Maxima And Minima

We have, the given equation as

%5Csin%20%5Cleft(e%5E%7Bx%7D%5Cright)%3D5%5E%7Bx%7D%2B5%5E%7B-x%7D

...(i)
Let

5%5E%7Bx%7D%3Dt

, then E (i), reduces to

%5Csin%20%5Cleft(e%5E%7Bx%7D%5Cright)%3Dt%2B%5Cfrac%7B1%7D%7Bt%7D

%5CRightarrow%20%5Csin%20%5Cleft(e%5E%7Bx%7D%5Cright)%3Dt%2B%5Cfrac%7B1%7D%7Bt%7D-2%2B2

%5CRightarrow%20%5Csin%20%5Cleft(e%5E%7Bx%7D%5Cright)%3D%5Cleft(%5Csqrt%7Bt%7D-%5Cfrac%7B1%7D%7B%5Csqrt%7Bt%7D%7D%5Cright)%5E%7B2%7D%2B2

%5Cleft%5C%7B%5Cbecause%205%5E%7Bx%7D%3E0%2C%20%5Ctherefore%20%5Csqrt%7B5%5E%7Bx%7D%7D%3D%5Csqrt%7Bt%7D%20%5Ctext%20%7B%20exists%20%7D%5Cright%5C%7D

%5CRightarrow%20%5Csin%20%5Cleft(e%5E%7Bx%7D%5Cright)%20%5Cgeq%202

which is not possible as

%5Csin%20%5Ctheta%20%5Cleq%201

.
Thus, given equation has no solution.

Chapter Questions
1 MCQs