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Question Number 60202 Answers: 0 Comments: 0

construct the point M^′ =(1/2)((((z+∣z∣))/2))

$${construct}\:{the}\:{point}\:{M}^{'} =\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\left({z}+\mid{z}\mid\right)}{\mathrm{2}}\right) \\ $$

Question Number 60197 Answers: 1 Comments: 1

valculste lim_(n→+∞) (ln((Π_(k=1) ^n (1+(k^3 /n^3 )))^(1/n) )

$${valculste}\:{lim}_{{n}\rightarrow+\infty} \left({ln}\left(\left(\prod_{{k}=\mathrm{1}} ^{{n}} \left(\mathrm{1}+\frac{{k}^{\mathrm{3}} }{{n}^{\mathrm{3}} }\right)\right)^{\frac{\mathrm{1}}{{n}}} \right)\right. \\ $$

Question Number 60198 Answers: 1 Comments: 0

find lim_(n→+∞) ln(Π_(k=1) ^n (1+(k^4 /n^4 ))^(1/n) )

$${find}\:{lim}_{{n}\rightarrow+\infty} \:{ln}\left(\prod_{{k}=\mathrm{1}} ^{{n}} \left(\mathrm{1}+\frac{{k}^{\mathrm{4}} }{{n}^{\mathrm{4}} }\right)^{\frac{\mathrm{1}}{{n}}} \right) \\ $$

Question Number 60189 Answers: 0 Comments: 0

Question Number 60175 Answers: 0 Comments: 2

solving u^v =w with u, v, w ∈C finding all possible solutions I tested this with several values and found no mistake. please review and comment. I hope this will help at least some of you.

$$\mathrm{solving}\:{u}^{{v}} ={w}\:\mathrm{with}\:{u},\:{v},\:{w}\:\in\mathbb{C} \\ $$$$\mathrm{finding}\:\mathrm{all}\:\mathrm{possible}\:\mathrm{solutions} \\ $$$$\mathrm{I}\:\mathrm{tested}\:\mathrm{this}\:\mathrm{with}\:\mathrm{several}\:\mathrm{values}\:\mathrm{and}\:\mathrm{found} \\ $$$$\mathrm{no}\:\mathrm{mistake}.\:\mathrm{please}\:\mathrm{review}\:\mathrm{and}\:\mathrm{comment}. \\ $$$$\mathrm{I}\:\mathrm{hope}\:\mathrm{this}\:\mathrm{will}\:\mathrm{help}\:\mathrm{at}\:\mathrm{least}\:\mathrm{some}\:\mathrm{of}\:\mathrm{you}. \\ $$

Question Number 60170 Answers: 0 Comments: 0

∫xsec^3 xdx

$$\int{x}\mathrm{sec}\:^{\mathrm{3}} {xdx} \\ $$

Question Number 60156 Answers: 3 Comments: 2

Prove by principle of mathematical induction sin(x) + sin(2x) + sin(3x) + ... + sin(nx) = ((cos((1/2)x) − cos(n + (1/2))x)/(2 sin((1/2)x)))

$$\mathrm{Prove}\:\mathrm{by}\:\mathrm{principle}\:\mathrm{of}\:\mathrm{mathematical}\:\mathrm{induction} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{sin}\left(\mathrm{x}\right)\:+\:\mathrm{sin}\left(\mathrm{2x}\right)\:+\:\mathrm{sin}\left(\mathrm{3x}\right)\:+\:...\:+\:\mathrm{sin}\left(\mathrm{nx}\right)\:\:=\:\:\frac{\mathrm{cos}\left(\frac{\mathrm{1}}{\mathrm{2}}\mathrm{x}\right)\:−\:\mathrm{cos}\left(\mathrm{n}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\right)\mathrm{x}}{\mathrm{2}\:\mathrm{sin}\left(\frac{\mathrm{1}}{\mathrm{2}}\mathrm{x}\right)} \\ $$

Question Number 60152 Answers: 0 Comments: 16

Join Telegram group @booksforjee To get evry books pdfs related to NEET, JEE(MAIN ADVANCED) and all engineering entrance exam books Also Books for class XII,XI,X,IX

$${Join}\:{Telegram}\:{group} \\ $$$$@{booksforjee} \\ $$$${To}\:{get}\:{evry}\:{books}\:{pdfs} \\ $$$${related}\:{to}\:{NEET},\:{JEE}\left({MAIN}\:{ADVANCED}\right) \\ $$$${and}\:{all}\:{engineering}\:{entrance}\:{exam}\:{books} \\ $$$${Also} \\ $$$${Books}\:{for}\:{class}\:{XII},{XI},{X},{IX} \\ $$

Question Number 60155 Answers: 1 Comments: 0

Show that: (1/2) + cos(x) + cos(2x) + ... + cos(nx) = ((sin(n + (1/2))x)/(2 sin((1/2))x)) By principle of mathematical induction

$$\mathrm{Show}\:\mathrm{that}: \\ $$$$\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{2}}\:+\:\mathrm{cos}\left(\mathrm{x}\right)\:+\:\mathrm{cos}\left(\mathrm{2x}\right)\:+\:...\:+\:\mathrm{cos}\left(\mathrm{nx}\right)\:\:=\:\:\frac{\mathrm{sin}\left(\mathrm{n}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\right)\mathrm{x}}{\mathrm{2}\:\mathrm{sin}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)\mathrm{x}} \\ $$$$\mathrm{By}\:\mathrm{principle}\:\mathrm{of}\:\mathrm{mathematical}\:\mathrm{induction} \\ $$

Question Number 60143 Answers: 1 Comments: 0

Two passenger trains, A and B, 450km apart, start to move towards each other at the same time and meet after 2 hours. If train B, travels (8/7) as fast as train A, find the speed of each train.

$$\mathrm{Two}\:\mathrm{passenger}\:\mathrm{trains},\:\mathrm{A}\:\mathrm{and}\:\mathrm{B},\:\mathrm{450km}\:\mathrm{apart}, \\ $$$$\mathrm{start}\:\mathrm{to}\:\mathrm{move}\:\mathrm{towards}\:\mathrm{each}\:\mathrm{other}\:\mathrm{at}\:\mathrm{the} \\ $$$$\mathrm{same}\:\mathrm{time}\:\mathrm{and}\:\mathrm{meet}\:\mathrm{after}\:\mathrm{2}\:\mathrm{hours}.\:\mathrm{If}\:\mathrm{train}\:\mathrm{B}, \\ $$$$\mathrm{travels}\:\frac{\mathrm{8}}{\mathrm{7}}\:\mathrm{as}\:\mathrm{fast}\:\mathrm{as}\:\mathrm{train}\:\mathrm{A},\:\mathrm{find}\:\mathrm{the}\:\mathrm{speed} \\ $$$$\mathrm{of}\:\mathrm{each}\:\mathrm{train}. \\ $$

Question Number 60135 Answers: 1 Comments: 0

Question Number 60133 Answers: 2 Comments: 1

Question Number 60132 Answers: 0 Comments: 1

Question Number 60121 Answers: 2 Comments: 3

Question Number 60115 Answers: 0 Comments: 2

Question Number 60095 Answers: 1 Comments: 1

Question Number 60088 Answers: 1 Comments: 1

Question Number 60085 Answers: 1 Comments: 4

Question Number 60058 Answers: 1 Comments: 1

Question Number 60056 Answers: 1 Comments: 1

Question Number 60054 Answers: 1 Comments: 1

Question Number 60053 Answers: 0 Comments: 0

Question Number 60052 Answers: 0 Comments: 0

Question Number 60050 Answers: 1 Comments: 1

calculate ∫_0 ^1 (x^3 −2)(√(x^2 +3))dx

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \left({x}^{\mathrm{3}} −\mathrm{2}\right)\sqrt{{x}^{\mathrm{2}} \:+\mathrm{3}}{dx} \\ $$

Question Number 60045 Answers: 1 Comments: 2

Question Number 60043 Answers: 2 Comments: 0

Show that in a 30°−60°−90° triangle the altitude on the hypotaneuse divides the hypotaneuse into segments whose length has the ratio 1/3. without using trigonometry.

$${Show}\:{that}\:{in}\:{a}\:\mathrm{30}°−\mathrm{60}°−\mathrm{90}°\:{triangle}\:{the}\: \\ $$$${altitude}\:{on}\:{the}\:{hypotaneuse}\:{divides}\:{the}\: \\ $$$${hypotaneuse}\:{into}\:{segments}\:{whose}\:{length} \\ $$$${has}\:{the}\:{ratio}\:\mathrm{1}/\mathrm{3}. \\ $$$${without}\:{using}\:{trigonometry}. \\ $$

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