Question

P(x) be a polynomial satisfying P(x) – 2P'(x) = 3x³ – 27x² + 38x + 1.

If function

f(x) = `{{:((P^n(x) + 18)/6, x ≠ π/2),(sin^-1(ab) + cos^-1(a + b - 3ab), x = π/2):}`

is continuous at x = ` π/2`, then (a + b) is equal to ______.

Options

• 0.00

• 1.00

• 2.00

• 3.00

Answer 1

P(x) be a polynomial satisfying P(x) – 2P'(x) = 3x³ – 27x² + 38x + 1.

If function

f(x) = `{{:((P^n(x) + 18)/6, x ≠ π/2),(sin^-1(ab) + cos^-1(a + b - 3ab), x = π/2):}`

is continuous at x = ` π/2`, then (a + b) is equal to 2.00.

Explanation:

P(x) = 3x³ – 9x² + 2x + 5  ...(From the given relation)

P’(x) = 9x – 18x + 2

P"(x) = 18x – 18

⇒ f(x) = `{{:(3x",", x ≠ π/2),(sin^-1(ab) + cos^-1(a + b - 3ab)",", x = π/2):}`

For continuity

sin^–1(ab) + cos^–1(a + b – 3ab) = `(3π)/2`

⇒ ab = 1 and a + b – 3ab = –1

⇒ a + b = 2