Question

Question #6cdd8

Answer 1

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`