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Question Number 107745 Answers: 2 Comments: 3

(i) L=lim_(x→0) [(((1+x)^(1/x) )/e)]^(1/x) = ? (ii) L=lim_(x→∞) [(x/e)−x((x/(x+1)))^x ] = ?

$$\left({i}\right)\:\:\:{L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left[\frac{\left(\mathrm{1}+{x}\right)^{\mathrm{1}/{x}} }{{e}}\right]^{\mathrm{1}/{x}} \:\:=\:? \\ $$$$\left({ii}\right)\:\:{L}=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left[\frac{{x}}{{e}}−{x}\left(\frac{{x}}{{x}+\mathrm{1}}\right)^{{x}} \right]\:=\:? \\ $$

Question Number 107741 Answers: 0 Comments: 2

Question Number 107737 Answers: 1 Comments: 0

Question Number 107729 Answers: 6 Comments: 3

1) solve the D.E : (dy/dx)−y tan(x)=−y^2 sec(x) 2)find x Π_(k=1) ^(25) (x+(x/3^k ))=1 3)solve : ∣Z^2 ∣−4Z=0

$$\left.\mathrm{1}\right)\:{solve}\:{the}\:{D}.{E}\:\:\:: \\ $$$$\frac{{dy}}{{dx}}−{y}\:{tan}\left({x}\right)=−{y}^{\mathrm{2}} {sec}\left({x}\right)\: \\ $$$$ \\ $$$$\left.\mathrm{2}\right){find}\:{x} \\ $$$$\underset{{k}=\mathrm{1}} {\overset{\mathrm{25}} {\prod}}\left({x}+\frac{{x}}{\mathrm{3}^{{k}} }\right)=\mathrm{1} \\ $$$$ \\ $$$$\left.\mathrm{3}\right){solve}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mid{Z}^{\mathrm{2}} \mid−\mathrm{4}{Z}=\mathrm{0} \\ $$

Question Number 107728 Answers: 1 Comments: 0

Question Number 107727 Answers: 0 Comments: 0

Determine all possible solutions to the equation ; (1+t^3 )x′(t)+t^2 x(t)+t(x(t))^2 =0

$$\mathrm{Determine}\:\mathrm{all}\:\mathrm{possible}\:\mathrm{solutions}\:\mathrm{to}\:\mathrm{the}\:\mathrm{equation}\:; \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{1}+\mathrm{t}^{\mathrm{3}} \right){x}'\left(\mathrm{t}\right)+\mathrm{t}^{\mathrm{2}} {x}\left(\mathrm{t}\right)+\mathrm{t}\left({x}\left(\mathrm{t}\right)\right)^{\mathrm{2}} =\mathrm{0} \\ $$

Question Number 107718 Answers: 1 Comments: 0

Question Number 107714 Answers: 2 Comments: 0

((✓BeMath✓)/(cooll)) lim_(x→0) (1−tan x)^(4/(sin^2 x)) =?

$$\:\:\:\frac{\checkmark\mathcal{B}{e}\mathcal{M}{ath}\checkmark}{{cooll}} \\ $$$$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\mathrm{1}−\mathrm{tan}\:{x}\right)^{\frac{\mathrm{4}}{\mathrm{sin}\:^{\mathrm{2}} {x}}} \:=? \\ $$

Question Number 107711 Answers: 1 Comments: 1

Question Number 107710 Answers: 1 Comments: 0

✓((BeMath✓)/(cooll)) lim_(x→∞) (((x+5)/(x−3)))^((3x+1)/(cos 2x)) ?

$$\:\:\:\checkmark\frac{\mathcal{B}{e}\mathcal{M}{ath}\checkmark}{{cooll}} \\ $$$$\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{{x}+\mathrm{5}}{{x}−\mathrm{3}}\right)^{\frac{\mathrm{3}{x}+\mathrm{1}}{\mathrm{cos}\:\mathrm{2}{x}}} \:? \\ $$

Question Number 107706 Answers: 4 Comments: 0

✓BeMath✓ (1) ∫_0 ^∞ ((√x)/(1+x^3 )) dx ? (2) lim_(x→0) ((sin (π cos^2 x))/x^2 ) (3) If g(x)= 1+(√x) and (g○f)(x)=3+2(√x) +x find f(x)

$$\:\:\:\:\:\:\:\:\:\:\:\:\checkmark\mathcal{B}{e}\mathcal{M}{ath}\checkmark \\ $$$$\:\left(\mathrm{1}\right)\:\:\:\:\:\:\:\:\:\:\:\underset{\mathrm{0}} {\overset{\infty} {\int}}\:\frac{\sqrt{{x}}}{\mathrm{1}+{x}^{\mathrm{3}} }\:{dx}\:? \\ $$$$\:\:\left(\mathrm{2}\right)\:\:\:\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left(\pi\:\mathrm{cos}\:^{\mathrm{2}} {x}\right)}{{x}^{\mathrm{2}} }\: \\ $$$$\left(\mathrm{3}\right)\:{If}\:{g}\left({x}\right)=\:\mathrm{1}+\sqrt{{x}}\:{and}\:\left({g}\circ{f}\right)\left({x}\right)=\mathrm{3}+\mathrm{2}\sqrt{{x}}\:+{x} \\ $$$$\:\:\:{find}\:{f}\left({x}\right) \\ $$

Question Number 107704 Answers: 0 Comments: 0

Question Number 107705 Answers: 0 Comments: 0

Question Number 107696 Answers: 1 Comments: 1

Question Number 107695 Answers: 1 Comments: 0

♠BeMath♠ ∫_0 ^1 ((x−1)/((x+1)ln x)) dx ?

$$\:\:\:\spadesuit\mathcal{B}{e}\mathcal{M}{ath}\spadesuit \\ $$$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{{x}−\mathrm{1}}{\left({x}+\mathrm{1}\right)\mathrm{ln}\:{x}}\:{dx}\:?\: \\ $$

Question Number 107690 Answers: 1 Comments: 0

“BeMath“ Let the complex number z satisfies the equation 3(z−1)= i(z+1) (1) find z in the form a+bi where a,b ∈R (2) find the value of ∣z∣ and ∣z−z^∗ ∣

$$\:\:\:\:\:\:\:\:``\mathcal{B}{e}\mathcal{M}{ath}`` \\ $$$${Let}\:{the}\:{complex}\:{number}\:{z}\:{satisfies}\:{the} \\ $$$${equation}\:\mathrm{3}\left({z}−\mathrm{1}\right)=\:{i}\left({z}+\mathrm{1}\right)\: \\ $$$$\left(\mathrm{1}\right)\:{find}\:{z}\:{in}\:{the}\:{form}\:{a}+{bi}\:{where}\:{a},{b}\:\in\mathbb{R}\: \\ $$$$\left(\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\mid{z}\mid\:{and}\:\mid{z}−{z}^{\ast} \mid\: \\ $$$$ \\ $$

Question Number 107687 Answers: 0 Comments: 0

Question Number 107684 Answers: 1 Comments: 0

“BeMath“ ln tan 1°+ln tan 2°+ln tan 3°+...+ln tan 89°=?

$$\:\:\:\:\:``\mathcal{B}{e}\mathcal{M}{ath}`` \\ $$$$\:\mathrm{ln}\:\mathrm{tan}\:\mathrm{1}°+\mathrm{ln}\:\mathrm{tan}\:\mathrm{2}°+\mathrm{ln}\:\mathrm{tan}\:\mathrm{3}°+...+\mathrm{ln}\:\mathrm{tan}\:\mathrm{89}°=? \\ $$

Question Number 107679 Answers: 0 Comments: 0

dear tinku tara Please add a option which gives us to save a file as pdf.

$$\mathrm{dear}\:\mathrm{tinku}\:\mathrm{tara}\: \\ $$$$\mathrm{Please}\:\mathrm{add}\:\mathrm{a}\:\mathrm{option}\:\mathrm{which}\:\mathrm{gives}\: \\ $$$$\mathrm{us}\:\mathrm{to}\:\mathrm{save}\:\mathrm{a}\:\mathrm{file}\:\mathrm{as}\:\mathrm{pdf}. \\ $$

Question Number 107674 Answers: 2 Comments: 0

f(x)=(√x)(√x) D_f =???

$${f}\left({x}\right)=\sqrt{{x}}\sqrt{{x}}\:\:\:\:\:\:\:{D}_{{f}} =??? \\ $$

Question Number 107673 Answers: 3 Comments: 0

Question Number 107672 Answers: 1 Comments: 2

♠BeMath♠ ((4sin (((2π)/7))+sec ((π/(14))))/(cot ((π/7)))) ?

$$\:\:\:\:\:\spadesuit\mathcal{B}{e}\mathcal{M}{ath}\spadesuit \\ $$$$\:\:\:\:\frac{\mathrm{4sin}\:\left(\frac{\mathrm{2}\pi}{\mathrm{7}}\right)+\mathrm{sec}\:\left(\frac{\pi}{\mathrm{14}}\right)}{\mathrm{cot}\:\left(\frac{\pi}{\mathrm{7}}\right)}\:? \\ $$

Question Number 107659 Answers: 1 Comments: 0

∮Bobhans∮ If all the letters of the word MISSISSIPPI are written down at random , the probability that all the four S appear consecutively is ___

$$\:\:\:\:\:\oint\mathbb{B}\mathrm{obhans}\oint \\ $$$$\mathrm{If}\:\mathrm{all}\:\mathrm{the}\:\mathrm{letters}\:\mathrm{of}\:\mathrm{the}\:\mathrm{word}\:\mathrm{MISSISSIPPI}\:\mathrm{are}\:\mathrm{written}\:\mathrm{down}\: \\ $$$$\mathrm{at}\:\mathrm{random}\:,\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{all}\:\mathrm{the}\:\mathrm{four}\:\mathrm{S}\:\mathrm{appear}\:\mathrm{consecutively}\:\mathrm{is}\:\_\_\_ \\ $$

Question Number 107658 Answers: 1 Comments: 0

⋇JS⋇ A metal box (without top) is tobe contructed from a square sheet of metal that is 10 dm on the side by first cutting the square pieces of the same size from the corners of the sheet and folding up sides. what size squares should be cut in order to maximize the volume of the box.

$$\:\:\:\divideontimes\mathcal{JS}\divideontimes \\ $$$${A}\:{metal}\:{box}\:\left({without}\:{top}\right)\:{is}\:{tobe} \\ $$$${contructed}\:{from}\:{a}\:{square}\:{sheet} \\ $$$${of}\:{metal}\:{that}\:{is}\:\mathrm{10}\:{dm}\:{on}\:{the} \\ $$$${side}\:{by}\:{first}\:{cutting}\:{the}\:{square} \\ $$$${pieces}\:{of}\:{the}\:{same}\:{size}\:{from}\:{the} \\ $$$${corners}\:{of}\:{the}\:{sheet}\:{and}\:{folding} \\ $$$${up}\:{sides}.\:{what}\:{size}\:{squares} \\ $$$${should}\:{be}\:{cut}\:{in}\:{order}\:{to} \\ $$$${maximize}\:{the}\:{volume}\:{of}\:{the}\:{box}. \\ $$

Question Number 107656 Answers: 3 Comments: 0

Question Number 107650 Answers: 0 Comments: 0

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