Question

Let x is a real number such that are functions involved are well defined then the value of `lim_(t→0)[max{(sin^-1  x/3 + cos^-1  x/3)^2, min(x^2 + 4x + 7)}]((sin^-1t)/t)` where [.] is greatest integer function and all other brackets are usual brackets.

विकल्प

• 0.00

• 1.00

• 2.00

• 3.00

Answer 1

3.00

Explanation:

For `sin^-1  x/3 + cos^-1  x/3` to well defined

–3 ≤ x ≤ 3 and `sin^-1  x/3 + cos^-1  x/3 = π/2`

x² + 4x + 7 = (x + 2)² + 3 is minimum at x = –2 and minimum is 3.

∵ Max `{π^2/4, 3}` = 3

`lim_("t"→0) (3sin^-1"t")/"t"` = 3