Question

Q-2: a) Find the limts of: 1: lim (x cotx) sin 7x 2: lim 4x x²+x-2 3: lim x-x (9 marks) b) Find the derivative of the functions: 1- y= In tanh 2x 2- y = cseh (x+1) (6marks)

Answer 1

DATE PAGE NO Onog lim (x cotx) a x=0 -cotx= tuge xx losx suna lim xo sinn xlosx fo-fon) X-70 Sima Lise L'Hospital's Rule tim ( lcosx) dx 70 a (sima) لانے lim losx-xsinx (ov) = udy+vdu कर da X70 Losx Losto) -o smto) Costo) 1. Ans. Lima cofx) - * 2 Lim Sm 7x x-70 use while applying. limitxo it takes L Hospitals Rule %. form. We we use Lim 149 ( 430) Lim Cos7x.7 4 7 Ans lim Smax 7 **D 4 4

lim x²+x-2 → x² + x → -fem DATE PAGE NO use thospital's Rule lim am (xx-2) 보기 a 1x²x) ده 92+1 lim x) ax-1 2 (l) +) 3 9(1)-1 lim x²+x-2 xl n2x "ONOS. In tanhax y = Differentiate both Stdes Luogo x dy a (tostanh 9x)) da dla 2 y using T tanhax cosh (3x)² chein rule follflesencia tien and a lnx = dx Simplity a tanhx 어가 Cash 12 9 Sinh (9x) cosh(x)

DATE PAGE NO of = (sch(x+1 Differenciale both sides with respect to se dy d ( (sch (+0) dix dx J Csch(x+1) * t-cothaiti) (sch (x+71) *9x) --4 sch (:) coth (x+1)x Y'= -4 (sch(x+1)² coth(x+1)x Thank you