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AllQuestion and Answers: Page 1080

Question Number 107401 Answers: 1 Comments: 0

sove y^(′′) =y^2

$$\mathrm{sove}\:\mathrm{y}^{''} \:=\mathrm{y}^{\mathrm{2}} \\ $$

Question Number 107761 Answers: 0 Comments: 2

Question Number 107377 Answers: 2 Comments: 0

lim_(x→0) ((x(1+acos x)−bsin x)/x^3 ) = 1 Find a and b .

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}\left(\mathrm{1}+{a}\mathrm{cos}\:{x}\right)−{b}\mathrm{sin}\:{x}}{{x}^{\mathrm{3}} }\:=\:\mathrm{1} \\ $$$${Find}\:\:{a}\:{and}\:{b}\:. \\ $$

Question Number 107373 Answers: 1 Comments: 0

(d^2 y/dx^2 )=((dy/dx))^n

$$\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }=\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{\mathrm{n}} \\ $$

Question Number 107372 Answers: 2 Comments: 0

⋗Bobhans⋖ lim_(x→∞) x (√(((2x−cos 5x)/(3x^3 )) )) ?

$$\:\:\:\gtrdot\boldsymbol{\mathcal{B}\mathrm{obhans}}\lessdot \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{x}\:\sqrt{\frac{\mathrm{2x}−\mathrm{cos}\:\mathrm{5x}}{\mathrm{3x}^{\mathrm{3}} }\:}\:? \\ $$

Question Number 107367 Answers: 0 Comments: 0

Question Number 107364 Answers: 4 Comments: 0

⊚BEMATH⊚ If tan x+sec x = b ⇒ cos x = ?

$$\:\:\:\:\:\:\circledcirc\mathscr{BEMATH}\circledcirc\: \\ $$$${If}\:\mathrm{tan}\:{x}+\mathrm{sec}\:{x}\:=\:{b}\:\Rightarrow\:\mathrm{cos}\:{x}\:=\:? \\ $$

Question Number 107362 Answers: 0 Comments: 1

∫_0 ^∞ x^π e^(−x) dx

$$\int_{\mathrm{0}} ^{\infty} \mathrm{x}^{\pi} \mathrm{e}^{−\mathrm{x}} \mathrm{dx} \\ $$

Question Number 107353 Answers: 2 Comments: 0

If a b 13 c d 25 are six consecutive terms of an AP .find tbe value of a b c and d.

$${If}\:\mathrm{a}\:\mathrm{b}\:\mathrm{13}\:\mathrm{c}\:\mathrm{d}\:\mathrm{25}\:\mathrm{are}\:\mathrm{six}\:\mathrm{consecutive}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{an}\:\mathrm{A}{P}\:.{find}\:{tbe}\:{value}\:{of}\:{a}\:{b}\:{c}\:{and}\:{d}. \\ $$

Question Number 107350 Answers: 1 Comments: 0

Question Number 107342 Answers: 1 Comments: 0

Evaluate: χ:=∫_0 ^( (π/4)) x^2 tan(x)dx= ??? ★prepared by:★ ♣♣♣ M.N ♣♣♣

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathscr{E}{valuate}: \\ $$$$\:\:\:\:\:\:\:\chi:=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} {x}^{\mathrm{2}} {tan}\left({x}\right){dx}=\:???\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\bigstar{prepared}\:{by}:\bigstar \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\clubsuit\clubsuit\clubsuit\:\:\:\mathscr{M}.\mathscr{N}\:\clubsuit\clubsuit\clubsuit \\ $$$$ \\ $$

Question Number 107385 Answers: 0 Comments: 7

⋰BeMath⋰ Given 6x^2 −6px+14p−2=0 has the roots are u & v where u,v ∉Z If u,v ≥ 1 , then the value of ∣u−v∣ . (a)14 (b)15 (c)16 (d)17 (e) 18

$$\:\:\:\:\:\iddots\mathcal{B}{e}\mathcal{M}{ath}\iddots \\ $$$${Given}\:\mathrm{6}{x}^{\mathrm{2}} −\mathrm{6}{px}+\mathrm{14}{p}−\mathrm{2}=\mathrm{0} \\ $$$${has}\:{the}\:{roots}\:{are}\:\:{u}\:\&\:{v}\:{where}\:{u},{v}\:\notin\mathbb{Z} \\ $$$${If}\:{u},{v}\:\geqslant\:\mathrm{1}\:,\:{then}\:{the}\:{value}\:{of}\:\mid{u}−{v}\mid\:. \\ $$$$\left({a}\right)\mathrm{14}\:\:\:\:\:\left({b}\right)\mathrm{15}\:\:\:\:\:\left({c}\right)\mathrm{16}\:\:\:\:\:\left({d}\right)\mathrm{17}\:\:\:\left({e}\right)\:\mathrm{18} \\ $$

Question Number 107352 Answers: 5 Comments: 0

⊚BeMath⊚ (1)1−(1/(√2)) +(1/(√3))−(1/(√4))+(1/(√5))−(1/(√6))+...=? (2) lim_(x→0) (1+sin x)^(1/x) ?

$$\:\:\:\:\:\:\:\:\circledcirc\mathcal{B}{e}\mathcal{M}{ath}\circledcirc \\ $$$$\left(\mathrm{1}\right)\mathrm{1}−\frac{\mathrm{1}}{\sqrt{\mathrm{2}}}\:+\frac{\mathrm{1}}{\sqrt{\mathrm{3}}}−\frac{\mathrm{1}}{\sqrt{\mathrm{4}}}+\frac{\mathrm{1}}{\sqrt{\mathrm{5}}}−\frac{\mathrm{1}}{\sqrt{\mathrm{6}}}+...=? \\ $$$$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\mathrm{1}+\mathrm{sin}\:{x}\right)^{\frac{\mathrm{1}}{{x}}} \:? \\ $$

Question Number 107331 Answers: 1 Comments: 0

If A is an invertible matrix, then det(A^(−1) ) is equal to

$$\mathrm{If}\:{A}\:\mathrm{is}\:\mathrm{an}\:\mathrm{invertible}\:\mathrm{matrix},\:\mathrm{then}\:\mathrm{det}\left({A}^{−\mathrm{1}} \right) \\ $$$$\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 107330 Answers: 2 Comments: 0

If a+b+c=0 one root of determinant (((a−x),( c),( b)),(( c),(b−x),( a)),(( b),( a),(c−x)))=0 is

$$\mathrm{If}\:\:\:{a}+{b}+{c}=\mathrm{0}\:\mathrm{one}\:\mathrm{root}\:\mathrm{of} \\ $$$$\begin{vmatrix}{{a}−{x}}&{\:\:\:\:{c}}&{\:\:\:{b}}\\{\:\:\:\:{c}}&{{b}−{x}}&{\:\:\:{a}}\\{\:\:\:\:{b}}&{\:\:\:{a}}&{{c}−{x}}\end{vmatrix}=\mathrm{0}\:\mathrm{is} \\ $$

Question Number 107328 Answers: 1 Comments: 6

Question Number 107327 Answers: 0 Comments: 0

1≤p≤k≤n show that Σ_(k=p) ^n C_(k−1) ^(p−1) =C_n ^p please i need help

$$\mathrm{1}\leqslant{p}\leqslant{k}\leqslant{n} \\ $$$${show}\:{that}\:\underset{{k}={p}} {\overset{{n}} {\sum}}\boldsymbol{{C}}_{{k}−\mathrm{1}} ^{{p}−\mathrm{1}} =\boldsymbol{{C}}_{{n}} ^{{p}} \\ $$$${please}\:{i}\:{need}\:{help} \\ $$

Question Number 107320 Answers: 1 Comments: 6

let x,y,z be a complex numbers as ∣x∣=∣y∣=∣z∣=1 { ((x+y+z=1)),((xyz=1)) :} calcul (1/x)+(1/y)+(1/z)=? x=? y=? z=? please i need a help

$${let}\:{x},{y},{z}\:{be}\:{a}\:{complex}\:{numbers} \\ $$$${as}\:\mid{x}\mid=\mid{y}\mid=\mid{z}\mid=\mathrm{1} \\ $$$$\begin{cases}{{x}+{y}+{z}=\mathrm{1}}\\{{xyz}=\mathrm{1}}\end{cases} \\ $$$${calcul}\:\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{y}}+\frac{\mathrm{1}}{{z}}=? \\ $$$$\:\:{x}=?\:{y}=?\:{z}=? \\ $$$${please}\:{i}\:{need}\:{a}\:{help} \\ $$

Question Number 107314 Answers: 2 Comments: 0

⌆bemath⌆ ∫_0 ^(2π) ln (1+sin x) dx ?

$$\:\:\:\:\:\:\:\:\doublebarwedge{bemath}\doublebarwedge \\ $$$$\:\:\:\:\:\underset{\mathrm{0}} {\overset{\mathrm{2}\pi} {\int}}\:\mathrm{ln}\:\left(\mathrm{1}+\mathrm{sin}\:{x}\right)\:{dx}\:? \\ $$

Question Number 107313 Answers: 2 Comments: 0

{ ((x+y(√x) = ((95)/8))),((y+x(√y) = ((93)/8))) :} . Find (√(xy))

$$\begin{cases}{{x}+{y}\sqrt{{x}}\:=\:\frac{\mathrm{95}}{\mathrm{8}}}\\{{y}+{x}\sqrt{{y}}\:=\:\frac{\mathrm{93}}{\mathrm{8}}}\end{cases}\:.\:\mathcal{F}{ind}\:\sqrt{{xy}} \\ $$

Question Number 107310 Answers: 3 Comments: 0

Question Number 107304 Answers: 2 Comments: 0

⋎bemath⋎ (1)Find domain of function f(x)= (√(log _(0.2) (((x+2)/(x−1)))−1)) (2) ((sin^2 (((9π)/8)−2x)−sin^2 (((7π)/8)−2x))/(sin (2018π+4x)))=?

$$\:\:\:\curlyvee{bemath}\curlyvee \\ $$$$\left(\mathrm{1}\right){Find}\:{domain}\:{of}\:{function}\: \\ $$$${f}\left({x}\right)=\:\sqrt{\mathrm{log}\:_{\mathrm{0}.\mathrm{2}} \left(\frac{{x}+\mathrm{2}}{{x}−\mathrm{1}}\right)−\mathrm{1}}\: \\ $$$$\left(\mathrm{2}\right)\:\frac{\mathrm{sin}\:^{\mathrm{2}} \left(\frac{\mathrm{9}\pi}{\mathrm{8}}−\mathrm{2}{x}\right)−\mathrm{sin}\:^{\mathrm{2}} \left(\frac{\mathrm{7}\pi}{\mathrm{8}}−\mathrm{2}{x}\right)}{\mathrm{sin}\:\left(\mathrm{2018}\pi+\mathrm{4}{x}\right)}=? \\ $$

Question Number 107299 Answers: 2 Comments: 0

✠bobhans✠ find without L′Hopital and series lim_(x→0) ((x−sin x)/x^3 ) ?

$$\:\:\:\:\:\:\maltese\mathrm{bobhans}\maltese \\ $$$$\mathrm{find}\:\mathrm{without}\:\mathrm{L}'\mathrm{Hopital}\:\mathrm{and}\:\mathrm{series}\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{x}−\mathrm{sin}\:\mathrm{x}}{\mathrm{x}^{\mathrm{3}} }\:? \\ $$

Question Number 107292 Answers: 0 Comments: 0

let U_n =Σ_(k=1) ^n sin((k/n))sin((k/n^2 )) calculate lim_(n→+∞) U_n

$$\mathrm{let}\:\mathrm{U}_{\mathrm{n}} =\sum_{\mathrm{k}=\mathrm{1}} ^{\mathrm{n}} \:\mathrm{sin}\left(\frac{\mathrm{k}}{\mathrm{n}}\right)\mathrm{sin}\left(\frac{\mathrm{k}}{\mathrm{n}^{\mathrm{2}} }\right) \\ $$$$\mathrm{calculate}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\mathrm{U}_{\mathrm{n}} \\ $$

Question Number 107291 Answers: 1 Comments: 0

let x∈R−{1,−1} explicit the function f(x) =∫_0 ^(2π) ln(x^2 −2xcosθ +1)dθ

$$\mathrm{let}\:\mathrm{x}\in\mathrm{R}−\left\{\mathrm{1},−\mathrm{1}\right\}\:\mathrm{explicit}\:\mathrm{the}\:\mathrm{function} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\mathrm{ln}\left(\mathrm{x}^{\mathrm{2}} −\mathrm{2xcos}\theta\:+\mathrm{1}\right)\mathrm{d}\theta \\ $$$$ \\ $$

Question Number 107290 Answers: 0 Comments: 0

find lim_(n→+∞) (1/n)Σ_(k=0) ^(n−1) (k/(√(4n^2 −k^2 )))

$$\mathrm{find}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \frac{\mathrm{1}}{\mathrm{n}}\sum_{\mathrm{k}=\mathrm{0}} ^{\mathrm{n}−\mathrm{1}} \:\frac{\mathrm{k}}{\sqrt{\mathrm{4n}^{\mathrm{2}} −\mathrm{k}^{\mathrm{2}} }} \\ $$

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