Let α be a positive real number. Let f : ℝ → ℝ and g : α , ∞ → ℝ be the functions defined by f x = sin π x 12 and g x = 2 log e x - α log e e x - e α . Then the value of lim x → α + f g x is ______.

Question

Let &#945; be a positive real number. Let f : &#8477; &#8594; &#8477; and g : &#945; , &#8734; &#8594; &#8477; be the functions defined by f x = sin &#960; x 12 and g x = 2 log e x - &#945; log e e x - e &#945; . Then the value of lim x &#8594; &#945; + f g x is ______.

Aicharya · Accepted Answer

lim x &#8594; &#945; + g x = lim x &#8594; &#945; + 2 log e x - &#945; log e e x - e &#945; = lim x &#8594; &#945; + 2 x - &#945; 1 2 x 1 e x - e &#945; 1 2 x e x = lim x &#8594; &#945; + e x - e &#945; x - &#945; 1 e x &#183; 2 = 2 e &#945; lim x &#8594; &#945; + e x &#183; 1 2 x 1 2 x = 2 lim x &#8594; &#945; + f g x = f lim x &#8594; &#945; + g x = f 2 = sin &#960; 6 = 1 2 = 0 . 50

Let α be a positive real number. Let f : ℝ → ℝ and g : α , ∞ →…

Solution

Let &#945; be a positive real number. Let f : &#8477; &#8594; &#8477; and g : &#945; , &#8734; &#8594;…

Solution

Let α be a positive real number. Let f : ℝ → ℝ and g : α , ∞ →…