x , x> y =– x , x< ( , ) ( , ) (– , – ) (– , – ) (– , – ) ( , ) (iv) x ′ y ′ O y = e x ( , ) - - Answers (v) x ′ y ′ O y = e – x ( , ) (vi) x ′ y ′ y = , x> y =– , x< O x = Exercise . .(i) (ii) (iii) (iv) (v) (vi) . a = ± . n = .
. f (– ) = Exercise . .(a) Not a continuous function at x = (b) continuous function at x = Exercise . (i) x (ii) e x - - (iii) x Exercise .
.(i) + (ii) (iii) e (iv) (v) x e (vi) x - (vii) - (viii) .(i) ( xe (ii) (iii) e e .(i) (ii) e (iii) log e ` j (iv) cos x (v) e x .(i) sin x (ii) sin x (iii) (iv) (v) n ax bx ax (vi) hh (vii) y = - - Exercise . .(i) (ii) (iii) – ( ax ay . m Exercise . .(i) log sin x (ii) sin cot log sin @ (iii) sec log sin tan x @ (iv) h $ Exercise .
.(i) t (ii) t cost (iii) tan θ (iv) cot . –tan x . sin Exercise . .(i) y (ii) log (iii) cosec i Exercise: .
(d) (c) (a) (b) (a) (a) (c) (a) (d) (a) (a) (d) (b) (a) (a) (a) (c) (b) (d) (a) (a) (c) (a) (b) (d) Miscellaneous Problems . x ′ y ′ ( , ) ( , ) (– , ) ( , ) (– , ) ( , ) (– , ) y = – x . . (i) continuous at = ; differentiable at x = (ii) not continuous at x = ; not differentiable at x =