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1 – limit x tends to 0 sin(pi cos 2 x) / x 2 2 – L = limit x tends to 0 a – (a 2 -x 2 ) 1/2 - x 2 4 ___________________ x 4 a>0 , if L is finite , find the values of a and l....???? plz provide detailed solution for the second question.....

1 – limit x tends to 0
      sin(pi cos2x) / x2
2 –  L = limit x tends to 0
    a – (a2-x2)1/2- x2
                        4
___________________
              x4
    a>0 , if L is finite , find the values of a and l....????
plz provide detailed solution for the second question.....

Grade:12

2 Answers

Shubham Singh
199 Points
6 years ago
for first question 
apply L’ Hopitol rule
second question is not clear
 
astha
11 Points
3 years ago
... lim (x→0) [ sin ( π cos² x ) ] / x² 

= lim (x→0) { sin [ π ( 1 - sin² x ) ] } / x² 

= lim (x→0) [ sin ( π - π sin² x ) ] / x² 

= lim (x→0) [ sin ( π sin² x ) / x² 

= lim (x→0) [ ( π sin² x ) / x² ] ....................... from (1) 

= π • [ lim (x→0) ( (sin x) / x ) ]² 

= π • [ 1 ]² 

= π ........................................... Ans. 

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