The Rolle's theorem is applicable in the interval α =(γ /3)=(6× 10-5/3)=2× 10-5/oc for the function

Question

The Rolle's theorem is applicable in the interval α =(&gamma; /3)=(6× 10-5/3)=2× 10-5/oc for the function (A)  I=4I0 cos 2(φ /2)  (B)  ⇒  (C)  φ =2π /3  (D)  Δ x× (2π /λ )=2π /3

Tardigrade Admin · Accepted Answer

Let f(x)=x2 ∴ f(1)=f(-1)=1 Also, f(x) is continuous and differentiable in the given interval.

Q. The Rolle's theorem is applicable in the interval $α = \frac{γ}{3} = \frac{6 \times 10 ^{- 5}}{3} = 2 \times 10^{- 5} /^{o} c$ for the function

$I = 4 I_{0} cos^{2} (ϕ /2)$

$\Rightarrow$

$ϕ = 2 π /3$

$Δ x \times (2 π / λ) = 2 π /3$

Let $f (x) = x^{2}$ $∴$ $f (1) = f (- 1) = 1$ Also, f(x) is continuous and differentiable in the given interval.

Q. The Rolle's theorem is applicable in the interval α=3γ​=36×10−5​=2×10−5/oc for the function

I=4I0​cos2(ϕ/2)

⇒

ϕ=2π/3

Δx×(2π/λ)=2π/3