14. lim (x + y)sec(x + y) - X sec X...
Question

# 14. lim (x + y)sec(x + y) - X sec X у-50 у

JEE/Engineering Exams
Maths
Solution
193
4.0 (1 ratings)
(x) ( 1 f(x+y) sec (x+y)-x sec x ) ( frac{1+x sec (x+y)+y sec (x+y)-x sec x}{y rightarrow 0} frac{y}{y} ) ( left.frac{7+x[5} circ frac{x}{y}left[frac{cos x-cos (x+y)}{cos (x+y) cos x}right]+sec x ] ( operatorname{lit}_{y rightarrow 0} frac{x}{1}left[frac{(cos x-cos (x+y))}{y} cdot frac{x}{cos (x+y) cdot cos x}right]+sec x ) ( frac{1+}{y rightarrow 0} cdotleft[frac{2 sin left(x+frac{y}{2}right) cdot sin (y / 2)}{(2 x y)} cdot frac{x}{cos (x+y) cdot cos x}right]+b operatorname{ccs} x ) [ left[because cos x-cos y=-2 sin left(frac{x+y}{2}right)right. ] ( cdot sin (x-y) ) ( int_{y rightarrow 0}^{y} fleft(x+frac{y}{2}right) cdot 1+frac{sin (y / 2)}{y+0} cdot frac{1+x}{y+0} frac{x}{(y / 2)^{prime}} cdot i sec x ) ( (sin x) cdot(1) cdotleft(frac{x}{cos x cdot cos x}right)+sec x ) ( therefore frac{x tan x}{cos x}+sec x Rightarrow x tan x cdot sec x+sec x )
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