If a and b are chosen randomly by throwing a pair of fair dice then the probability that undersetx arrow 0 textLim ((ax+bx/2))(2/x)=6 equals

Question

If a and b are chosen randomly by throwing a pair of fair dice then the probability that undersetx arrow 0 textLim ((ax+bx/2))(2/x)=6 equals (A) (4/9) (B) (2/9) (C) (3/9) (D) (1/9)

Tardigrade Admin · Accepted Answer

e textLimx arrow 0 x (2/)((ax-1+bx-1/2))=e ln a b=a b=6 (a, b)=(1,6)(6,1)(2,3)(3,2) ⇒ P(E)=(4/36)=(1/9)

Q. If $a$ and $b$ are chosen randomly by throwing a pair of fair dice then the probability that $x \to 0 Lim (\frac{a ^{x} + b ^{x}}{2})^{\frac{2}{x}} = 6$ equals

$\frac{4}{9}$

$\frac{2}{9}$

$\frac{3}{9}$

$\frac{1}{9}$

$e^{Lim_{x \to 0 x} 2 (\frac{a ^{x} - 1 + b ^{x} - 1}{2})} = e^{l n ab} = ab = 6$
$(a, b) = (1, 6) (6, 1) (2, 3) (3, 2)$
$\Rightarrow P (E) = \frac{4}{36} = \frac{1}{9}$

Q. If a and b are chosen randomly by throwing a pair of fair dice then the probability that x→0Lim​(2ax+bx​)x2​=6 equals

94​

92​

93​

91​