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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

Question Number 78655 Answers: 1 Comments: 2

Question Number 78652 Answers: 1 Comments: 0

Question Number 78650 Answers: 2 Comments: 4

Question Number 78643 Answers: 0 Comments: 2

sin 20×sin 40×sin 80=(√(3/8))

$$\mathrm{sin}\:\mathrm{20}×\mathrm{sin}\:\mathrm{40}×\mathrm{sin}\:\mathrm{80}=\sqrt{\mathrm{3}/\mathrm{8}} \\ $$

Question Number 78635 Answers: 1 Comments: 8

Question Number 78627 Answers: 0 Comments: 0

explicite f(x)=∫_(−∞) ^(+∞) ((arctan(xt +1))/(t^2 +x^2 ))dt with x>0

$${explicite}\:{f}\left({x}\right)=\int_{−\infty} ^{+\infty} \:\frac{{arctan}\left({xt}\:+\mathrm{1}\right)}{{t}^{\mathrm{2}} \:+{x}^{\mathrm{2}} }{dt}\:\:{with}\:{x}>\mathrm{0} \\ $$

Question Number 78625 Answers: 0 Comments: 1

calculate ∫_(−∞) ^(+∞) ((arctan(x^2 −3))/((x^2 +x+1)^2 ))dx

$${calculate}\:\:\int_{−\infty} ^{+\infty} \:\frac{{arctan}\left({x}^{\mathrm{2}} −\mathrm{3}\right)}{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 78624 Answers: 0 Comments: 0

calculate ∫_0 ^(π/4) e^(−2x) ln(1+cosx)dx

$${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {e}^{−\mathrm{2}{x}} {ln}\left(\mathrm{1}+{cosx}\right){dx} \\ $$

Question Number 78623 Answers: 1 Comments: 0

calculate lim_(x→0) (((√(1+x+x^2 +....+x^n )) −1)/x^(n/2) )

$${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\frac{\sqrt{\mathrm{1}+{x}+{x}^{\mathrm{2}} +....+{x}^{{n}} }\:\:−\mathrm{1}}{{x}^{\frac{{n}}{\mathrm{2}}} } \\ $$

Question Number 78622 Answers: 0 Comments: 1

calculate lim_(n→+∞) ∫_0 ^n (1−(t/n))^n ln(1+nt)dt

$${calculate}\:{lim}_{{n}\rightarrow+\infty} \:\:\:\:\:\int_{\mathrm{0}} ^{{n}} \left(\mathrm{1}−\frac{{t}}{{n}}\right)^{{n}} {ln}\left(\mathrm{1}+{nt}\right){dt} \\ $$

Question Number 78621 Answers: 0 Comments: 1

calculate lim_(x→1) ∫_x ^x^3 ((sh(xt^2 ))/(sin(xt)))dt

$${calculate}\:{lim}_{{x}\rightarrow\mathrm{1}} \:\:\:\:\int_{{x}} ^{{x}^{\mathrm{3}} } \:\:\frac{{sh}\left({xt}^{\mathrm{2}} \right)}{{sin}\left({xt}\right)}{dt} \\ $$

Question Number 78620 Answers: 1 Comments: 0

explicit f(x) =∫_0 ^(+∞) ln(1−xe^(−t) )dt with ∣x∣<1

$${explicit}\:\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{+\infty} {ln}\left(\mathrm{1}−{xe}^{−{t}} \right){dt}\:\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$

Question Number 78609 Answers: 0 Comments: 0

Question Number 78628 Answers: 2 Comments: 1

Find minimum value of y = ((2x)/(x^2 + x + 1)) x , y ∈ R Without Differential

$${Find}\:\:{minimum}\:\:{value}\:\:{of} \\ $$$$\:\:\:\:\:\:\:{y}\:\:=\:\:\frac{\mathrm{2}{x}}{{x}^{\mathrm{2}} \:+\:{x}\:+\:\mathrm{1}} \\ $$$${x}\:,\:{y}\:\:\in\:\:\mathbb{R} \\ $$$${Without}\:\:{Differential} \\ $$

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