Question and Answers Forum

All Questions Topic List

AllQuestion and Answers: Page 177

Question Number 205219 Answers: 2 Comments: 0

{ ((sinx + cosx = 1)),((sinx − cosy = 1)) :} ⇒ x = ?

$$\begin{cases}{\mathrm{sinx}\:+\:\mathrm{cosx}\:=\:\mathrm{1}}\\{\mathrm{sinx}\:−\:\mathrm{cosy}\:=\:\mathrm{1}}\end{cases} \\ $$$$\Rightarrow\:\mathrm{x}\:=\:? \\ $$

Question Number 205218 Answers: 1 Comments: 0

∣ sinx∣ + ∣ cosx ∣ = 1 ⇒ x = ?

$$\mid\:\mathrm{sinx}\mid\:+\:\mid\:\mathrm{cosx}\:\mid\:=\:\mathrm{1} \\ $$$$\Rightarrow\:\mathrm{x}\:=\:? \\ $$

Question Number 205217 Answers: 1 Comments: 0

4 sin (x/2) ∙ cos (x/2) = 1 ⇒ x = ?

$$\mathrm{4}\:\mathrm{sin}\:\frac{\mathrm{x}}{\mathrm{2}}\:\centerdot\:\mathrm{cos}\:\frac{\mathrm{x}}{\mathrm{2}}\:=\:\mathrm{1} \\ $$$$\Rightarrow\:\mathrm{x}\:=\:? \\ $$

Question Number 205211 Answers: 1 Comments: 0

Question Number 205216 Answers: 0 Comments: 0

∫ ((arccos^3 x)/( (√(1−x^3 )))) dx =?

$$\:\:\:\:\:\int\:\frac{\mathrm{arccos}\:^{\mathrm{3}} \mathrm{x}}{\:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{3}} }}\:\mathrm{dx}\:=? \\ $$

Question Number 205203 Answers: 0 Comments: 0

If x,y,z>0 then in △ABC holds: Σ ((yz)/h_a ^2 ) ≤ (R^2 /(4F^2 )) (x + y + z)^2

$$\mathrm{If}\:\:\:\mathrm{x},\mathrm{y},\mathrm{z}>\mathrm{0}\:\:\:\mathrm{then}\:\mathrm{in}\:\:\:\bigtriangleup\mathrm{ABC}\:\:\:\mathrm{holds}: \\ $$$$\Sigma\:\:\frac{\mathrm{yz}}{\mathrm{h}_{\boldsymbol{\mathrm{a}}} ^{\mathrm{2}} }\:\:\leqslant\:\:\frac{\mathrm{R}^{\mathrm{2}} }{\mathrm{4F}^{\mathrm{2}} }\:\:\left(\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\right)^{\mathrm{2}} \\ $$

Question Number 205200 Answers: 1 Comments: 0

∫_1 ^∞ (x/(x^3 +lnx)) dx=?

$$\int_{\mathrm{1}} ^{\infty} \:\frac{{x}}{{x}^{\mathrm{3}} +{lnx}}\:{dx}=? \\ $$

Question Number 205184 Answers: 0 Comments: 0

Resuelve la siguiente ecuacio^ n diferencial (dx/dy) + x^2 = (1/y^4 )

$${Resuelve}\:{la}\:{siguiente}\:{ecuaci}\acute {{o}n}\:{diferencial} \\ $$$$\frac{{dx}}{{dy}}\:+\:{x}^{\mathrm{2}} \:=\:\frac{\mathrm{1}}{{y}^{\mathrm{4}} } \\ $$

Question Number 205175 Answers: 4 Comments: 0

Question Number 205174 Answers: 2 Comments: 0

lim_(x→∞) {x^(1/x) } = ? where {.} is a fractional part of x

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left\{{x}^{\mathrm{1}/{x}} \right\}\:=\:?\:{where}\:\left\{.\right\}\:{is}\:{a}\:{fractional}\:{part}\:{of}\:{x} \\ $$

Question Number 205173 Answers: 1 Comments: 2

find S=Σ_(n=1) ^∞ (1/((a^2 +n^2 )^2 ))

$${find} \\ $$$${S}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left({a}^{\mathrm{2}} +{n}^{\mathrm{2}} \right)^{\mathrm{2}} } \\ $$

Question Number 205172 Answers: 0 Comments: 1

x(t)=c+tx′(t) ∣ c is constant. (1) Find x(t). (2) Find x(t) when x(0)=x_0 .

$${x}\left({t}\right)={c}+{tx}'\left({t}\right)\:\mid\:{c}\:\mathrm{is}\:\mathrm{constant}. \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Find}\:{x}\left({t}\right). \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Find}\:{x}\left({t}\right)\:\mathrm{when}\:{x}\left(\mathrm{0}\right)={x}_{\mathrm{0}} . \\ $$

Question Number 205164 Answers: 1 Comments: 0

Find the determinant: determinant (((1−x),2,3,…,n),(1,(2−x),3,…,n),(1,2,(3−x),…,n),(⋮,⋮,⋮,⋱,⋮),(1,2,3,…,(n−x)))

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{determinant}: \\ $$$$\begin{vmatrix}{\mathrm{1}−{x}}&{\mathrm{2}}&{\mathrm{3}}&{\ldots}&{{n}}\\{\mathrm{1}}&{\mathrm{2}−{x}}&{\mathrm{3}}&{\ldots}&{{n}}\\{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}−{x}}&{\ldots}&{{n}}\\{\vdots}&{\vdots}&{\vdots}&{\ddots}&{\vdots}\\{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}}&{\ldots}&{{n}−{x}}\end{vmatrix} \\ $$

Question Number 205163 Answers: 1 Comments: 0

∫_0 ^1 ((sin(lnx))/(lnx))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{sin}\left({lnx}\right)}{{lnx}}{dx} \\ $$

Question Number 205160 Answers: 2 Comments: 0

Question Number 205161 Answers: 1 Comments: 1

Calculate the area of the green shaded portions

$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{green}\:\mathrm{shaded}\:\mathrm{portions} \\ $$

Question Number 205156 Answers: 1 Comments: 0

Find the determinant: determinant ((5,3,0,0,…,0,0),(2,5,3,0,…,0,0),(0,2,5,3,…,0,0),(⋮,⋮,⋮,⋮,⋱,⋮,⋮),(0,0,0,0,…,5,3),(0,0,0,0,…,2,5))

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{determinant}: \\ $$$$\begin{vmatrix}{\mathrm{5}}&{\mathrm{3}}&{\mathrm{0}}&{\mathrm{0}}&{\ldots}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{2}}&{\mathrm{5}}&{\mathrm{3}}&{\mathrm{0}}&{\ldots}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{2}}&{\mathrm{5}}&{\mathrm{3}}&{\ldots}&{\mathrm{0}}&{\mathrm{0}}\\{\vdots}&{\vdots}&{\vdots}&{\vdots}&{\ddots}&{\vdots}&{\vdots}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\ldots}&{\mathrm{5}}&{\mathrm{3}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\ldots}&{\mathrm{2}}&{\mathrm{5}}\end{vmatrix} \\ $$

Question Number 205153 Answers: 0 Comments: 0

Question Number 205151 Answers: 1 Comments: 0

find ∫_0 ^∞ ((ln^2 x)/(1+x^4 ))dx

$${find}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{ln}^{\mathrm{2}} {x}}{\mathrm{1}+{x}^{\mathrm{4}} }{dx} \\ $$

Question Number 205147 Answers: 2 Comments: 0

solve for z∈C zln z =z−2

$$\mathrm{solve}\:\mathrm{for}\:{z}\in\mathbb{C} \\ $$$${z}\mathrm{ln}\:{z}\:={z}−\mathrm{2} \\ $$

Question Number 205142 Answers: 1 Comments: 0

lim_(n→∞) n^(−n^2 ) [(n+1)(n+(1/2))(n+(1/2^2 ))...(n+(1/2^(n−1) ))]^n =?

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{n}^{−\mathrm{n}^{\mathrm{2}} } \left[\left(\mathrm{n}+\mathrm{1}\right)\left(\mathrm{n}+\frac{\mathrm{1}}{\mathrm{2}}\right)\left(\mathrm{n}+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }\right)...\left(\mathrm{n}+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{n}−\mathrm{1}} }\right)\right]^{\mathrm{n}} =? \\ $$

Question Number 205141 Answers: 0 Comments: 0

Server is back up and running. Post a message if you face any issues.

$$\mathrm{Server}\:\mathrm{is}\:\mathrm{back}\:\mathrm{up}\:\mathrm{and}\:\mathrm{running}. \\ $$$$\mathrm{Post}\:\mathrm{a}\:\mathrm{message}\:\mathrm{if}\:\mathrm{you}\:\mathrm{face}\:\mathrm{any}\:\mathrm{issues}. \\ $$

Question Number 205138 Answers: 0 Comments: 0

A=lim_(x→0 ) ((1−cos2x)/(2x^2 )) =lim_(x→0) ((2sin^2 x)/(2x^2 )) =lim_(x→0) (((sinx)/x))^2 =1 B=lim_(x→0) (1/(xcotx)) =lim_(x→0) ((tanx)/x)=lim_(x→0) ((sinx)/x)×(1/(cosx))=1

$${A}=\underset{{x}\rightarrow\mathrm{0}\:\:} {\mathrm{lim}}\frac{\mathrm{1}−\mathrm{cos2}{x}}{\mathrm{2}{x}^{\mathrm{2}} } \\ $$$$\:\:\:\:=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{2sin}^{\mathrm{2}} {x}}{\mathrm{2}{x}^{\mathrm{2}} } \\ $$$$\:\:\:\:=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{sin}{x}}{{x}}\right)^{\mathrm{2}} =\mathrm{1} \\ $$$${B}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{{x}\mathrm{cot}{x}} \\ $$$$\:\:\:\:=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}{x}}{{x}}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}{x}}{{x}}×\frac{\mathrm{1}}{\mathrm{cos}{x}}=\mathrm{1} \\ $$

Question Number 205135 Answers: 1 Comments: 1

Question Number 205134 Answers: 1 Comments: 0

Question Number 205130 Answers: 1 Comments: 1

Pg 172 Pg 173 Pg 174 Pg 175 Pg 176 Pg 177 Pg 178 Pg 179 Pg 180 Pg 181

Terms of Service

Contact: info@tinkutara.com