Question

Find the approximate value of tan⁻¹(1.001)

Answer 1

this is the answer of this week

Answer 2

Answer:

Tan⁻¹(1.001) ≈ π /4 + 0.0005

Step-by-step explanation:

f(x) = Tan⁻¹(x)

f'(x) = 1/(1 + x²)

f(1) = Tan⁻¹(1) = π /4

f'(1) = 1 /(1 + 1²) = 1/2

Tan⁻¹(1.001) = f(1.001) = f(1 + 0.001)

=>Tan⁻¹(1.001) ≈ f(1) + (0.001)f'(1)

=> Tan⁻¹(1.001) ≈ π /4 + (0.001)(1/2)

=> Tan⁻¹(1.001) ≈ π /4 + 0.0005