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Question Number 80343 Answers: 0 Comments: 3

lim_(x→0) ((ln(tan x+1)−sin x)/(xsin x))

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{ln}\left(\mathrm{tan}\:{x}+\mathrm{1}\right)−\mathrm{sin}\:{x}}{{x}\mathrm{sin}\:{x}} \\ $$

Question Number 80312 Answers: 1 Comments: 17

Question Number 80306 Answers: 0 Comments: 1

Question Number 80300 Answers: 0 Comments: 4

Question Number 80347 Answers: 1 Comments: 6

let x and y be positif real number such that 1≤x+y≤9 and x≤2y≤3x. what is the largest value of ((9−y)/(9−x))

$${let}\:{x}\:{and}\:{y}\:{be}\:{positif}\:{real}\:{number} \\ $$$${such}\:{that}\:\mathrm{1}\leqslant{x}+{y}\leqslant\mathrm{9}\:{and} \\ $$$${x}\leqslant\mathrm{2}{y}\leqslant\mathrm{3}{x}.\:{what}\:{is}\:{the}\: \\ $$$${largest}\:{value}\:{of}\:\:\:\frac{\mathrm{9}−{y}}{\mathrm{9}−{x}} \\ $$$$ \\ $$

Question Number 80296 Answers: 0 Comments: 3

what is the value of lim_(x→−∞ ) e^((6x^2 +x)/(3x+5)) ? 0 or ∞ ?

$${what}\:{is}\:{the}\:{value}\:{of}\: \\ $$$$\underset{{x}\rightarrow−\infty\:} {\mathrm{lim}}\:{e}^{\frac{\mathrm{6}{x}^{\mathrm{2}} +{x}}{\mathrm{3}{x}+\mathrm{5}}} \:? \\ $$$$\mathrm{0}\:{or}\:\infty\:? \\ $$

Question Number 80293 Answers: 0 Comments: 12

Find all functions that satisfy to (E): ∀ x∈R xf(x)+∫_0 ^x f(x−t)cos(2t)dt=sin(2x)

$${Find}\:{all}\:{functions}\:{that}\:\:{satisfy}\:{to}\:\: \\ $$$$\left({E}\right):\:\forall\:{x}\in\mathbb{R}\:\:\:\:\:\:{xf}\left({x}\right)+\int_{\mathrm{0}} ^{{x}} {f}\left({x}−{t}\right){cos}\left(\mathrm{2}{t}\right){dt}={sin}\left(\mathrm{2}{x}\right) \\ $$$$\: \\ $$

Question Number 80284 Answers: 0 Comments: 0

Question Number 80276 Answers: 1 Comments: 1

lim_(x→0) ((e^x −e^(−x) −2x)/(x−sin(x)))=L >0 , L∈R find L with out using hopital and Taylor methods

$$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\:\frac{{e}^{{x}} −{e}^{−{x}} −\mathrm{2}{x}}{{x}−{sin}\left({x}\right)}={L}\:\:>\mathrm{0}\:,\:{L}\in{R} \\ $$$${find}\:{L} \\ $$$$ \\ $$$${with}\:{out}\:{using}\:{hopital}\:{and}\:{Taylor}\:{methods} \\ $$

Question Number 80262 Answers: 0 Comments: 2

Question Number 80261 Answers: 0 Comments: 1

Question Number 80260 Answers: 0 Comments: 3

Question Number 80243 Answers: 0 Comments: 7

if x+(1/x)=a (a∈R) find x^n +(1/x^n )=? (n∈N)

$${if}\:{x}+\frac{\mathrm{1}}{{x}}={a}\:\left({a}\in\mathbb{R}\right) \\ $$$${find}\:{x}^{{n}} +\frac{\mathrm{1}}{{x}^{{n}} }=? \\ $$$$\left({n}\in\mathbb{N}\right) \\ $$

Question Number 80237 Answers: 1 Comments: 5

Question Number 80230 Answers: 1 Comments: 0

Question Number 80227 Answers: 0 Comments: 5

how to prove ∫_0 ^1 x^n (1−x)^(m ) dx = ((m! ×n!)/((m+n)!)) via Gamma function

$${how}\:{to}\:{prove} \\ $$$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:{x}^{{n}} \:\left(\mathrm{1}−{x}\right)^{{m}\:} \:{dx}\:=\:\frac{{m}!\:×{n}!}{\left({m}+{n}\right)!} \\ $$$${via}\:{Gamma}\:{function} \\ $$

Question Number 80222 Answers: 1 Comments: 2

Question Number 80220 Answers: 0 Comments: 3

Question Number 80219 Answers: 1 Comments: 0

Question Number 80209 Answers: 2 Comments: 1

Question Number 80208 Answers: 0 Comments: 0

Question Number 80207 Answers: 0 Comments: 6

Question Number 80206 Answers: 1 Comments: 2

Question Number 80204 Answers: 0 Comments: 2

Question Number 80199 Answers: 2 Comments: 1

Question Number 80180 Answers: 1 Comments: 0

h(x)=((x−x^2 )/(x+1)) we defined this function on R−{−1}→R 1) Study the variations of h then draw up its table of variation. please sirs i need your kind help

$$\mathrm{h}\left({x}\right)=\frac{{x}−{x}^{\mathrm{2}} }{{x}+\mathrm{1}} \\ $$$${we}\:{defined}\:{this}\:{function}\:{on} \\ $$$$\mathbb{R}−\left\{−\mathrm{1}\right\}\rightarrow\mathbb{R} \\ $$$$ \\ $$$$\left.\mathrm{1}\right)\:\mathrm{Study}\:\mathrm{the}\:\mathrm{variations}\:\mathrm{of}\:\mathrm{h}\:\mathrm{then} \\ $$$$\mathrm{draw}\:\mathrm{up}\:\mathrm{its}\:\mathrm{table}\:\mathrm{of}\:\mathrm{variation}. \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{sirs}\:\mathrm{i}\:\mathrm{need}\:\mathrm{your}\:\mathrm{kind}\:\mathrm{help} \\ $$

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