Question and Answers Forum

All Questions Topic List

AllQuestion and Answers: Page 1207

Question Number 84556 Answers: 1 Comments: 1

∫ sin^(−1) (((2x+2)/(√(4x^2 +8x+13)))) dx

$$\int\:\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{2x}+\mathrm{2}}{\sqrt{\mathrm{4x}^{\mathrm{2}} +\mathrm{8x}+\mathrm{13}}}\right)\:\mathrm{dx} \\ $$

Question Number 84553 Answers: 0 Comments: 3

Find mininum value of n such that both n + 3 and 2020n + 1 are square numbers .

$${Find}\:\:{mininum}\:\:{value}\:\:{of}\:\:{n}\:\:{such}\:\:{that} \\ $$$${both}\:\:{n}\:+\:\mathrm{3}\:\:\:{and}\:\:\mathrm{2020}{n}\:+\:\mathrm{1}\:\:{are}\:\:{square}\:\:{numbers}\:. \\ $$

Question Number 84549 Answers: 1 Comments: 0

Question Number 84544 Answers: 0 Comments: 0

solve xy^(′′) =y^′ (e^y −1)

$${solve}\: \\ $$$${xy}^{''} ={y}^{'} \left({e}^{{y}} −\mathrm{1}\right) \\ $$

Question Number 84543 Answers: 0 Comments: 3

Determine the value of a,b ,c so that _(x→0) ^(lim) (((a +b cos x) x−c sin x)/x^5 )=1

$$\boldsymbol{\mathrm{Determine}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}}\:,\boldsymbol{\mathrm{c}}\:\:\boldsymbol{\mathrm{so}}\:\boldsymbol{\mathrm{that}} \\ $$$$\:\:\underset{\mathrm{x}\rightarrow\mathrm{0}} {\overset{\mathrm{lim}} {\:}}\:\frac{\left(\boldsymbol{\mathrm{a}}\:+\boldsymbol{\mathrm{b}}\:\mathrm{cos}\:\mathrm{x}\right)\:\mathrm{x}−\boldsymbol{\mathrm{c}}\:\mathrm{sin}\:\mathrm{x}}{\mathrm{x}^{\mathrm{5}} }=\mathrm{1} \\ $$

Question Number 84532 Answers: 1 Comments: 1

x> 0 , y > 0 prove that ((xy)/(x+y)) < x

$$\mathrm{x}>\:\mathrm{0}\:,\:\mathrm{y}\:>\:\mathrm{0}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{xy}}{\mathrm{x}+\mathrm{y}}\:<\:\mathrm{x} \\ $$

Question Number 84531 Answers: 1 Comments: 2

find for equation of image ellipse (x^2 /9) + (y^2 /8) = 1 if reflected with line x + y = −4

$$\mathrm{find}\:\mathrm{for}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{image}\:\mathrm{ellipse} \\ $$$$\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{9}}\:+\:\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{8}}\:=\:\mathrm{1}\:\mathrm{if}\:\mathrm{reflected}\:\mathrm{with}\:\mathrm{line} \\ $$$$\mathrm{x}\:+\:\mathrm{y}\:=\:−\mathrm{4} \\ $$

Question Number 84528 Answers: 0 Comments: 3

1=2

$$\mathrm{1}=\mathrm{2} \\ $$

Question Number 84515 Answers: 1 Comments: 0

Q.solve x^3 −x=x!

$${Q}.{solve} \\ $$$${x}^{\mathrm{3}} −{x}={x}! \\ $$

Question Number 84512 Answers: 1 Comments: 0

Question Number 84510 Answers: 2 Comments: 0

Question Number 84505 Answers: 0 Comments: 1

2)calculate I(ξ) =∫_ξ ^1 (dx/(√(1+ξx^2 −(√(1−ξx^2 ))))) 1)find lim_(ξ→0) I(ξ)

$$\left.\mathrm{2}\right){calculate}\:\:\:{I}\left(\xi\right)\:=\int_{\xi} ^{\mathrm{1}} \:\:\:\:\:\:\frac{{dx}}{\sqrt{\mathrm{1}+\xi{x}^{\mathrm{2}} −\sqrt{\mathrm{1}−\xi{x}^{\mathrm{2}} }}} \\ $$$$\left.\mathrm{1}\right){find}\:{lim}_{\xi\rightarrow\mathrm{0}} \:\:{I}\left(\xi\right) \\ $$

Question Number 84498 Answers: 0 Comments: 1

∫(√x) cos(√x) dx

$$\int\sqrt{{x}}\:{cos}\sqrt{{x}}\:{dx} \\ $$

Question Number 84497 Answers: 0 Comments: 1

∫(x^2 /(1+x^5 )) dx

$$\int\frac{{x}^{\mathrm{2}} }{\mathrm{1}+{x}^{\mathrm{5}} }\:{dx} \\ $$$$ \\ $$

Question Number 84496 Answers: 1 Comments: 1

Question Number 84492 Answers: 0 Comments: 3

lim_(x→(π/3)) ((sin (x−(π/3)))/(1−2cos (x))) =

$$\underset{{x}\rightarrow\frac{\pi}{\mathrm{3}}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left({x}−\frac{\pi}{\mathrm{3}}\right)}{\mathrm{1}−\mathrm{2cos}\:\left({x}\right)}\:=\: \\ $$

Question Number 84477 Answers: 2 Comments: 0

(ycos x+2xe^y )dx+(sin x+x^2 e^y −1)dy=0

$$\left(\mathrm{ycos}\:\mathrm{x}+\mathrm{2xe}^{\mathrm{y}} \right)\mathrm{dx}+\left(\mathrm{sin}\:\mathrm{x}+\mathrm{x}^{\mathrm{2}} \mathrm{e}^{\mathrm{y}} −\mathrm{1}\right)\mathrm{dy}=\mathrm{0} \\ $$

Question Number 84469 Answers: 1 Comments: 0

prove that sin 3b + (cos b+sin b)(1−2sin 2b) = cos 3b

$$\mathrm{prove}\:\mathrm{that}\: \\ $$$$\mathrm{sin}\:\mathrm{3b}\:+\:\left(\mathrm{cos}\:\mathrm{b}+\mathrm{sin}\:\mathrm{b}\right)\left(\mathrm{1}−\mathrm{2sin}\:\mathrm{2b}\right) \\ $$$$=\:\mathrm{cos}\:\mathrm{3b} \\ $$

Question Number 84467 Answers: 0 Comments: 0

∫ ln(tan^(−1) (x)) dx

$$\int\:\mathrm{ln}\left(\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{x}\right)\right)\:\mathrm{dx} \\ $$

Question Number 84461 Answers: 0 Comments: 2

p^2 +3q^2 =11907, p,q∈Z,find p&q

$${p}^{\mathrm{2}} +\mathrm{3}{q}^{\mathrm{2}} =\mathrm{11907},\:{p},{q}\in\mathbb{Z},{find}\:{p\&q} \\ $$

Question Number 84460 Answers: 0 Comments: 2

lim_(x→0) ((sin (2+x)−sin (2−x))/x)

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left(\mathrm{2}+\mathrm{x}\right)−\mathrm{sin}\:\left(\mathrm{2}−\mathrm{x}\right)}{\mathrm{x}} \\ $$

Question Number 84459 Answers: 1 Comments: 2

{ ((log_(10) (x)+((log_(10) (x)+8log_(10) (y))/(log_(10) ^2 (x)+log_(10) ^2 (y)))=3)),((log_(10) (y)+((8log_(10) (x)−log_(10) (y))/(log_(10) ^2 (x)+log_(10) ^2 (y)))=0)) :} find x & y

$$\begin{cases}{\mathrm{log}_{\mathrm{10}} \left(\mathrm{x}\right)+\frac{\mathrm{log}_{\mathrm{10}} \left(\mathrm{x}\right)+\mathrm{8log}_{\mathrm{10}} \left(\mathrm{y}\right)}{\mathrm{log}_{\mathrm{10}} ^{\mathrm{2}} \left(\mathrm{x}\right)+\mathrm{log}_{\mathrm{10}} ^{\mathrm{2}} \left(\mathrm{y}\right)}=\mathrm{3}}\\{\mathrm{log}_{\mathrm{10}} \left(\mathrm{y}\right)+\frac{\mathrm{8log}_{\mathrm{10}} \left(\mathrm{x}\right)−\mathrm{log}_{\mathrm{10}} \left(\mathrm{y}\right)}{\mathrm{log}_{\mathrm{10}} ^{\mathrm{2}} \left(\mathrm{x}\right)+\mathrm{log}_{\mathrm{10}} ^{\mathrm{2}} \left(\mathrm{y}\right)}=\mathrm{0}}\end{cases} \\ $$$$\mathrm{find}\:\mathrm{x}\:\&\:\mathrm{y} \\ $$

Question Number 84456 Answers: 0 Comments: 1

y=ln(√((a+sin(x))/(b−sin(x)))) if ((dy/dx))^2 −tan^2 (x)=1 show that a=b

$${y}={ln}\sqrt{\frac{{a}+{sin}\left({x}\right)}{{b}−{sin}\left({x}\right)}} \\ $$$${if}\:\left(\frac{{dy}}{{dx}}\right)^{\mathrm{2}} −{tan}^{\mathrm{2}} \left({x}\right)=\mathrm{1} \\ $$$${show}\:{that}\:{a}={b} \\ $$

Question Number 84448 Answers: 1 Comments: 0

5^((x^2 −7∣x∣+10)/(x^2 −6x+9)) < 1

$$\mathrm{5}^{\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{7}\mid\mathrm{x}\mid+\mathrm{10}}{\mathrm{x}^{\mathrm{2}} −\mathrm{6x}+\mathrm{9}}} \:<\:\mathrm{1} \\ $$

Question Number 84442 Answers: 1 Comments: 0

Question Number 84441 Answers: 1 Comments: 1

Pg 1202 Pg 1203 Pg 1204 Pg 1205 Pg 1206 Pg 1207 Pg 1208 Pg 1209 Pg 1210 Pg 1211

Terms of Service

Contact: info@tinkutara.com