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AllQuestion and Answers: Page 1825

Question Number 26300 Answers: 0 Comments: 1

y=a^(arctg(√x)) y′=?

$${y}={a}^{\mathrm{arc}{tg}\sqrt{{x}}} \\ $$$${y}'=? \\ $$

Question Number 26299 Answers: 0 Comments: 1

y=((1+e^x )/(1−e^x )) y′=?

$${y}=\frac{\mathrm{1}+{e}^{{x}} }{\mathrm{1}−{e}^{{x}} } \\ $$$${y}'=? \\ $$

Question Number 26298 Answers: 0 Comments: 2

y=sin^4 x y′=? differential

$${y}=\mathrm{sin}\:^{\mathrm{4}} {x} \\ $$$${y}'=?\:{differential} \\ $$

Question Number 26297 Answers: 1 Comments: 0

y=x−(2/x^4 )−(1/(3x^3 )) y′=?

$${y}={x}−\frac{\mathrm{2}}{{x}^{\mathrm{4}} }−\frac{\mathrm{1}}{\mathrm{3}{x}^{\mathrm{3}} } \\ $$$${y}'=? \\ $$

Question Number 26294 Answers: 0 Comments: 1

lim_(x→0) (((√(1+xsin x ))−(√(cos 2x)))/(tg^2 (x/2)))

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\sqrt{\mathrm{1}+{x}\mathrm{sin}\:{x}\:}−\sqrt{\mathrm{cos}\:\mathrm{2}{x}}}{{tg}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}} \\ $$

Question Number 26293 Answers: 1 Comments: 0

lim_(x→∞) (3(√(1−x^3 +x)))

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{3}\sqrt{\left.\mathrm{1}−{x}^{\mathrm{3}} +{x}\right)}\right. \\ $$

Question Number 26290 Answers: 0 Comments: 1

f(x)=4x^2 +1 x_0 =2

$${f}\left({x}\right)=\mathrm{4}{x}^{\mathrm{2}} +\mathrm{1}\: \\ $$$${x}_{\mathrm{0}} =\mathrm{2} \\ $$

Question Number 26289 Answers: 1 Comments: 0

lim_(x→2) ((1/(x−2))−((12)/(x^3 −8)))

$$\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\left(\frac{\mathrm{1}}{{x}−\mathrm{2}}−\frac{\mathrm{12}}{{x}^{\mathrm{3}} −\mathrm{8}}\right) \\ $$

Question Number 26288 Answers: 2 Comments: 0

(d/dx) ((x−4)/(2(√x)))

$$\frac{\boldsymbol{{d}}}{\boldsymbol{{dx}}}\:\frac{\boldsymbol{{x}}−\mathrm{4}}{\mathrm{2}\sqrt{\boldsymbol{{x}}}} \\ $$

Question Number 26313 Answers: 0 Comments: 0

If domain of y = f(x) is [−3, 2] and g(x) = f(∣[x]∣) ([∙] denotes the greatest integer function), then domain of g(x) is

$$\mathrm{If}\:\mathrm{domain}\:\mathrm{of}\:{y}\:=\:{f}\left({x}\right)\:\mathrm{is}\:\left[−\mathrm{3},\:\mathrm{2}\right]\:\mathrm{and} \\ $$$${g}\left({x}\right)\:=\:{f}\left(\mid\left[{x}\right]\mid\right)\:\left(\left[\centerdot\right]\:\mathrm{denotes}\:\mathrm{the}\:\mathrm{greatest}\right. \\ $$$$\left.\mathrm{integer}\:\mathrm{function}\right),\:\mathrm{then}\:\mathrm{domain}\:\mathrm{of}\:{g}\left({x}\right) \\ $$$$\mathrm{is} \\ $$

Question Number 26354 Answers: 1 Comments: 0

Question Number 26281 Answers: 1 Comments: 0

If f(x) is a function satisfying f(x+y)=f(x) f(y) for all x, y ∈ N such that f(1)=3 and Σ_(x=1) ^n f(x)=120. Then the value of n is

$$\mathrm{If}\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{function}\:\mathrm{satisfying} \\ $$$$\:{f}\left({x}+{y}\right)={f}\left({x}\right)\:{f}\left({y}\right)\:\mathrm{for}\:\mathrm{all}\:{x},\:{y}\:\in\:{N}\:\:\mathrm{such} \\ $$$$\mathrm{that}\:{f}\left(\mathrm{1}\right)=\mathrm{3}\:\mathrm{and}\:\underset{{x}=\mathrm{1}} {\overset{{n}} {\sum}}\:{f}\left({x}\right)=\mathrm{120}.\:\mathrm{Then} \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{n}\:\mathrm{is} \\ $$

Question Number 26274 Answers: 0 Comments: 2

could there be an analytical or numerical meghod for solving this non-linear simultaneous equation x+y=5 x^x +y^y =31 please help if possible

$${could}\:{there}\:{be}\:{an}\:{analytical}\:{or} \\ $$$${numerical}\:{meghod}\:{for}\:{solving} \\ $$$${this}\:{non}-{linear}\:{simultaneous} \\ $$$${equation} \\ $$$${x}+{y}=\mathrm{5} \\ $$$${x}^{{x}} +{y}^{{y}} =\mathrm{31} \\ $$$$ \\ $$$${please}\:{help}\:{if}\:{possible} \\ $$

Question Number 26270 Answers: 0 Comments: 1

∫(√(cosec(x)))dx

$$\int\sqrt{{cosec}\left({x}\right)}{dx} \\ $$

Question Number 26269 Answers: 1 Comments: 0

if x^x =2 what is the value of x?

$${if}\:{x}^{{x}} =\mathrm{2}\:{what}\:{is}\:{the}\:{value}\:{of}\:{x}? \\ $$

Question Number 26264 Answers: 1 Comments: 0

(x/3)+2x=14

$$\frac{\mathrm{x}}{\mathrm{3}}+\mathrm{2x}=\mathrm{14} \\ $$

Question Number 26262 Answers: 1 Comments: 0

(x+5) (x−2)=17−x find the value of x

$$\left(\mathrm{x}+\mathrm{5}\right)\:\left(\mathrm{x}−\mathrm{2}\right)=\mathrm{17}−\mathrm{x}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x} \\ $$

Question Number 26256 Answers: 1 Comments: 1

Question Number 26255 Answers: 0 Comments: 1

if two dice are tossed together what is probability of sim of number on the dice being an even number

$${if}\:{two}\:{dice}\:{are}\:{tossed}\:{together}\:{what}\:{is}\:{probability}\:{of}\:{sim}\:{of}\:{number}\:{on}\:{the}\:{dice}\:{being}\:{an}\:{even}\:{number} \\ $$

Question Number 26250 Answers: 1 Comments: 0

someone should help witb solution please x^3 +y^3 =3x^2 −6x−3y+4 x^2 −y^2 −6x+y−10=(√((y+5)))−(√((4x+y)))

$${someone}\:{should}\:{help}\:{witb}\:{solution}\:{please} \\ $$$${x}^{\mathrm{3}} +{y}^{\mathrm{3}} =\mathrm{3}{x}^{\mathrm{2}} −\mathrm{6}{x}−\mathrm{3}{y}+\mathrm{4} \\ $$$${x}^{\mathrm{2}} −{y}^{\mathrm{2}} −\mathrm{6}{x}+{y}−\mathrm{10}=\sqrt{\left({y}+\mathrm{5}\right)}−\sqrt{\left(\mathrm{4}{x}+{y}\right)} \\ $$

Question Number 26249 Answers: 0 Comments: 1

If x, y, z are in GP and a^x = b^y = c^z , then

$$\mathrm{If}\:\:\:{x},\:{y},\:{z}\:\mathrm{are}\:\mathrm{in}\:\mathrm{GP}\:\mathrm{and}\:{a}^{{x}} =\:{b}^{{y}} =\:{c}^{{z}} ,\:\mathrm{then} \\ $$

Question Number 26248 Answers: 0 Comments: 0

lim_(n→∞) ∫_0 ^1 (x^n /(cos x))dx=

$$\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{{n}} }{\mathrm{cos}\:{x}}{dx}= \\ $$

Question Number 26246 Answers: 0 Comments: 0

If normal plasma is 7.4 and normal CO_2 is 1.2mm, what is the normal (H_2 CO_3 ^− )

$$\mathrm{If}\:\:\mathrm{normal}\:\mathrm{plasma}\:\mathrm{is}\:\mathrm{7}.\mathrm{4}\:\mathrm{and}\:\mathrm{normal}\:\:\mathrm{CO}_{\mathrm{2}} \:\mathrm{is}\:\mathrm{1}.\mathrm{2mm},\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{normal}\:\left(\mathrm{H}_{\mathrm{2}} \mathrm{CO}_{\mathrm{3}} ^{−} \right) \\ $$

Question Number 26244 Answers: 0 Comments: 1

(x_i )_(1≤i≤n) n real number positifs wish verfy Σ_(i=1) ^(i=n) x_i =1 prove that Σ_(1≤i≤n) x_i ^2 ≥ (1/n) .

$$\:\left({x}_{{i}} \:\right)_{\mathrm{1}\leqslant{i}\leqslant{n}} \:\:{n}\:{real}\:{number}\:\:{positifs}\:{wish}\:{verfy}\:\:\:\sum_{{i}=\mathrm{1}} ^{{i}={n}} \:{x}_{{i}} =\mathrm{1} \\ $$$${prove}\:{that}\:\:\:\sum_{\mathrm{1}\leqslant{i}\leqslant{n}} {x}_{{i}} ^{\mathrm{2}} \:\:\:\geqslant\:\:\frac{\mathrm{1}}{{n}}\:\:\:. \\ $$

Question Number 26243 Answers: 0 Comments: 1

let put U_n = Σ_(1≤i<j≤n) (1/(ij)) find lim_(n−>∝) U_n

$${let}\:{put}\:{U}_{{n}} \:\:=\:\sum_{\mathrm{1}\leqslant{i}<{j}\leqslant{n}} \:\:\:\frac{\mathrm{1}}{{ij}}\:\:\:\:{find}\:\:{lim}_{{n}−>\propto} \:\:{U}_{{n}} \\ $$

Question Number 26242 Answers: 0 Comments: 1

prove that Σ_(k=0) ^(k=n) cos^2 (kx)= ((n+1)/2) + ((sin((n+1)x)cos(nx))/(2 sinx)) x from R−{ kπ.kεZ}then find the value of integral ∫_0 ^π ((sin((n+1)x)cos(nx))/(sinx))dx

$${prove}\:{that}\:\:\sum_{{k}=\mathrm{0}} ^{{k}={n}} \:\:{cos}^{\mathrm{2}} \left({kx}\right)=\:\frac{{n}+\mathrm{1}}{\mathrm{2}}\:\:+\:\frac{{sin}\left(\left({n}+\mathrm{1}\right){x}\right){cos}\left({nx}\right)}{\mathrm{2}\:{sinx}} \\ $$$${x}\:{from}\:{R}−\left\{\:{k}\pi.{k}\varepsilon{Z}\right\}{then}\:{find}\:{the}\:{value}\:{of}\:{integral} \\ $$$$\int_{\mathrm{0}} ^{\pi} \:\:\frac{{sin}\left(\left({n}+\mathrm{1}\right){x}\right){cos}\left({nx}\right)}{{sinx}}{dx} \\ $$$$ \\ $$

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