Name:... Batch:... TOPIC: II (C) 1 sec 3 2x - 3 sec 2x. 6 é ë. logtan x (A) log (tan x) (B) cot (log x) (C) log log (tan x) (D) tan (log x) cos x (C)
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1 Nm:... Bch:... TOPIC: II. ( + ) d cos ( ) co( ) n( ) ( ) n (D) non of hs. n sc d sc + sc é ësc sc ù û sc sc é ë ù û (D) non of hs. sc cosc d logn log (n ) co (log ) log log (n ) (D) n (log ). cos log( sin ) d is qul o sin cos sin (D) non of hs. ( ) d is qul o æ ö ç c + è ø æ ö ç è ø æ ö ç + è ø (D) non of hs. ( + ) ( + ) log log d quls æ + ö log è ø é æ + öù log c ê + ú ë è øû é æ + öù logêlog ú ë è øû ë (D) c élog( + ) ( log) ù û 7. sin cos sin cos d is qul o sin sin sin cos sin + cos (D) cos sin 8. If d log + b hn is qul o + (D) 9... ( log ) d is qul o ( log) c + ( log ) (D) non of hs FIITJEE KUKATPALLY CENTRE: # 97, Plo No., Opp. Pl Kun Hud Prk, Vijyngr Colony, Hydrbd Ph.: 000 FIITJEE (Hydrbd Clsss) Limid., 9/B, Sifbd, (Opp. Scrri) Hydrbd Phon: F:
2 0. cos d is qul o cos sin + log (sc n ) sin + log (sc + n ) sin log (sc n ) (D) sin log (sc + n ) log. d log log log log log + log + (D) non of hs.. sin d sin cos cos + sin + cos ( cos ) ( os ) ìï üï í ýd ïî éë cos ùû ïþ æ log (sc + n ) n ö è ø æ log (sc n ) n ö è ø sin (D) sin cos + sin æ log (sc + n ) + n ö è ø (D) non of hs. ( ) d ( ) ( ) + + ( ) ( ) (D) non of hs. { ( ) + ( )} sin log cos log d sin (log ) cos (log ) log (sin ) (D) log (cos ) d. is qul o cos + sin log (n co ) n (n co ) log (co n ) (D) n ( co ) + cos 7. d is qul o (+ cos ) æ sin ö è cos + ø æ cos ö è sin+ ø æ cos ö è cos + ø (D) æ sin ö è sin + ø 8. I (+ + ) d is qul o (+ ) n + æ ç ö è ø n + æ ö è ø n æ ç ö è ø (D) non of hs FIITJEE KUKATPALLY CENTRE: # 97, Plo No., Opp. Pl Kun Hud Prk, Vijyngr Colony, Hydrbd Ph.: 000 FIITJEE (Hydrbd Clsss) Limid., 9/B, Sifbd, (Opp. Scrri) Hydrbd Phon: F:
3 9. I d is qul o ln sin n ln sin ASSIGNMENT æ sin ö ln n è ø (D) non of hs log + sin cos d is qul o sin os sin cos sin sin os (cos )/ (D) sin os sin 0. ( ) FIITJEE KUKATPALLY CENTRE: # 97, Plo No., Opp. Pl Kun Hud Prk, Vijyngr Colony, Hydrbd Ph.: 000 FIITJEE (Hydrbd Clsss) Limid., 9/B, Sifbd, (Opp. Scrri) Hydrbd Phon: F:
4 SOLUTIONS. Pu \ I sc d n n ( ) ; Hnc is h corrc nswr.. I n n sc d ( sc ) sc nd Pu sc \ sc n d d \ I ( ) d æ ö ç è ( sc sc ) ø Hnc is h corrc nswr.. pu log n sc d d n sc cosc d d d log log (log n ) Hnc is h corrc nswr.. logsin sin \ cos sin d Pu cos cos Þ d Hnc is h corrc nswr.. I \ ( ) d. Pu d d,\ I d / / æ ö. c / ç + è ø Hnc is h corrc nswr. æ + ö logç. I è ø. d + 7. I ( ) Now pu + + \ d d \ I log. d ( log ) éæ + ö ù logê ú+ c êë è ø úû Hnc is h corrc nswr. sin sin cos d s sin (sin cos ) sin Hnc cos d Pu sin Þ cos d d d sin. Hnc is h corrc nswr. FIITJEE KUKATPALLY CENTRE: # 97, Plo No., Opp. Pl Kun Hud Prk, Vijyngr Colony, Hydrbd Ph.: 000 FIITJEE (Hydrbd Clsss) Limid., 9/B, Sifbd, (Opp. Scrri) Hydrbd Phon: F:
5 8. Muliplying bov nd blow by nd pu \ d d d \ I. log + I log \ + Hnc is h corrc nswr. 9. Pu \ I gin pu z \ I Hnc is h corrc nswr.. d log z z dz log ( log) ( log ) cos 0. I d cos I ( cos sc ) d cos d sc d Hnc (D) is h corrc nswr. log log. (by propry of ponnil funcion) sin log sc + n log + log log d d log + Hnc is h corrc nswr. log log. By prs I cos + sin os wih lrn +, sign. Diffrniion Ingrion sin cos sin 0 cos Hnc is h corrc nswr.. Hr w hv cos bu is d.c. i.., sin is no prsn in h numrior nd s such w cnno mk h subsiuion of cos. bu w simply pu cos o spli h ingrnd ino pril frcions. cos æ ö æ ö ç ç cos os + è + ø è cos + cos ø ( ) ( ) \ I æ ö ç è cos + cos ø d æ ö æ ö ç sc sc d log (sc + n ) n è ø è ø Hnc is h corrc nswr.. Pu ( ) d d d ( ) ( ) d Hnc is h corrc nswr. ( ) ( ).. Pu log Þ d d I ( sin os ) d sin sin (log ). Hnc is h corrc nswr. FIITJEE KUKATPALLY CENTRE: # 97, Plo No., Opp. Pl Kun Hud Prk, Vijyngr Colony, Hydrbd Ph.: 000 FIITJEE (Hydrbd Clsss) Limid., 9/B, Sifbd, (Opp. Scrri) Hydrbd Phon: F:
6 d sc (+ n ) sc d. L I d cos + sin + n + n If n p, hn sc d dp æ ö p ç + (+ p ) dp (+ p ) dp + p è p ø dp p p + æ ö p ç p + è p ø dk \ I n (k) k + æ ö If p k, hnç + dp dk p è p ø n ç p n (n co ) n ( co ) è pø Hnc nd (D) r h corrc nswrs. æ ö + cos 7. L I d (+ cos ) Muliplying Nr. & Dr. by cosc ( cos c + co cos c ) Þ I d (cos c + co ) æ sin ö. cosc + co è + cos ø Hnc is h corrc nswr. (cos c + co ) cos c co cos c d 8. Subsiuing p, d p dp p (p + p + p) (p + p + ) I dp dp æ ö p (+ p ) p dp dp (p + ) + è p + ø p + n p n + æ ö. è ø Hnc is h corrc nswr. 9. d d d, pu sin z dz d dz cos cz dz sin z Hnc is h corrc nswr. ln z n + k ln æ sin ö n + k è ø 0. log cos I cos d+ sin cos d sin os Hnc is h corrc nswr. FIITJEE KUKATPALLY CENTRE: # 97, Plo No., Opp. Pl Kun Hud Prk, Vijyngr Colony, Hydrbd Ph.: 000 FIITJEE (Hydrbd Clsss) Limid., 9/B, Sifbd, (Opp. Scrri) Hydrbd Phon: F:
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