PESIT Bangalore South Campus Hosur road, 1km before Electronic City, Bengaluru -100 Department of Basic Science and Humanities

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1 P E PESIT Bglo South Cpus Hosu od, k bfo Elctoic Cit, Bgluu -00 Dptt of Bsic Scic d Huitis INTERNAL ASSESSMENT TEST Dt : 0/0/07 Mks: 0 Subjct & Cod : Egiig Mthtics I 5MAT Sc : ALL N of fcult : GVR,GKJ,RR,SV,NHM,DN,KR, JMS,NLS Ti ::0 to 0:00 AM Not: Asw FIVE full qustios, slctig ONE full qustio fo ch pt. Mks PART Fid th th divtiv of si sih log If 0 th pov tht 0 Fid th gl btw th cuvs PART log d log b d s Fid d d s fo th cuv d d Fid th divtiv of c lgth t logt t /, si t b Fid th gl btw th cuvs si d 6si. PART 5 Show tht th cuvs d b si itsct ch oth othogoll. b Fid th pdl qutio of 6 Fid th gl btw dius vcto d th tgt d lso fid th slop of th tgt to th cuv si t 7 b Fid th pdl qutio of PART Pov tht th dius of cuvtu ρ t poit, o th cuv is giv b b b b Show tht th dius of cuvtu t poit of th ccloid si, is PART 5 9 Epd t s fo s th t cotiig, usig Mclui s sis 0 Obti Tlo s sis psio of log bout th poit = π/ up to th fouth dg t. BE I sst

2 P E PESIT Bglo South Cpus Hosu od, k bfo Elctoic Cit, Bgluu -00 Dptt of Bsic Scic d Huitis INTERNAL ASSESSMENT TEST - SOLUTIONS Dt : 0/0/07 Mks: 0 Subjct & Cod : Egiig Mthtics I 5MAT Sc : ALL N of fcult : GVR,GKJ,RR,SV,NHM,DN,KR, JMS,NLS Ti ::0 to 0:00 AM Not: Asw FIVE full qustios, slctig ONE full qustio fo ch pt. Mks PART Fid th th divtiv of si sih log Solutio: = si sih log 0 0 Cosid si sih...mks Difftitig tis, w gt = [ { t / } { t / }. / ] ì í î ü ý þ... Mks Cosid log = 0 log log 0 log 0 Difftitig tis, w gt = log log!! = log 0... Mk BE I sst

3 P E PESIT Bglo South Cpus Hosu od, k bfo Elctoic Cit, Bgluu -00 Dptt of Bsic Scic d Huitis BE I sst = 0 log!....mks Thfo þ ý ü î í ì 0 log!...mk If th pov tht 0 Solutio: 0 ±...k Lt th Difftitig with spct to, w gt! If w tk th! Cobiig both w gt ±... Mks Squig o both sids w gt...mk Difftitig gi, w gt Dividig b o both sids, w gt...mk Difftitig tis usig Libitz ul, w gt 0... Mks

4 P E PESIT Bglo South Cpus Hosu od, k bfo Elctoic Cit, Bgluu -00 Dptt of Bsic Scic d Huitis PART Fid th gl btw th cuvs log d log Solutio: log Difftitig with spct to θ, w gt d log. d t log...mk Cosid log Difftitig with spct to θ, w gt d log. d log t log...mk Solvig t log d w gt θ=. log t t log = t t log...mk t...mk b d s Fid d Solutio: d d s fo th cuv d d si d Thfo, d s d d d si BE I sst

5 P E PESIT Bglo South Cpus Hosu od, k bfo Elctoic Cit, Bgluu -00 Dptt of Bsic Scic d Huitis si = = siθ/... Mks d s d d d \ si sic... Mks Fid th divtiv of c lgth t logt t /, si t Solutio: t logt t / Difftitig with spct to t, w gt d d t sc t si t t t = / /. t si t... Mk si t si t si t Difftitig with spct to t, w gt d t... Mk d t d s d t d d t t si t d... Mk d t = t t t si t = ct t t si t si t = c t t= cot t... Mk BE I sst

6 P E PESIT Bglo South Cpus Hosu od, k bfo Elctoic Cit, Bgluu -00 Dptt of Bsic Scic d Huitis b Fid th gl btw th cuvs si d 6si. Solutio: si Difftitig with spct to θ, w gt d t d t t This iplis...mk Cosid 6si. Difftitig with spct to θ, w gt d t d t t This iplis...mk Thfo, Solvig si d 6si. W hv...mk Thfo...Mk PART 5 Show tht th cuvs d b si itsct ch oth othogoll. Solutio: Difftitig with spct to θ, w gt d cot d t cot...mk Cosid b si Difftitig with spct to θ, w gt d t d t t...mk BE I sst

7 P E PESIT Bglo South Cpus Hosu od, k bfo Elctoic Cit, Bgluu -00 Dptt of Bsic Scic d Huitis t t cot t....mk Hc th giv cuvs itsct othogoll....mk b Fid th pdl qutio of Solutio: Difftitig with spct to θ, w gt d si...mk d W hv p d...mk d = si = sic...mk Hc =p...mk 6 Fid th gl btw dius vcto d th tgt d lso fid th slop of th tgt to th cuv si t Solutio: si Difftitig with spct to θ, w gt d t d t t this iplis...mk If, th...mk 6 W hv...mk 6 BE I sst

8 P E PESIT Bglo South Cpus Hosu od, k bfo Elctoic Cit, Bgluu -00 Dptt of Bsic Scic d Huitis Thfo, th slop of th tgt = t t...mk b Fid th pdl qutio of Solutio: Difftitig with spct to θ, w gt d si...mk d W hv p d...mk d = si = sic...mk 7 Hc p =...Mk PART Pov tht th dius of cuvtu ρ t poit, o th cuv b is giv b b b Solutio: b Difftitig with spct to, w gt... 0 b...mk b Difftitig gi, w gt BE I sst

9 P E PESIT Bglo South Cpus Hosu od, k bfo Elctoic Cit, Bgluu -00 Dptt of Bsic Scic d Huitis.. b b. b b b b. b b b b b b Thfo é b ù ê ú ê ú ë û b b b...mks...mk...mk Show tht th dius of cuvtu t poit of th ccloid si, is Solutio: si si si...mk...mk BE I sst

10 P E PESIT Bglo South Cpus Hosu od, k bfo Elctoic Cit, Bgluu -00 Dptt of Bsic Scic d Huitis...Mk...Mks PART 5 9 Epd t s f s th t cotiig, usig Mclui s sis Solutio: t Þ 0... Mk Þ 0... Mk Þ 0... Mk ì í î ü Þ ý þ 0... Mk Þ Mk Mk!!! Mks 0 Obti Tlo s sis psio of log bout th poit = π/ up to th fouth dg t. Solutio: f = log fπ/ = log/= - log... Mk f' =-t f'π/ =... Mk f" = -sc f"π/ = -... Mk f"'= - sc t f"'π/ =... Mk f iv = - sc t - sc f iv π/ = Mk f = fπ/ + -π/f'π/+-π/ f"π/ Mk log=...mks BE I sst

11 P E PESIT Bglo South Cpus Hosu od, k bfo Elctoic Cit, Bgluu -00 Dptt of Bsic Scic d Huitis BE I sst

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