Question

Using L'hosipital's rule
limit 2 cos(-3 x) sec (7 x)
x->pi/2

Answer 1

@ranga help

Answer 2

To apply L'Hopital's rule the original expression should be of the form f(x) / g(x). Here we can easily rewrite the problem by replacing sec(7x) with 1/cos(7x).
Find limit x ->pi/2 of 2cos(-3x) / cos(7x)
When we try to find the limit as x->pi/2, the ratio becomes 0/0 which is indeterminate and and so we use L'Hopital's rule. Take the derivative of the numerator and divide it by the derivative of the denominator. Now find the limit as x->pi/2. Is the limit defined now? In this case the answer is yes. But if the limit is still indeterminate you can apply the L'Hopital's rule again.
You can apply L'Hopital's rule if the limit takes the indeterminate form +/- 0/0, +/- infinity/infinity.