Question #6cdd8

1 Answer
Manasvini Nittala
Oct 24, 2017

the answer is #a=-250#

Explanation:

the given question is #lim_(trarr0)(at-tan(5t))/(t^3)=-125/3#
on applying L'Hospital's Rule we get
#lim_(trarr0)(a-5sec^2(5t))/(3t^2)=-125/3#
since it is in indeterminate form again applying L'Hospital's Rule
#lim_(trarr0)(a-50tan(5t)sec^2(5t))/(6t)=-125/3#
on apllying L'Hospital's Rule again
#lim_(trarr0)(a-500sec^4(5t)tan(5t))/6=-125/3#
on applying limit and solving we get #a=-250#

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