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Question Number 40709 Answers: 1 Comments: 1

calculate lim_(x→0) ((cos(x−sinx)−1)/(x^2 ))

$${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\frac{{cos}\left({x}−{sinx}\right)−\mathrm{1}}{{x}^{\mathrm{2}} \:} \\ $$

Question Number 40700 Answers: 1 Comments: 0

A charge q_1 =2.0×10^(−9) C is placed at the point,(x=0,y=4cm) and another charge,q_2 =−3.0×10^(−9) C is located at the point,(x=3cm,y=4cm). If a third charge,q_3 =4.0×10^(−9) C is placed at the origin, a)obtain the x and y component of the total force on q_3 b)Calculate the magnitude and direction of the total force on q_(3.)

$${A}\:{charge}\:{q}_{\mathrm{1}} =\mathrm{2}.\mathrm{0}×\mathrm{10}^{−\mathrm{9}} {C}\:{is}\:{placed} \\ $$$${at}\:{the}\:{point},\left({x}=\mathrm{0},{y}=\mathrm{4}{cm}\right)\:{and} \\ $$$${another}\:{charge},{q}_{\mathrm{2}} =−\mathrm{3}.\mathrm{0}×\mathrm{10}^{−\mathrm{9}} {C} \\ $$$${is}\:{located}\:{at}\:{the}\:{point},\left({x}=\mathrm{3}{cm},{y}=\mathrm{4}{cm}\right). \\ $$$${If}\:{a}\:{third}\:{charge},{q}_{\mathrm{3}} =\mathrm{4}.\mathrm{0}×\mathrm{10}^{−\mathrm{9}} {C} \\ $$$${is}\:{placed}\:{at}\:{the}\:{origin}, \\ $$$$\left.{a}\right){obtain}\:{the}\:{x}\:{and}\:{y}\:{component}\:{of} \\ $$$${the}\:{total}\:{force}\:{on}\:{q}_{\mathrm{3}} \\ $$$$\left.{b}\right){Calculate}\:{the}\:{magnitude}\:{and} \\ $$$${direction}\:{of}\:{the}\:{total}\:{force}\:{on}\:{q}_{\mathrm{3}.} \\ $$

Question Number 40699 Answers: 1 Comments: 0

Two point charges q_1 =1.5×10^(−9) C and q_2 =3.0×10^(−9) C are seperated by a distance of 200cm.Calculate the point at which the total electric field is zero.

$${Two}\:{point}\:{charges}\:{q}_{\mathrm{1}} =\mathrm{1}.\mathrm{5}×\mathrm{10}^{−\mathrm{9}} {C} \\ $$$${and}\:{q}_{\mathrm{2}} =\mathrm{3}.\mathrm{0}×\mathrm{10}^{−\mathrm{9}} {C}\:{are}\:{seperated} \\ $$$${by}\:{a}\:{distance}\:{of}\:\mathrm{200}{cm}.{Calculate} \\ $$$${the}\:{point}\:{at}\:{which}\:{the}\:{total}\:{electric} \\ $$$${field}\:{is}\:{zero}. \\ $$

Question Number 40686 Answers: 0 Comments: 6

Question Number 40684 Answers: 0 Comments: 1

∫((x^7 −1)/(logx))dx

$$\int\frac{\mathrm{x}^{\mathrm{7}} −\mathrm{1}}{\mathrm{logx}}\mathrm{dx} \\ $$

Question Number 40675 Answers: 1 Comments: 2

Question Number 40667 Answers: 1 Comments: 2

find the value lim_(x→0) g(x) must have, if g complies the statement about limit. Suppose lim_(x→ −4) [x lim_(x→0) g(x)] = 2

$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{g}\left(\mathrm{x}\right)\:\:\mathrm{must}\:\mathrm{have},\:\mathrm{if}\:\mathrm{g}\:\mathrm{complies}\:\mathrm{the}\:\mathrm{statement}\: \\ $$$$\mathrm{about}\:\mathrm{limit}.\:\mathrm{Suppose}\:\:\:\underset{{x}\rightarrow\:−\mathrm{4}} {\mathrm{lim}}\:\:\left[\mathrm{x}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\mathrm{g}\left(\mathrm{x}\right)\right]\:\:=\:\:\mathrm{2} \\ $$

Question Number 40665 Answers: 1 Comments: 0

−5−( )=3 −5−x=3 x=3+5 x=8(give sign of greater number) −5−8=3

$$−\mathrm{5}−\left(\:\:\right)=\mathrm{3} \\ $$$$−\mathrm{5}−{x}=\mathrm{3} \\ $$$${x}=\mathrm{3}+\mathrm{5} \\ $$$${x}=\mathrm{8}\left({give}\:{sign}\:{of}\:{greater}\:{number}\right) \\ $$$$−\mathrm{5}−\mathrm{8}=\mathrm{3} \\ $$

Question Number 40664 Answers: 1 Comments: 0

Factorise: x^(19) − x^(17) + x^(10) + x^8 + 1

$$\mathrm{Factorise}:\:\:\:\:\:\mathrm{x}^{\mathrm{19}} \:−\:\mathrm{x}^{\mathrm{17}} \:+\:\mathrm{x}^{\mathrm{10}} \:+\:\mathrm{x}^{\mathrm{8}} \:+\:\mathrm{1} \\ $$

Question Number 40662 Answers: 1 Comments: 5

Question Number 40661 Answers: 0 Comments: 4

1)find g(x)=∫_0 ^(π/2) ln(1−x^2 cos^2 θ)dθ with x from R 2) find the value of ∫_0 ^(π/2) ln(1−2 cos^2 θ)dθ and 3) find the value of A(α)=∫_0 ^(π/2) ln(1−cos^2 α cos^2 θ)dθ

$$\left.\mathrm{1}\right){find}\:\:{g}\left({x}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\mathrm{1}−{x}^{\mathrm{2}} {cos}^{\mathrm{2}} \theta\right){d}\theta\:\:{with}\:{x}\:{from}\:{R} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\mathrm{1}−\mathrm{2}\:{cos}^{\mathrm{2}} \theta\right){d}\theta\:{and} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\: \\ $$$${A}\left(\alpha\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\mathrm{1}−{cos}^{\mathrm{2}} \alpha\:{cos}^{\mathrm{2}} \theta\right){d}\theta\: \\ $$

Question Number 40660 Answers: 0 Comments: 0

let f(t) = ∫_0 ^∞ ((arctan(tcosx))/(1+x^2 ))dx 1) find another form of f(t) 2) calculate ∫_0 ^∞ ((arctan(2cosx))/(1+x^2 ))dx .

$${let}\:{f}\left({t}\right)\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left({tcosx}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{another}\:{form}\:{of}\:{f}\left({t}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\:\frac{{arctan}\left(\mathrm{2}{cosx}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}\:. \\ $$

Question Number 40658 Answers: 0 Comments: 1

find ∫_0 ^(π/4) ((x−1)/(2+cosx))dx .

$${find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\frac{{x}−\mathrm{1}}{\mathrm{2}+{cosx}}{dx}\:. \\ $$

Question Number 40657 Answers: 1 Comments: 0

Question Number 40656 Answers: 1 Comments: 0

(((a 0 0)),((0 a 0)) ) 0 0 a then the value of mod of adjA is

$$\begin{pmatrix}{\mathrm{a}\:\mathrm{0}\:\mathrm{0}}\\{\mathrm{0}\:\mathrm{a}\:\mathrm{0}}\end{pmatrix} \\ $$$$\:\:\:\mathrm{0}\:\mathrm{0}\:\mathrm{a}\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{mod}\:\mathrm{of}\:\mathrm{adjA}\:\mathrm{is} \\ $$$$ \\ $$

Question Number 40640 Answers: 2 Comments: 0

evaluate sin 72^.

$${evaluate} \\ $$$$\mathrm{sin}\:\mathrm{72}\:^{.} \\ $$

Question Number 41351 Answers: 1 Comments: 3

∫_0 ^∞ [(5/e^x )]dx=

$$\int_{\mathrm{0}} ^{\infty} \left[\frac{\mathrm{5}}{\mathrm{e}^{\mathrm{x}} }\right]\mathrm{dx}= \\ $$

Question Number 40637 Answers: 2 Comments: 0

Question Number 40625 Answers: 2 Comments: 0

Question Number 40624 Answers: 0 Comments: 0

let f(x)=∫_0 ^(π/2) ln(((1−xsint)/(1+xsint)))dt . 1) find the value of I = ∫_0 ^(π/2) ln(1−xsint)dt and J = ∫_0 ^(π/2) ln(1+xsint)dt 2) find a simple form of f(x) 3) developp f at integr serie

$${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\frac{\mathrm{1}−{xsint}}{\mathrm{1}+{xsint}}\right){dt}\:\:. \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{value}\:{of}\:\:{I}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{ln}\left(\mathrm{1}−{xsint}\right){dt} \\ $$$${and}\:{J}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\mathrm{1}+{xsint}\right){dt} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$

Question Number 40621 Answers: 2 Comments: 0

let f(x)=∫_0 ^(π/2) ln(1+xcosθ)dθ 1) calculate f(1) 2) find a simple form of f(x) 3) developp f at ontehr serie

$${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\mathrm{1}+{xcos}\theta\right){d}\theta\: \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left(\mathrm{1}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{developp}\:{f}\:{at}\:{ontehr}\:{serie} \\ $$

Question Number 40620 Answers: 3 Comments: 0

find ∫ ((x+1)(√(1+x^2 )) +(1+x^2 )(√(x+1)))dx

$${find}\:\:\int\:\:\:\left(\left({x}+\mathrm{1}\right)\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:+\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\sqrt{{x}+\mathrm{1}}\right){dx} \\ $$

Question Number 40619 Answers: 0 Comments: 2

let f(x)=∫_0 ^(π/2) (dθ/(x +cos^2 θ)) with x>0 . 1) calculate f(x) and f^′ (x) 2) find f^((n)) (x) and f^((n)) (0) 3) developp f at integr serie.

$${let}\:\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{d}\theta}{{x}\:\:+{cos}^{\mathrm{2}} \theta}\:\:{with}\:{x}>\mathrm{0}\:. \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({x}\right)\:{and}\:{f}^{'} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}. \\ $$

Question Number 40615 Answers: 1 Comments: 2

Question Number 40610 Answers: 1 Comments: 0

Question Number 40594 Answers: 1 Comments: 1

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