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Question Number 95323    Answers: 1   Comments: 0

lim_(x→0) ∫_x ^(2x) ((ln(2+t))/t)dt = (ln2)^2

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\int_{{x}} ^{\mathrm{2}{x}} \:\frac{{ln}\left(\mathrm{2}+{t}\right)}{{t}}{dt}\:=\:\left({ln}\mathrm{2}\right)^{\mathrm{2}} \\ $$

Question Number 95316    Answers: 1   Comments: 0

(dy/dx)−y = xy^5

$$\frac{{dy}}{{dx}}−{y}\:=\:{xy}^{\mathrm{5}} \: \\ $$

Question Number 95309    Answers: 1   Comments: 0

if y = [ 2x+5 ] = 3[x−4] then [ 3x+y ] = ?

$$\mathrm{if}\:\mathrm{y}\:=\:\left[\:\mathrm{2x}+\mathrm{5}\:\right]\:=\:\mathrm{3}\left[\mathrm{x}−\mathrm{4}\right]\: \\ $$$$\mathrm{then}\:\left[\:\mathrm{3x}+\mathrm{y}\:\right]\:=\:?\: \\ $$

Question Number 95294    Answers: 1   Comments: 2

3 men, 4 women & 6 boy together working a job within 25 day. if 2 men , 3 women and 4 boy working the same job, complete in ?

$$\mathrm{3}\:\mathrm{men},\:\mathrm{4}\:\mathrm{women}\:\&\:\mathrm{6}\:\mathrm{boy}\:\mathrm{together} \\ $$$$\mathrm{working}\:\mathrm{a}\:\mathrm{job}\:\mathrm{within}\:\mathrm{25}\:\mathrm{day}.\:\mathrm{if}\:\mathrm{2}\:\mathrm{men}\: \\ $$$$,\:\mathrm{3}\:\mathrm{women}\:\mathrm{and}\:\mathrm{4}\:\mathrm{boy}\:\mathrm{working}\:\mathrm{the}\: \\ $$$$\mathrm{same}\:\mathrm{job},\:\mathrm{complete}\:\mathrm{in}\:? \\ $$

Question Number 95277    Answers: 2   Comments: 4

Question Number 95269    Answers: 0   Comments: 3

Question Number 100664    Answers: 1   Comments: 0

A matrix 2x2 & B = (((−2 3)),(( 2 4)) ) such that A^T B+3A^T = ((( 5 4)),((−1 1)) ) so find det(4A^(−1) )

$$\mathrm{A}\:\mathrm{matrix}\:\mathrm{2x2}\:\&\:\mathrm{B}\:=\:\begin{pmatrix}{−\mathrm{2}\:\:\:\:\mathrm{3}}\\{\:\:\mathrm{2}\:\:\:\:\:\:\mathrm{4}}\end{pmatrix}\:\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\mathrm{A}^{\mathrm{T}} \mathrm{B}+\mathrm{3A}^{\mathrm{T}} \:=\:\begin{pmatrix}{\:\:\:\mathrm{5}\:\:\:\:\mathrm{4}}\\{−\mathrm{1}\:\:\:\mathrm{1}}\end{pmatrix}\:\:\mathrm{so}\:\mathrm{find}\:\mathrm{det}\left(\mathrm{4A}^{−\mathrm{1}} \right) \\ $$

Question Number 95262    Answers: 3   Comments: 0

3x^2 +5x^4 −7 plz help to solve this equation

$$\mathrm{3x}^{\mathrm{2}} +\mathrm{5x}^{\mathrm{4}} −\mathrm{7} \\ $$$$\mathrm{plz}\:\mathrm{help}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{this}\:\mathrm{equation} \\ $$

Question Number 95260    Answers: 1   Comments: 3

if the line 3x+2y−1=0 transformed by matrix A= (((1 a)),((b 2)) ) such that the image is the line 2x+8y+c=0 find the value of a×b×c

$$\mathrm{if}\:\mathrm{the}\:\mathrm{line}\:\mathrm{3x}+\mathrm{2y}−\mathrm{1}=\mathrm{0}\:\mathrm{transformed} \\ $$$$\mathrm{by}\:\mathrm{matrix}\:\mathrm{A}=\begin{pmatrix}{\mathrm{1}\:\:\:\mathrm{a}}\\{\mathrm{b}\:\:\:\mathrm{2}}\end{pmatrix}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{image}\:\mathrm{is}\:\mathrm{the}\:\mathrm{line}\:\mathrm{2x}+\mathrm{8y}+\mathrm{c}=\mathrm{0} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{a}×\mathrm{b}×\mathrm{c}\: \\ $$

Question Number 95259    Answers: 1   Comments: 1

find all roots ((√6) −(√2)i)^(1/3) by using demover theorem ?

$${find}\:{all}\:{roots}\:\left(\sqrt{\mathrm{6}}\:−\sqrt{\mathrm{2}}{i}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} {by}\:{using}\:{demover}\:{theorem}\:? \\ $$

Question Number 95246    Answers: 4   Comments: 0

Question Number 95232    Answers: 3   Comments: 6

Question Number 95230    Answers: 1   Comments: 0

lim_(x→0^+ ) ((7^(√x) −1)/(2^(√x) −1)) = ?

$$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\frac{\mathrm{7}^{\sqrt{\mathrm{x}}} \:−\mathrm{1}}{\mathrm{2}^{\sqrt{\mathrm{x}}} \:−\mathrm{1}}\:=\:? \\ $$

Question Number 95339    Answers: 6   Comments: 0

f(x)=∣2x+3∣ f ′(x)=...?

$$\mathrm{f}\left(\mathrm{x}\right)=\mid\mathrm{2x}+\mathrm{3}\mid \\ $$$$\mathrm{f}\:'\left(\mathrm{x}\right)=...? \\ $$

Question Number 95227    Answers: 1   Comments: 0

∫_(−π) ^π ∣sin x + cos x ∣ dx =?

$$\underset{−\pi} {\overset{\pi} {\int}}\:\mid\mathrm{sin}\:\mathrm{x}\:+\:\mathrm{cos}\:\mathrm{x}\:\mid\:\mathrm{dx}\:=?\: \\ $$

Question Number 95222    Answers: 1   Comments: 0

{ ((x^2 + x ((xy^2 ))^(1/(3 )) = 80 )),((y^2 + y ((x^2 y))^(1/(3 )) = 5 )) :} find x and y

$$\begin{cases}{{x}^{\mathrm{2}} \:+\:{x}\:\sqrt[{\mathrm{3}\:\:}]{{xy}^{\mathrm{2}} }\:=\:\mathrm{80}\:}\\{{y}^{\mathrm{2}} \:+\:{y}\:\sqrt[{\mathrm{3}\:\:}]{{x}^{\mathrm{2}} {y}}\:=\:\mathrm{5}\:}\end{cases} \\ $$$${find}\:{x}\:{and}\:{y}\: \\ $$

Question Number 95221    Answers: 1   Comments: 0

calculate ∫_0 ^π ln(2+cosθ)dθ

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\pi} \mathrm{ln}\left(\mathrm{2}+\mathrm{cos}\theta\right)\mathrm{d}\theta \\ $$

Question Number 95218    Answers: 0   Comments: 0

calculate Σ_(n=1) ^∞ (((−1)^n )/(n^3 (n+1)^3 ))

$$\mathrm{calculate}\:\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{n}^{\mathrm{3}} \left(\mathrm{n}+\mathrm{1}\right)^{\mathrm{3}} } \\ $$

Question Number 95217    Answers: 1   Comments: 0

calculate Σ_(n=1) ^∞ (((−1)^n )/(n^2 (n+2)^3 ))

$$\mathrm{calculate}\:\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{n}^{\mathrm{2}} \left(\mathrm{n}+\mathrm{2}\right)^{\mathrm{3}} } \\ $$

Question Number 95216    Answers: 1   Comments: 0

calculste Σ_(n=0) ^∞ (n/((2n+1)^2 (n+3)))

$$\mathrm{calculste}\:\sum_{\mathrm{n}=\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{n}}{\left(\mathrm{2n}+\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{n}+\mathrm{3}\right)} \\ $$

Question Number 95215    Answers: 1   Comments: 0

calculate Σ_(n=0) ^∞ (((−1)^n )/(4n+1))

$$\mathrm{calculate}\:\sum_{\mathrm{n}=\mathrm{0}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{4n}+\mathrm{1}} \\ $$

Question Number 95213    Answers: 0   Comments: 0

find ∫ ((√(x(x+1)))/(√(x+3)))dx

$$\mathrm{find}\:\int\:\frac{\sqrt{\mathrm{x}\left(\mathrm{x}+\mathrm{1}\right)}}{\sqrt{\mathrm{x}+\mathrm{3}}}\mathrm{dx} \\ $$

Question Number 95212    Answers: 1   Comments: 0

solve by Laplace transform y^(′′) +5y^′ +2y =x^2 cosx with y(o)=1 and y^′ (0) =2

$$\mathrm{solve}\:\mathrm{by}\:\mathrm{Laplace}\:\mathrm{transform} \\ $$$$\mathrm{y}^{''} \:+\mathrm{5y}^{'} \:+\mathrm{2y}\:=\mathrm{x}^{\mathrm{2}} \mathrm{cosx}\:\:\mathrm{with}\:\mathrm{y}\left(\mathrm{o}\right)=\mathrm{1}\:\mathrm{and}\:\mathrm{y}^{'} \left(\mathrm{0}\right)\:=\mathrm{2} \\ $$

Question Number 95211    Answers: 0   Comments: 0

solve by Laplace transform (x+1)y^′ −x^2 y =sin(2x)

$$\mathrm{solve}\:\mathrm{by}\:\mathrm{Laplace}\:\mathrm{transform} \\ $$$$\left(\mathrm{x}+\mathrm{1}\right)\mathrm{y}^{'} \:−\mathrm{x}^{\mathrm{2}} \mathrm{y}\:=\mathrm{sin}\left(\mathrm{2x}\right) \\ $$

Question Number 95209    Answers: 0   Comments: 0

∫(√(1+x^3 ))dx

$$\int\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{3}} }\mathrm{dx} \\ $$

Question Number 95208    Answers: 0   Comments: 0

i\ ∫((sinx)/x)dx ii\ ∫((cosx)/x)dx iii\ ∫(1/(lnx))dx iv\ ∫(√(1−k^2 sin^2 x))dx v\ ∫(√(sinx))dx vi\ ∫sin(x^2 )dx vii\ ∫cos(x^2 )dx viii\ ∫xtanxdx ix\ ∫e^(−x^2 ) dx x\∫e^x^2 dx xi\ ∫(x^2 /(1+x^5 ))dx xii\ ∫((1+x^2 ))^(1/3) dx

$$\mathrm{i}\backslash\:\int\frac{\mathrm{sinx}}{\mathrm{x}}\mathrm{dx}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{ii}\backslash\:\int\frac{\mathrm{cosx}}{\mathrm{x}}\mathrm{dx} \\ $$$$\mathrm{iii}\backslash\:\int\frac{\mathrm{1}}{\mathrm{lnx}}\mathrm{dx}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{iv}\backslash\:\int\sqrt{\mathrm{1}−\mathrm{k}^{\mathrm{2}} \mathrm{sin}^{\mathrm{2}} \mathrm{x}}\mathrm{dx} \\ $$$$\mathrm{v}\backslash\:\int\sqrt{\mathrm{sinx}}\mathrm{dx}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{vi}\backslash\:\int\mathrm{sin}\left(\mathrm{x}^{\mathrm{2}} \right)\mathrm{dx} \\ $$$$\mathrm{vii}\backslash\:\int\mathrm{cos}\left(\mathrm{x}^{\mathrm{2}} \right)\mathrm{dx}\:\:\:\:\:\:\mathrm{viii}\backslash\:\int\mathrm{xtanxdx} \\ $$$$\mathrm{ix}\backslash\:\int\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} } \mathrm{dx}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}\backslash\int\mathrm{e}^{\mathrm{x}^{\mathrm{2}} } \mathrm{dx} \\ $$$$\mathrm{xi}\backslash\:\int\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{1}+\mathrm{x}^{\mathrm{5}} }\mathrm{dx}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{xii}\backslash\:\int\sqrt[{\mathrm{3}}]{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx} \\ $$

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