AP EAMCET20226 Jul 2022Morning ShiftMathematicsLimitsActual
If a >0, ~b >0 then _ n ( a+b^ 1 / n -1 a )^n=
Options
- Aa^b
- Bb^a
- Cb^ 1 / a
- Da^ 1 / b
Correct answer
C. b^ 1 / a
Step-by-step solution
y= _ h | a + b ^ 1 n -1 a | now, _e|y|= _ h n _e | a+b^ 1 2 -1 a |^ n _ e | y |= _ h n [ _ e | a + b ^ 1 n -1 |^ n - _ e | a | ] _ e |y|= _ h n [ _ e | a + b ^ 1 n -1 |^ n - _ e | a | (1 / n ) ] _ e | y |= _ h ( 1 a + b ^ 1 n -1 ) b ^ 1 n _ e ( b ) (- 1 n ^2 ) (- 1 n ^2 ) _ e |y|= _ b ( 1 a+b^ 1 n -1 ) (b)^ 1 n _ e (b) _ e | y |= 1 a _ e ( b ) _ e | y |= _ e ( b )^ 1 2 y ( b )^ 1 a