Question

integrate...........!!

Answer 1

$\blue{\bold{\underline{\underline{Answer:-}}}}$

f(x) is continuous for all x

f(0) = - 1 < 0

and

f(1) = e - 2 < 0

So By the Intermediate Value Theorem

f(c) = 0 for some number c between x = 0 and x = 1

So, f has at least one real root

Assume that f(x) has another real root say, b Such that f(b) = f(c) = 0

Hence

f is continuous on [b , c]

f is differentiable on (b, c)

So, by Rolle's Theorem, there exists a real number say d in (b, c) such that f'(d) = 0

Answer 2

Step-by-step explanation:

\blue{\bold{\underline{\underline{Answer:-}}}}

Answer:−

f(x) is continuous for all x

f(0) = - 1 < 0

and

f(1) = e - 2 < 0

So By the Intermediate Value Theorem

f(c) = 0 for some number c between x = 0 and x = 1

So, f has at least one real root

Assume that f(x) has another real root say, b Such that f(b) = f(c) = 0

Hence

f is continuous on [b , c]

f is differentiable on (b, c)

So, by Rolle's Theorem, there exists a real number say d in (b, c) such that f'(d) = 0