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Question Number 80442 Answers: 1 Comments: 4

Question Number 80433 Answers: 1 Comments: 6

find the solution of (√(4−x))−2≤x∣x−3∣+4x

$${find}\:{the}\:{solution}\:{of} \\ $$$$\sqrt{\mathrm{4}−{x}}−\mathrm{2}\leqslant{x}\mid{x}−\mathrm{3}\mid+\mathrm{4}{x} \\ $$

Question Number 80432 Answers: 0 Comments: 7

Question Number 80417 Answers: 0 Comments: 5

lim_(x→0) (((1+x)^(1/x) −e)/x) = ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}+{x}\right)^{\frac{\mathrm{1}}{{x}}} −{e}}{{x}}\:=\:? \\ $$

Question Number 80416 Answers: 1 Comments: 0

∫_0 ^(π/2) ((xcos x)/((1+sin x)^2 )) dx ?

$$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{{x}\mathrm{cos}\:{x}}{\left(\mathrm{1}+\mathrm{sin}\:{x}\right)^{\mathrm{2}} }\:{dx}\:? \\ $$

Question Number 80405 Answers: 1 Comments: 11

Solve: (a) (x − 3)^2 > − 5 (b) 3x^2 > − 12

$$\mathrm{Solve}: \\ $$$$\left(\mathrm{a}\right)\:\:\:\:\:\:\:\:\:\left(\mathrm{x}\:−\:\mathrm{3}\right)^{\mathrm{2}} \:\:>\:\:−\:\mathrm{5} \\ $$$$\left(\mathrm{b}\right)\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{3x}^{\mathrm{2}} \:\:>\:\:−\:\mathrm{12} \\ $$

Question Number 80404 Answers: 1 Comments: 0

Question Number 80402 Answers: 0 Comments: 0

Question Number 80397 Answers: 0 Comments: 3

show that ∫_0 ^(π/2) ∫_0 ^∞ (1/((x^π )^(1/y) +1)) dx dy =2c whrre c denote tha catalan^, s constant

$${show}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}}{\sqrt[{{y}}]{{x}^{\pi} }\:+\mathrm{1}}\:{dx}\:{dy}\:=\mathrm{2}{c}\: \\ $$$${whrre}\:{c}\:{denote}\:{tha}\:{catalan}^{,} {s}\:{constant} \\ $$

Question Number 80386 Answers: 1 Comments: 2

Question Number 80376 Answers: 1 Comments: 2

Question Number 80374 Answers: 0 Comments: 5

Question Number 80369 Answers: 0 Comments: 1

Question Number 80365 Answers: 1 Comments: 6

Question Number 80362 Answers: 1 Comments: 0

Question Number 80341 Answers: 1 Comments: 0

A particle moves round the polar curve r = a(1 + cos θ) with constant angular velocity ω . Find the transverse component of the velocity.

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{moves}\:\mathrm{round}\:\mathrm{the}\:\mathrm{polar}\:\mathrm{curve} \\ $$$${r}\:=\:{a}\left(\mathrm{1}\:+\:\mathrm{cos}\:\theta\right)\:\mathrm{with}\:\mathrm{constant}\:\mathrm{angular}\: \\ $$$$\mathrm{velocity}\:\omega\:.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{transverse}\:\mathrm{component} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{velocity}. \\ $$

Question Number 80340 Answers: 1 Comments: 0

If P = ((a,b,c,d),(c,d,a,b) ) , Q = ((a,b,c,d),(b,a,d,c) ) are permutations of the elements (a,b,c,d), then QP ≡

$$\mathrm{If}\:{P}\:=\:\begin{pmatrix}{{a}}&{{b}}&{{c}}&{{d}}\\{{c}}&{{d}}&{{a}}&{{b}}\end{pmatrix}\:\:,\:{Q}\:=\:\begin{pmatrix}{{a}}&{{b}}&{{c}}&{{d}}\\{{b}}&{{a}}&{{d}}&{{c}}\end{pmatrix}\:\mathrm{are} \\ $$$$\mathrm{permutations}\:\mathrm{of}\:\mathrm{the}\:\mathrm{elements}\:\left({a},{b},{c},{d}\right),\:\mathrm{then}\: \\ $$$${QP}\:\equiv \\ $$$$\: \\ $$

Question Number 80334 Answers: 0 Comments: 1

let f∈L^1 (R) let u_n = ∫_a ^b f(t)sin(nt)dt , v_n =∫_a ^b ((f(t))/t)sin(nt) 1)Prove that lim_(n→∞) u_n =0 2)Deduce in term of a,b,f(0) the value of lim_(n→∞) v_n

$$\:{let}\:\:\:{f}\in{L}^{\mathrm{1}} \left(\mathbb{R}\right)\:\:\: \\ $$$${let}\:\:{u}_{{n}} =\:\int_{{a}} ^{{b}} {f}\left({t}\right){sin}\left({nt}\right){dt}\:,\:{v}_{{n}} =\int_{{a}} ^{{b}} \frac{{f}\left({t}\right)}{{t}}{sin}\left({nt}\right)\: \\ $$$$\left.\mathrm{1}\right){Prove}\:{that}\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{u}_{{n}} =\mathrm{0} \\ $$$$\left.\mathrm{2}\right){Deduce}\:\:{in}\:{term}\:{of}\:{a},{b},{f}\left(\mathrm{0}\right)\:{the}\:{value}\:{of}\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{v}_{{n}} \:\: \\ $$

Question Number 80332 Answers: 0 Comments: 1

let α ∈R and a_n =Σ_(k=1) ^n ((sin(kα))/(n+k)) Find lim_(n→∞) a_n

$$\:\:{let}\:\alpha\:\in\mathbb{R}\:\:{and}\:\:\:\:{a}_{{n}} =\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{{sin}\left({k}\alpha\right)}{{n}+{k}} \\ $$$${Find}\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\:{a}_{{n}} \: \\ $$

Question Number 80346 Answers: 0 Comments: 0

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 ∞ ?

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

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