Question

Find the value of bc......

Answer 1

Lt(x→1) (1 + ax + bx²)^c/(x -1) = e^3

according to question ,
if we let Limit is in the from of 1^∞ ,
then,
1 + a(1) + b(1)² = 1
a + b = 0 -------(1)

now,
= e^Lt(x→1) c/(x-1)log(1 + ax + bx²)

= e^Lt(x→1) c/(x -1)×(ax + bx²)

= e^c(ax + bx²)/(x -1)

put x = 1
you can see limit is in the. form of 0/0

so, = e^c(a + 2bx) = e^c(a + 2b) = e^3

e^c(a + b+ b ) = e^3

a +b = 0

so,
e^c(b) = e^3

bc = 3