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Question Number 79824 Answers: 2 Comments: 7

Question Number 79816 Answers: 1 Comments: 0

hello mister. i need help explaining how determine the range of function of rational functions like (i) f(x)=((ax^2 +bx+c)/(px^2 +qx+r)) (ii) f(x)=((ax^2 +bx+c)/(px+q))

$$\mathrm{hello}\:\mathrm{mister}. \\ $$$$\mathrm{i}\:\mathrm{need}\:\mathrm{help}\:\mathrm{explaining}\:\mathrm{how}\:\mathrm{determine} \\ $$$$\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:\mathrm{function} \\ $$$$\mathrm{of}\:\mathrm{rational}\:\mathrm{functions} \\ $$$$\mathrm{like}\:\left(\mathrm{i}\right)\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}+\mathrm{c}}{\mathrm{px}^{\mathrm{2}} +\mathrm{qx}+\mathrm{r}} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}+\mathrm{c}}{\mathrm{px}+\mathrm{q}} \\ $$

Question Number 79814 Answers: 0 Comments: 5

Question Number 79807 Answers: 2 Comments: 2

Question Number 79798 Answers: 0 Comments: 7

Question Number 79794 Answers: 1 Comments: 2

Question Number 79792 Answers: 1 Comments: 1

JUST FOR FUN (1/2), (2/3), 1, (8/5), (8/3), ? what do you think is the next number ? why?

$${JUST}\:{FOR}\:{FUN} \\ $$$$ \\ $$$$\frac{\mathrm{1}}{\mathrm{2}},\:\frac{\mathrm{2}}{\mathrm{3}},\:\mathrm{1},\:\frac{\mathrm{8}}{\mathrm{5}},\:\frac{\mathrm{8}}{\mathrm{3}},\:? \\ $$$${what}\:{do}\:{you}\:{think}\:{is}\:{the}\:{next}\:{number}\:? \\ $$$${why}? \\ $$

Question Number 79766 Answers: 1 Comments: 0

what is x 2^x =(1+tan 0.01^o )(1+tan 0.02^o ) (1+tan 0.03^o )...(1+tan 44.99^o )

$$\mathrm{what}\:\mathrm{is}\:\mathrm{x} \\ $$$$\mathrm{2}^{\mathrm{x}} =\left(\mathrm{1}+\mathrm{tan}\:\mathrm{0}.\mathrm{01}^{\mathrm{o}} \right)\left(\mathrm{1}+\mathrm{tan}\:\mathrm{0}.\mathrm{02}^{\mathrm{o}} \right) \\ $$$$\left(\mathrm{1}+\mathrm{tan}\:\mathrm{0}.\mathrm{03}^{\mathrm{o}} \right)...\left(\mathrm{1}+\mathrm{tan}\:\mathrm{44}.\mathrm{99}^{\mathrm{o}} \right) \\ $$

Question Number 79763 Answers: 1 Comments: 2

calculate ∫_0 ^π {cos^8 x +sin^8 x}dx

$${calculate}\:\int_{\mathrm{0}} ^{\pi} \left\{{cos}^{\mathrm{8}} {x}\:+{sin}^{\mathrm{8}} {x}\right\}{dx} \\ $$

Question Number 79761 Answers: 1 Comments: 1

(x^2 +2)y′′ + xy = 0

$$\left({x}^{\mathrm{2}} +\mathrm{2}\right){y}''\:+\:{xy}\:=\:\mathrm{0} \\ $$

Question Number 79758 Answers: 0 Comments: 1

find value of ∫_0 ^1 ln(1+ix^2 )dx and ∫_0 ^1 ln(1−ix^2 )dx with i=(√(−1))

$${find}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{ix}^{\mathrm{2}} \right){dx}\:{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}−{ix}^{\mathrm{2}} \right){dx}\:{with}\:{i}=\sqrt{−\mathrm{1}} \\ $$

Question Number 79757 Answers: 0 Comments: 1

And equation of a circle is x^2 +y^2 −2x+4y=0. (T) is his his tangent line at M(x_0 ;y_0 ) passing by D(2;1). a) Show that y verify y_0 ^2 +y_0 =0 b) deduct others tangent′s equations to Circle passing by D.

$$\mathrm{And}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{is} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{4}{y}=\mathrm{0}. \\ $$$$\left({T}\right)\:\mathrm{is}\:\mathrm{his}\:\mathrm{his}\:\mathrm{tangent}\:\mathrm{line}\:\mathrm{at}\:\mathrm{M}\left({x}_{\mathrm{0}} ;{y}_{\mathrm{0}} \right) \\ $$$${passing}\:{by}\:{D}\left(\mathrm{2};\mathrm{1}\right). \\ $$$$ \\ $$$$\left.\mathrm{a}\right)\:\mathrm{Show}\:\mathrm{that}\:\mathrm{y}\:\mathrm{verify}\:\mathrm{y}_{\mathrm{0}} ^{\mathrm{2}} +\mathrm{y}_{\mathrm{0}} =\mathrm{0} \\ $$$$\left.\mathrm{b}\right)\:\mathrm{deduct}\:\mathrm{others}\:\mathrm{tangent}'\mathrm{s}\: \\ $$$$\mathrm{equations}\:\mathrm{to}\:\mathrm{Circle}\:\mathrm{passing}\:\mathrm{by}\:\mathrm{D}. \\ $$

Question Number 79751 Answers: 2 Comments: 0

prove that cos^6 θ + sin^6 θ = 1 − (3/4) sin^2 2θ

$${prove}\:{that}\:\mathrm{cos}\:^{\mathrm{6}} \theta\:+\:\mathrm{sin}\:^{\mathrm{6}} \theta\:=\:\mathrm{1}\:−\:\frac{\mathrm{3}}{\mathrm{4}}\:\mathrm{sin}\:^{\mathrm{2}} \mathrm{2}\theta \\ $$

Question Number 79738 Answers: 0 Comments: 0

The forces F_1 = (2i + bj) N, F_2 = (−i + 2j) N and F_3 = (ai −4j)N act through the points with position vectors r_1 = (i + 3j)m ,r_2 =(xi + 5j) m and r_3 =(−i + j)m respectively . Given that this system of forces is equivalent to a couple of magnitude 12 N m, find a) the valueof the scalars a and b b) the possible values of the scalar x.

$${The}\:{forces}\:\boldsymbol{\mathrm{F}}_{\mathrm{1}} =\:\left(\mathrm{2}\boldsymbol{{i}}\:+\:{b}\boldsymbol{{j}}\right)\:{N},\:\boldsymbol{{F}}_{\mathrm{2}} =\:\left(−\boldsymbol{{i}}\:+\:\mathrm{2}\boldsymbol{{j}}\right)\:{N} \\ $$$${and}\:\boldsymbol{{F}}_{\mathrm{3}} =\:\left({a}\boldsymbol{{i}}\:−\mathrm{4}\boldsymbol{{j}}\right){N}\:{act}\:{through}\:{the}\:{points}\:{with} \\ $$$${position}\:{vectors}\:\boldsymbol{{r}}_{\mathrm{1}} =\:\left(\boldsymbol{{i}}\:+\:\mathrm{3}\boldsymbol{{j}}\right){m}\:,\boldsymbol{{r}}_{\mathrm{2}} =\left({x}\boldsymbol{{i}}\:+\:\mathrm{5}\boldsymbol{{j}}\right)\:{m} \\ $$$${and}\:\boldsymbol{{r}}_{\mathrm{3}} =\left(−\boldsymbol{{i}}\:+\:\boldsymbol{{j}}\right){m}\:{respectively}\:. \\ $$$${Given}\:{that}\:{this}\:{system}\:{of}\:{forces}\:{is}\:{equivalent}\:{to}\:{a}\:{couple} \\ $$$${of}\:{magnitude}\:\mathrm{12}\:{N}\:{m},\:{find}\: \\ $$$$\left.{a}\right)\:{the}\:{valueof}\:{the}\:{scalars}\:{a}\:{and}\:{b} \\ $$$$\left.{b}\right)\:{the}\:{possible}\:{values}\:{of}\:{the}\:{scalar}\:{x}. \\ $$

Question Number 79735 Answers: 1 Comments: 0

write tanhx in terms of e, hence prove that tanh2x = ((2tanhx)/(1+tanh^2 x))

$${write}\:{tanhx}\:{in}\:{terms}\:{of}\:{e},\:{hence}\:{prove}\:{that}\: \\ $$$${tanh}\mathrm{2}{x}\:=\:\frac{\mathrm{2}{tanhx}}{\mathrm{1}+{tanh}^{\mathrm{2}} {x}} \\ $$

Question Number 79731 Answers: 1 Comments: 5

Question Number 79730 Answers: 1 Comments: 1

I) For witch value of α the integral C=∫_0 ^( ∞) ((1/(√(1+2x^2 )))−(1/(x+1)))dx conveege ? And in this case calculate α. II) Let Δ={(x; y)/ ∣x∣+∣y∣≤2} a) Calculate I_1 = ∫∫_Δ dxdy and ∫∫_Δ ((dxdy)/((∣x∣+∣y∣)^2 +4))

$$\left.{I}\right)\:\:{For}\:{witch}\:{value}\:{of}\:\alpha\:{the}\:{integral} \\ $$$$\:{C}=\int_{\mathrm{0}} ^{\:\infty} \left(\frac{\mathrm{1}}{\sqrt{\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} }}−\frac{\mathrm{1}}{{x}+\mathrm{1}}\right){dx}\:\:{conveege}\:\:? \\ $$$${And}\:{in}\:{this}\:{case}\:{calculate}\:\alpha. \\ $$$$\left.{II}\right)\:\:{Let}\:\Delta=\left\{\left({x};\:{y}\right)/\:\mid{x}\mid+\mid{y}\mid\leqslant\mathrm{2}\right\} \\ $$$$\left.\:\:\:\:\:{a}\right)\:{Calculate}\:{I}_{\mathrm{1}} =\:\int\int_{\Delta} {dxdy}\:\:\:{and}\:\:\int\int_{\Delta} \frac{{dxdy}}{\left(\mid{x}\mid+\mid{y}\mid\right)^{\mathrm{2}} +\mathrm{4}} \\ $$

Question Number 79756 Answers: 0 Comments: 2

calculate lim_(x→1) ((sin(πx))/(1−x^2 )) without hospital rule

$${calculate}\:{lim}_{{x}\rightarrow\mathrm{1}} \:\:\frac{{sin}\left(\pi{x}\right)}{\mathrm{1}−{x}^{\mathrm{2}} }\:\:{without}\:{hospital}\:{rule} \\ $$

Question Number 79719 Answers: 1 Comments: 1

(((2.39)^2 −(1.61)^2 )/(2.39−1.61))...?

$$\frac{\left(\mathrm{2}.\mathrm{39}\overset{\mathrm{2}} {\right)}−\left(\mathrm{1}.\mathrm{61}\overset{\mathrm{2}} {\right)}}{\mathrm{2}.\mathrm{39}−\mathrm{1}.\mathrm{61}}...? \\ $$$$ \\ $$

Question Number 79718 Answers: 0 Comments: 0

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Question Number 79705 Answers: 0 Comments: 3

if L{f(t)}=L{g(t)} then why f(t)=g(t)? is there any proof

$$\mathrm{if}\:\mathscr{L}\left\{\mathrm{f}\left(\mathrm{t}\right)\right\}=\mathscr{L}\left\{\mathrm{g}\left(\mathrm{t}\right)\right\} \\ $$$$\mathrm{then}\:\mathrm{why}\:\mathrm{f}\left(\mathrm{t}\right)=\mathrm{g}\left(\mathrm{t}\right)? \\ $$$$\mathrm{is}\:\mathrm{there}\:\mathrm{any}\:\mathrm{proof} \\ $$