Question

If `lim_(x→∞) 1/(x + 1) tan((πx + 1)/(2x + 2)) = a/(π - b)(a, b ∈ N)`; then the value of a + b is ______.

Options

• 0.00

• 1.00

• 2.00

• 3.00

Answer 1

If `lim_(x→∞) 1/(x + 1) tan((πx + 1)/(2x + 2)) = a/(π - b)(a, b ∈ N)`; then the value of a + b is 3.00.

Explanation:

`lim_(x→∞)1/(x + 1) cot(π/2 - (πx + 1)/(2x + 2))`

= `lim_(x→∞)1/(x + 1)cot((2π - 2)/(4(x + 1)))`

= `lim_(x→∞)((π - 1)/(2(x + 1)))/(tan  ((π - 1))/(2(x + 1))`

= `2/(π - 1)`

Now, a + b = 2 + 1 = 3