Question Number 149184 by liberty last updated on 03/Aug/21

Ω =lim_(x→1) ((tan (√(3x+2))−tan (√(2x+3)))/(tan (√(5x+4))−tan (√(4x+5)))) =?

Answered by EDWIN88 last updated on 03/Aug/21

Ω=lim_(x→1) (((3/(2(√(3x+2)))) sec ^2 (√(3x+2))−(1/( (√(2x+3))))sec ^2 (√(2x+3)))/((5/(2(√(5x+4))))sec ^2 (√(5x+4))−(2/( (√(4x+5))))sec ^2 (√(4x+5)))) =(((3/(2(√5) cos ^2 (√5)))−(1/( (√5) cos ^2 (√5))))/((5/(6 cos ^2 3))−(2/(3 cos ^2 3)))) =((1/(2(√5) cos ^2 (√5)))/(1/(6 cos ^2 3))) = ((6cos ^2 3)/(2(√5) cos ^2 (√5))) = (3/( (√5))) ((cos ^2 3)/(cos ^2 (√5))) = 3(√(1/5)).(((cos 3)/(cos (√5))))^2