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Answer 1 · 2017-06-15T00:51:22

$lim_(x->-1/2pi) (4cos(-3x)sec(-7x))=12/7$

$4cos(-3(-pi/2))sec(-7(pi/2))=0/0$ so we can use L'hopital's rule

$lim_(x->-1/2pi) (4cos(-3x)sec(-7x))$

$=lim_(x->-1/2pi) ((4cos(-3x))/cos(-7x))$

$=lim_(x->-1/2pi) ((d/dx[4cos(-3x)])/(d/dx[cos(-7x)]))$

$=lim_(x->-1/2pi) ((-12sin(-3x))/(-7sin(-7x)))$

$=(-12sin(-3(-1/2pi)))/(-7sin(-7(-1/2pi)))$

$=12/7$