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Question Number 78794 Answers: 1 Comments: 0

f(x + (1/x)) = ((x^6 + 1)/(27)) f(x) = ...

$${f}\left({x}\:+\:\frac{\mathrm{1}}{{x}}\right)\:\:=\:\:\frac{{x}^{\mathrm{6}} \:+\:\mathrm{1}}{\mathrm{27}} \\ $$$${f}\left({x}\right)\:\:=\:\:... \\ $$

Question Number 78791 Answers: 1 Comments: 0

lim_(x→∞) (√(2+3x−x^2 )) −(√(x^2 −2x+2)) ?

$$ \\ $$$$ \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\sqrt{\mathrm{2}+\mathrm{3x}−\mathrm{x}^{\mathrm{2}} }\:−\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{2x}+\mathrm{2}}\:? \\ $$

Question Number 78785 Answers: 1 Comments: 0

(1+sin (π/7))^(3−cos 2x) = (sin (π/(14))+cos (π/(14)))^(10 sin x) find solution

$$ \\ $$$$ \\ $$$$\left(\mathrm{1}+\mathrm{sin}\:\frac{\pi}{\mathrm{7}}\right)^{\mathrm{3}−\mathrm{cos}\:\mathrm{2x}} =\:\left(\mathrm{sin}\:\frac{\pi}{\mathrm{14}}+\mathrm{cos}\:\frac{\pi}{\mathrm{14}}\right)^{\mathrm{10}\:\mathrm{sin}\:\mathrm{x}} \\ $$$$\mathrm{find}\:\mathrm{solution} \\ $$

Question Number 78770 Answers: 0 Comments: 0

Question Number 78762 Answers: 1 Comments: 1

3acr^2 (1−r)+3apr(1−r)(pa+qb) +3bqr(1−r)(pa+qb) = 3(1−r)^2 (pa+qb)^2 +r^2 b^2 Find p, q, r such that the equation is satisfied for general any values of a,b,c.

$$\mathrm{3}{acr}^{\mathrm{2}} \left(\mathrm{1}−{r}\right)+\mathrm{3}{apr}\left(\mathrm{1}−{r}\right)\left({pa}+{qb}\right) \\ $$$$+\mathrm{3}{bqr}\left(\mathrm{1}−{r}\right)\left({pa}+{qb}\right) \\ $$$$\:\:\:=\:\mathrm{3}\left(\mathrm{1}−{r}\right)^{\mathrm{2}} \left({pa}+{qb}\right)^{\mathrm{2}} +{r}^{\mathrm{2}} {b}^{\mathrm{2}} \\ $$$${Find}\:{p},\:{q},\:{r}\:{such}\:{that}\:{the}\:{equation} \\ $$$${is}\:{satisfied}\:{for}\:{general}\:{any} \\ $$$${values}\:{of}\:{a},{b},{c}.\: \\ $$

Question Number 78755 Answers: 0 Comments: 2

Solve the equation: xy + 5x + 5y = − 25 ... (i) yz + 3y + 5z = − 15 ... (ii) xz + 5z + 3x = − 15 ... (iii)

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\:\:\:\:\mathrm{xy}\:+\:\mathrm{5x}\:+\:\mathrm{5y}\:\:=\:\:−\:\mathrm{25}\:\:\:\:\:\:...\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\mathrm{yz}\:+\:\mathrm{3y}\:+\:\mathrm{5z}\:\:=\:\:−\:\mathrm{15}\:\:\:\:\:\:...\:\left(\mathrm{ii}\right) \\ $$$$\:\:\:\:\mathrm{xz}\:+\:\mathrm{5z}\:+\:\mathrm{3x}\:\:=\:\:−\:\mathrm{15}\:\:\:\:\:\:...\:\left(\mathrm{iii}\right) \\ $$

Question Number 78766 Answers: 1 Comments: 0

∫2 e^(1/(2(x−2)^2 )) dx

$$\int\mathrm{2}\:{e}^{\frac{\mathrm{1}}{\mathrm{2}\left({x}−\mathrm{2}\right)^{\mathrm{2}} }} \:{dx} \\ $$

Question Number 78732 Answers: 0 Comments: 2

Question Number 78767 Answers: 0 Comments: 13

what is minimum value of y = sin x+cos^4 x

$$\mathrm{what}\:\mathrm{is}\:\mathrm{minimum} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{y}\:=\:\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:^{\mathrm{4}} \mathrm{x} \\ $$

Question Number 78717 Answers: 0 Comments: 2

given ∫ f(x) dx = (1/(2 ((g(x)))^(1/(3 )) )) . g′(1)= g(1) = 8 ⇒f(1)=?

$$\mathrm{given}\: \\ $$$$\int\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:=\:\frac{\mathrm{1}}{\mathrm{2}\:\sqrt[{\mathrm{3}\:}]{\mathrm{g}\left(\mathrm{x}\right)}}\:.\: \\ $$$$\mathrm{g}'\left(\mathrm{1}\right)=\:\mathrm{g}\left(\mathrm{1}\right)\:=\:\mathrm{8}\:\Rightarrow\mathrm{f}\left(\mathrm{1}\right)=? \\ $$$$ \\ $$

Question Number 78709 Answers: 2 Comments: 1

if sin^2 x+sin x = 1 what is cos^(12) x+3cos^(10) x+3cos^8 x+cos^6 x

$$\mathrm{if}\:\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}+\mathrm{sin}\:\mathrm{x}\:=\:\mathrm{1} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{cos}\:^{\mathrm{12}} \mathrm{x}+\mathrm{3cos}\:^{\mathrm{10}} \mathrm{x}+\mathrm{3cos}\:^{\mathrm{8}} \mathrm{x}+\mathrm{cos}\:^{\mathrm{6}} \mathrm{x} \\ $$

Question Number 78708 Answers: 2 Comments: 1

calculate ∫_0 ^∞ (e^(−x) /x)(sinx)^(2 ) dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{e}^{−{x}} }{{x}}\left({sinx}\right)^{\mathrm{2}\:} {dx} \\ $$

Question Number 78707 Answers: 1 Comments: 0

let I =∫_0 ^1 ((ln(1+x))/(1+x^2 ))dx and J =∫∫_([0,1]^2 ) (x/((1+x^2 )(1+xy)))dxdy find J by two method and deduce the valueof I

$${let}\:{I}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}\:{and}\: \\ $$$${J}\:=\int\int_{\left[\mathrm{0},\mathrm{1}\right]^{\mathrm{2}} } \:\:\:\:\frac{{x}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{xy}\right)}{dxdy} \\ $$$${find}\:{J}\:{by}\:{two}\:{method}\:{and}\:{deduce}\:\:{the}\:{valueof}\:{I} \\ $$

Question Number 78706 Answers: 1 Comments: 0

calculate ∫∫_([0,1]^2 ) ((dxdy)/((x+y+1)^2 ))

$${calculate}\:\int\int_{\left[\mathrm{0},\mathrm{1}\right]^{\mathrm{2}} } \:\:\:\frac{{dxdy}}{\left({x}+{y}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 78705 Answers: 1 Comments: 0

calculate ∫∫_D (x^2 +y^2 )dxdy D ={(x,y)∈R^2 / (1/2)≤x^2 +y^2 ≤3 and y≥0}

$${calculate}\:\int\int_{{D}} \:\left({x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \right){dxdy}\: \\ $$$${D}\:=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:\frac{\mathrm{1}}{\mathrm{2}}\leqslant{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \leqslant\mathrm{3}\:{and}\:{y}\geqslant\mathrm{0}\right\} \\ $$

Question Number 78703 Answers: 1 Comments: 0

let a>0 calculate ∫∫_D_a ((xdxdy)/(a^2 +x^2 +y^2 )) and D_a ={(x,y)∈R^2 / x^2 +y^2 ≤a^2 and x>0}

$${let}\:{a}>\mathrm{0}\:\:{calculate}\:\int\int_{{D}_{{a}} } \:\:\:\:\frac{{xdxdy}}{{a}^{\mathrm{2}} \:+{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} } \\ $$$${and}\:{D}_{{a}} =\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \leqslant{a}^{\mathrm{2}} \:\:{and}\:{x}>\mathrm{0}\right\} \\ $$

Question Number 78701 Answers: 0 Comments: 1

calculate ∫∫_D ((dxdy)/((1+x^2 )(1+y^2 ))) with D ={(x,h)∈R^2 /0≤x≤1 and 0≤y ≤x}

$${calculate}\:\int\int_{{D}} \:\:\frac{{dxdy}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{y}^{\mathrm{2}} \right)} \\ $$$${with}\:{D}\:=\left\{\left({x},{h}\right)\in{R}^{\mathrm{2}} \:\:/\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:{and}\:\:\mathrm{0}\leqslant{y}\:\leqslant{x}\right\} \\ $$

Question Number 78700 Answers: 0 Comments: 1

calculate ∫∫_D ((∣x−2∣)/y)dxdy with D={(x,y)∈R^2 /0≤x≤3 and 1≤y≤e}

$${calculate}\:\int\int_{{D}} \:\frac{\mid{x}−\mathrm{2}\mid}{{y}}{dxdy}\:{with} \\ $$$${D}=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\mathrm{0}\leqslant{x}\leqslant\mathrm{3}\:{and}\:\:\mathrm{1}\leqslant{y}\leqslant{e}\right\} \\ $$

Question Number 78685 Answers: 1 Comments: 1

is g ={(1. 1).(2.3).(3 .5).(4.7)} a function? justify if this is described by the relation g(x)=ax+b then what values should be assigned to a and b ?

$${is}\:{g}\:=\left\{\left(\mathrm{1}.\:\mathrm{1}\right).\left(\mathrm{2}.\mathrm{3}\right).\left(\mathrm{3}\:.\mathrm{5}\right).\left(\mathrm{4}.\mathrm{7}\right)\right\}\:{a}\:{function}?\:{justify}\:{if}\:{this}\:{is}\:{described}\:{by}\:{the}\:{relation}\:{g}\left({x}\right)={ax}+{b}\:{then}\:{what}\:{values}\:{should}\:{be}\:{assigned}\:{to}\:{a}\:{and}\:{b}\:? \\ $$

Question Number 78683 Answers: 0 Comments: 4

solve x^4 −18x−35=0 by using substitution x= u+v

$${solve}\:{x}^{\mathrm{4}} −\mathrm{18}{x}−\mathrm{35}=\mathrm{0}\:{by}\:{using}\:{substitution}\:{x}=\:{u}+{v} \\ $$

Question Number 78671 Answers: 1 Comments: 0

prove p⇒q and negetion of q⇒negation of p

$${prove}\:{p}\Rightarrow{q}\:{and}\:{negetion}\:{of}\:{q}\Rightarrow{negation}\:{of}\:{p} \\ $$

Question Number 78670 Answers: 0 Comments: 2

let A= [((a b)),((c d)) ]use the augmented matrix[A I] and elementary row operation to show A^(−1) = (1/(ad bc)) [((a b)),((c d)) ]and show that det(A^(−1) )=(1/(det(A)))

$${let}\:{A}=\begin{bmatrix}{{a}\:\:{b}}\\{{c}\:\:{d}}\end{bmatrix}{use}\:{the}\:{augmented}\:{matrix}\left[{A}\:{I}\right]\:{and}\:{elementary}\:{row}\:{operation}\:{to}\:{show}\:{A}^{−\mathrm{1}} =\:\frac{\mathrm{1}}{{ad}\:{bc}}\begin{bmatrix}{{a}\:\:{b}}\\{{c}\:\:\:{d}}\end{bmatrix}{and}\:{show}\:{that}\:{det}\left({A}^{−\mathrm{1}} \right)=\frac{\mathrm{1}}{{det}\left({A}\right)} \\ $$$$ \\ $$

Question Number 78682 Answers: 0 Comments: 2

Question Number 78667 Answers: 1 Comments: 0

let f(x)=(x+1)(((x+1)(x−3)^2 )/((x−1)^2 (x−4) )) then a. find x and y intercepts b. find vertical asymptote and horizontal asymtote c. find domain and range of f d. draw the graph of f

$${let}\:{f}\left({x}\right)=\left({x}+\mathrm{1}\right)\frac{\left({x}+\mathrm{1}\right)\left({x}−\mathrm{3}\right)^{\mathrm{2}} }{\left({x}−\mathrm{1}\right)^{\mathrm{2}} \left({x}−\mathrm{4}\right)\:}\:{then} \\ $$$${a}.\:{find}\:{x}\:{and}\:{y}\:{intercepts} \\ $$$${b}.\:{find}\:{vertical}\:{asymptote}\:{and}\:{horizontal}\:{asymtote} \\ $$$${c}.\:{find}\:{domain}\:{and}\:{range}\:{of}\:{f} \\ $$$${d}.\:{draw}\:{the}\:{graph}\:{of}\:{f} \\ $$

Question Number 78694 Answers: 6 Comments: 2

Solve the equation. x^2 − (y − z)^2 = 10 ... (i) y^2 − (z − x)^2 = 5 ... (ii) z^2 − (x − y)^2 = 2 ... (iii)

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}. \\ $$$$\:\:\:\:\:\mathrm{x}^{\mathrm{2}} \:−\:\left(\mathrm{y}\:−\:\mathrm{z}\right)^{\mathrm{2}} \:\:=\:\:\mathrm{10}\:\:\:\:\:\:...\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\mathrm{y}^{\mathrm{2}} \:−\:\left(\mathrm{z}\:−\:\mathrm{x}\right)^{\mathrm{2}} \:\:=\:\:\mathrm{5}\:\:\:\:\:\:...\:\left(\mathrm{ii}\right) \\ $$$$\:\:\:\:\:\mathrm{z}^{\mathrm{2}} \:−\:\left(\mathrm{x}\:\:−\:\mathrm{y}\right)^{\mathrm{2}} \:\:=\:\:\mathrm{2}\:\:\:\:\:\:...\:\left(\mathrm{iii}\right) \\ $$

Question Number 78693 Answers: 1 Comments: 3

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