Q) 

Asked by araima2001 | 12th Jul, 2017, 08:08: PM

Expert Answer:

begin mathsize 16px style limit as straight n rightwards arrow infinity of space open parentheses sin to the power of straight n space 1 plus cos to the power of straight n space 1 close parentheses to the power of 1 over straight n end exponent
rightwards double arrow limit as straight n rightwards arrow infinity of space open square brackets sin to the power of straight n space 1 open parentheses 1 plus tan to the power of straight n space 1 close parentheses close square brackets to the power of 1 over straight n end exponent
rightwards double arrow limit as straight n rightwards arrow infinity of open parentheses sin to the power of straight n space 1 close parentheses to the power of 1 over straight n end exponent open parentheses 1 plus tan to the power of straight n space 1 close parentheses to the power of 1 over straight n end exponent
rightwards double arrow limit as straight n rightwards arrow infinity of open parentheses sin space 1 close parentheses open parentheses 1 plus tan to the power of straight n space 1 close parentheses to the power of fraction numerator 1 over denominator tan to the power of straight n space 1 end fraction cross times fraction numerator tan to the power of straight n space 1 over denominator straight n end fraction end exponent
rightwards double arrow sin space 1 cross times limit as straight n rightwards arrow infinity of straight e to the power of fraction numerator tan to the power of straight n space 1 over denominator straight n end fraction end exponent
rightwards double arrow sin space 1 cross times straight e to the power of 0........................ left parenthesis As space tan space 1 equals 0 right parenthesis
rightwards double arrow sin space 1


NOTE colon space
In space the space question space limit as straight n rightwards arrow infinity of space open parentheses sin to the power of straight n space 1 plus cos to the power of straight n space 1 close parentheses to the power of 1 over straight n end exponent space instead space of space limit as straight n rightwards arrow infinity of space open parentheses sin to the power of straight n space 1 plus cos to the power of straight n space 1 close parentheses to the power of straight n
then space only space value space will space be space sin space 1 space otherwise space it space will space tends space to space zero
as space sin to the power of straight n space 1 space tends space to space 0 space if space straight n space tends space to space infinity. end style

Answered by Sneha shidid | 13th Jul, 2017, 10:02: AM