Let m and n be two positive integers greater than 1. If lim α → 0 ⁡ e c o s ⁡ ( α n   ) - e α m =   - e 2 then the value of m n is

Question

Let m and n be two positive integers greater than 1. If lim &#945; &#8594; 0 &#8289; e c o s &#8289; ( &#945; n &#160; ) - e &#945; m = &#160; - e 2 then the value of m n is

Aicharya · Accepted Answer

lim α → 0 ⁡ e cos ⁡ α n - e α m = - e 2 ⇒ Using L'Hospital's Rule lim α → 0 ⁡ e cos ⁡ α n &sdot; - sin ⁡ α n &sdot; n α n - 1 m &sdot; α m - 1 = - e 2 ⇒ m n = 2 .

Let m and n be two positive integers greater than 1. If lim α → 0 ⁡ e c o s ⁡ ( &#945…

Solution

Let m and n be two positive integers greater than 1. If lim &#945; &#8594; 0 &#8289; e c o s &#8289; ( &#945…

Solution

Let m and n be two positive integers greater than 1. If lim α → 0 ⁡ e c o s ⁡ ( &#945…