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 a0 , if L is finite , find the values of a and l....???? plz provide detailed solution for the second question.....

Question

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.....

Shubham Singh · Answer

for first question apply L’ Hopitol rule second question is not clear

astha · Answer

... 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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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.....

2 Answers

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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) / x22 – 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.....

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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.....