Question

Prove that if a>b, the expression (a cosh x +b sinh x) has the minimum value (√a²-b²) ,but if a<b it has neither a maximum value nor a minimum value​

Answer 1

Answer:

Let the radius of base of hemisphere and cone, each be r unit. 

Let the height of the cone be h unit.

Volume of the cone=31πr2h

Volume of the hemisphere =32πr3

According to the question. 31πr2h=32πr3

⇒h=2r

⇒ Height of the cone =2r unit

Height of the hemisphere = Radius of the hemisphere =r

∴ Ratio of the heights of cone and hemisphere =2r:r=2:1

Answer 2

Step-by-step explanation:

Correct option is A)

sinhx=0 for x=0 and sinhx→∞ as x→∞ and sinhx→−∞ as x→−∞

∴sinhx has maximum or minimum value

But for,

coshx has its minimum value of 1 for x=0, and coshx→∞ as x→+/−∞

and

tanhx=0 for x=0 and tanhx→1 as x→∞ and tanhx→−1 as x→−∞