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Please solve question number 54 step by step...................................

Please solve question number 54 step by step................................... 

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Grade:12th pass

1 Answers

Aditya Gupta
2081 Points
4 years ago
obviously lim x tends to 0 sqrt(a+x)= sqrt(a)
so now we have lim x tends to 0 x^3/(bx – sinx)= sqrt(a)
now use series expansion of sinx= x – x^3/3! + O(x^5)
so, we get lim x tends to 0 x^3/(x(b – 1) + x^3/3! – O(x^5))= sqrt(a)
if b – 1 is not equal to zero, then the lim would be 0 as well which means a= 0 too. but then the original limit wont equal 1. so that b – 1 has to be 0. or b= 1.
now, lim becomes lim x tends to 0 x^3/(x^3/3! – O(x^5))= lim x tends to 0 1/(1/3! – 0)= sqrt(a)
or 6= sqrt(a)
or a= 36
kindly approve yar, r u not able to understand and approve even my correct answers?!!

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