Transcribed Image Text:11. M. b) i. The curve C has equation y= 1 3 x Write down the equations of the asymptotes of curve C. Find the coordinates of the point where curve C crosses the y-axis and, without using calculus, show that there is a minimum at this point. Sketch curve C (this must not be done on graph paper). Show clearly the asymptotes and the coordinates of the point where the curve crosses they – axis. Use the identity cosh²x – sinh²x = 1 to show that 1 = cosech²x. coth²x Solve the equation 6 coth²x - 5 cosech x = 5. Give your answers in terms of natural logarithms and in exact form.
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