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t I Exercise A.5 (B) Show that y = 3a²x-³ is strictly increasing for a < x 2a. Hint: put x = 2a cosh o and use the relation cosh³ = (cosh 30+3 cosh o)/4.

t I Exercise A.5 (B) Show that y = 3a²x-³ is strictly increasing for a < x 2a. Hint: put x = 2a cosh o and use the relation cosh³ = (cosh 30+3 cosh o)/4.

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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How about part c？
8:04 PM Sat 16 Sep X < 00 00 M820 ✓ Ans (a) P So 00 Exercise A.5 (B) Show that y = 3a²x - x³ is strictly increasing for −a < x < a and that on this interval y increases from -2a³ to 2a³. m820_solutions_itm50... → be By putting a = 2a sino and using the identity sin³ 6 = (3 sin 6 – sin 36)/4, show that the equation becomes y = 2a³ sin 30 and hence that (y) = 2a sin (203)). (c) Find the inverse for x > 2a. Hint: put x = 2a cosho and use the relation cosh³ = (cosh 30 + 3 cosh o)/4. 0 A function is increasing if f'ox xo. (X) y² = 3a² - 3x² >0 a + x > 0 -a x > -a So the interval 0 T > $ → increases y <x< a the function is increasing. f(a) < foxo < feas -2a²³ < y < 2a²³ m820_mn2_itm50992... → (a-x) (a+x) >o a-x>0 a > x sin-1 83% from -2a³ to 2a³. ↑
Transcribed Image Text:8:04 PM Sat 16 Sep X < 00 00 M820 ✓ Ans (a) P So 00 Exercise A.5 (B) Show that y = 3a²x - x³ is strictly increasing for −a < x < a and that on this interval y increases from -2a³ to 2a³. m820_solutions_itm50... → be By putting a = 2a sino and using the identity sin³ 6 = (3 sin 6 – sin 36)/4, show that the equation becomes y = 2a³ sin 30 and hence that (y) = 2a sin (203)). (c) Find the inverse for x > 2a. Hint: put x = 2a cosho and use the relation cosh³ = (cosh 30 + 3 cosh o)/4. 0 A function is increasing if f'ox xo. (X) y² = 3a² - 3x² >0 a + x > 0 -a x > -a So the interval 0 T > $ → increases y <x< a the function is increasing. f(a) < foxo < feas -2a²³ < y < 2a²³ m820_mn2_itm50992... → (a-x) (a+x) >o a-x>0 a > x sin-1 83% from -2a³ to 2a³. ↑
B y Since = 6a³ sin & - 8 a³ sin ³ & баз = 2a²³ (3 sin & -4 sin ³0) = 2 11 So y = 20²³ sin 34 sin 3p = 介 => 3a²x - x³ 3 3a² (2a sin 4) - (2a sin 8)³ ↑ ↑ 3 2a³ sin (34) 34 X = $ = y 2a³ sin" _x cys = I sin m (3) 2a sin & La sin ( — Sin" Las) = Ja sin ( — sin¹ = 13)
Transcribed Image Text:B y Since = 6a³ sin & - 8 a³ sin ³ & баз = 2a²³ (3 sin & -4 sin ³0) = 2 11 So y = 20²³ sin 34 sin 3p = 介 => 3a²x - x³ 3 3a² (2a sin 4) - (2a sin 8)³ ↑ ↑ 3 2a³ sin (34) 34 X = $ = y 2a³ sin" _x cys = I sin m (3) 2a sin & La sin ( — Sin" Las) = Ja sin ( — sin¹ = 13)
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