Question

2. Find the intervals on which the following function is continuous. tan r B( ) = V4-12 3. Find the derivatives of the following functions (a) f(z)= /5x +1 (b) gla) = (2r -3)(a2 +2) (c) y = In (x + Vx2 - 1) 4. Find the intervals on which the following function is decreasing. f(z) = 36x +3r2 - 2r 5. Evaluate the following integrals. r dr (a) sec2 tan (b) dar 3 (c) da 5x+1 1. Sketch the region enclosed by the given curves and find its area (a) y12 2 y= x2 - 6 (b) x 22, y=2 sin , -/3 x

Answer 1

etvaves Given (K)J SI a(sxti) 2 St sto 2 2 S 25xt g (2x-3) (+2) duv uvtuy', ^^"nxh) dr g'c ') )*(r-3) (x*r2) + 2x3)4 (C)2) g'c 2x3) xp

= 42x-3) (2u)-0) &2) G(27-3)4 ( (2*+o) 2(2-3)ca2}S 2) 2x-3) 8 (2x-3) 236412 (2 3) 4 (27-3 (2)+32) 4C2-3 2*+46qx )= 42x-3)^*a2Y (8x^ qx+4) (e) An (7+ 2

2Ed 2x 2 2

(J-

Entegvals Se -Sy: 4 by drtfecnhanng 5dr= du hPーニ人P Se SY Se 二入P Secx tan tanx Sinx OSx Secxニー Sec dx Sec2 x CoSx Sin2 COs2 tan2 Sec x Sec Sec Sint

Sc2x ay Sin2 ニCSL |-. Ssczdx=-cotx Se .Cotxz tanx tany Sec2i tanzy - tanx 2 d from enO St Considen Cex by differenhah ng SX41=U (= CR P P hPXP S Jn lul+c ^= SW+ SXHI n 2

Gnl sca n l041) = a Jn n (16) (14г LInC16) 5 d \+XS П