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AllQuestion and Answers: Page 269

Question Number 194928 Answers: 1 Comments: 0

lim_(x→∞) ((√(x^2 +5x+1)) +(√(x^2 −2x+1))+(√(x^2 +3))+(√(x^2 −4x+9))−(√(16x^2 −8)) =?

$$\:\:\:\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\sqrt{{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{1}}\:+\sqrt{{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{1}}+\sqrt{{x}^{\mathrm{2}} +\mathrm{3}}+\sqrt{{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{9}}−\sqrt{\mathrm{16}{x}^{\mathrm{2}} −\mathrm{8}}\:=?\right. \\ $$

Question Number 194903 Answers: 1 Comments: 1

Question Number 194915 Answers: 2 Comments: 4

(3/(x−3))+(5/(x−5))+(7/(x−17))+((19)/(x−19))=x^2 −11x−4

$$ \\ $$$$\frac{\mathrm{3}}{{x}−\mathrm{3}}+\frac{\mathrm{5}}{{x}−\mathrm{5}}+\frac{\mathrm{7}}{{x}−\mathrm{17}}+\frac{\mathrm{19}}{{x}−\mathrm{19}}={x}^{\mathrm{2}} −\mathrm{11}{x}−\mathrm{4} \\ $$

Question Number 194914 Answers: 2 Comments: 0

Question Number 194913 Answers: 2 Comments: 0

Question Number 194899 Answers: 1 Comments: 0

Question Number 194900 Answers: 1 Comments: 0

Given d = (((2+ (√5)))^(1/3) /(1+(√5))) then d^3 −4d^2 +8d −2 =?

$$\:\:\:\:\:\:{Given}\:\:\:{d}\:=\:\frac{\sqrt[{\mathrm{3}}]{\mathrm{2}+\:\sqrt{\mathrm{5}}}}{\mathrm{1}+\sqrt{\mathrm{5}}}\:\: \\ $$$$\:\:\:\:\:\:{then}\:\:{d}^{\mathrm{3}} −\mathrm{4}{d}^{\mathrm{2}} \:+\mathrm{8}{d}\:−\mathrm{2}\:=?\: \\ $$$$\:\:\:\:\: \\ $$

Question Number 194896 Answers: 1 Comments: 0

x^4 + f^( 2) (x) = 1+ 2x^2 f(x) x∈R ,

$$\:\:\:\:\:\: \\ $$$$ {x}^{\mathrm{4}} \:+\:{f}^{\:\mathrm{2}} \left({x}\right)\:=\:\mathrm{1}+\:\mathrm{2}{x}^{\mathrm{2}} \:{f}\left({x}\right) \\ $$$$\:\:\:\:\:{x}\in{R}\:,\: \\ $$

Question Number 194891 Answers: 1 Comments: 0

lim_(x→3^+ ) ((((√x)−(√(x−3))−(√3))/( (√(x^2 −9)))) )=?

$$\:\:\:\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{3}^{+} } {\mathrm{lim}}\:\left(\frac{\sqrt{{x}}−\sqrt{{x}−\mathrm{3}}−\sqrt{\mathrm{3}}}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{9}}}\:\right)=? \\ $$

Question Number 194888 Answers: 1 Comments: 0

Question Number 194887 Answers: 1 Comments: 0

What is the Inverse laplace transform of ((S + 2)/(S^2 +4S + 7)) Urgent!

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{Inverse}\:\mathrm{laplace}\:\mathrm{transform}\:\mathrm{of} \\ $$$$\frac{\mathrm{S}\:+\:\mathrm{2}}{\mathrm{S}^{\mathrm{2}} \:+\mathrm{4S}\:+\:\mathrm{7}} \\ $$$$ \\ $$$$\mathrm{Urgent}! \\ $$

Question Number 194881 Answers: 1 Comments: 0

Give △ABC Proof: sin A + sin B + sin C > 2

$${Give}\:\bigtriangleup{ABC}\: \\ $$$${Proof}:\:{sin}\:{A}\:+\:{sin}\:{B}\:+\:{sin}\:{C}\:>\:\mathrm{2} \\ $$

Question Number 194884 Answers: 1 Comments: 0

x! = 6!. 7! x^2 =?

$$\:\:\:\:\:\:{x}!\:=\:\mathrm{6}!.\:\mathrm{7}!\: \\ $$$$\:\:\:\:\:\:{x}^{\mathrm{2}} \:=?\: \\ $$

Question Number 194879 Answers: 1 Comments: 0

Question Number 194878 Answers: 2 Comments: 0

Question Number 194877 Answers: 0 Comments: 1

without calculator Prove: ((π^5 +π^4 ))^(1/6) <e

$${without}\:{calculator}\:{Prove}:\:\sqrt[{\mathrm{6}}]{\pi^{\mathrm{5}} +\pi^{\mathrm{4}} }<{e} \\ $$

Question Number 194869 Answers: 1 Comments: 0

Question Number 194868 Answers: 1 Comments: 0

Prove that ∀n∈IN ∫^( 1) _( 0) t sin^(2n) (lnt)dt= (1/(1−e^(−2π) )) ∫^( π) _( 0) e^(−2t) sin^(2n) (t)dt

$$\mathrm{Prove}\:\mathrm{that}\:\forall{n}\in\mathrm{IN} \\ $$$$\underset{\:\mathrm{0}} {\int}^{\:\mathrm{1}} {t}\:{sin}^{\mathrm{2}{n}} \left({lnt}\right){dt}=\:\frac{\mathrm{1}}{\mathrm{1}−{e}^{−\mathrm{2}\pi} }\:\underset{\:\mathrm{0}} {\int}^{\:\pi} {e}^{−\mathrm{2}{t}} {sin}^{\mathrm{2}{n}} \left({t}\right){dt} \\ $$

Question Number 194861 Answers: 1 Comments: 0

Question Number 194853 Answers: 3 Comments: 0

Question Number 194852 Answers: 1 Comments: 0

lim_(x→0) (cosx)^(log(x)) =?

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\mathrm{cosx}\right)^{\mathrm{log}\left(\mathrm{x}\right)} =? \\ $$$$ \\ $$

Question Number 194847 Answers: 0 Comments: 2

z^n = −512+512i find n.

$$\:\:\:\:\: {z}^{{n}} =\:−\mathrm{512}+\mathrm{512}{i}\: \\ $$$$\:\:\:\:{find}\:{n}. \\ $$

Question Number 194846 Answers: 1 Comments: 0

x=((((10+6(√3)))^(1/3) ((√3)−1))/( (√(6+2(√5)))−(√5))) G=(12x^3 +4x^2 −55)^(2023) =?

$$\:\:\:\:\: {x}=\frac{\sqrt[{\mathrm{3}}]{\mathrm{10}+\mathrm{6}\sqrt{\mathrm{3}}}\:\left(\sqrt{\mathrm{3}}−\mathrm{1}\right)}{\:\sqrt{\mathrm{6}+\mathrm{2}\sqrt{\mathrm{5}}}−\sqrt{\mathrm{5}}} \\ $$$$\:\:\:\: {G}=\left(\mathrm{12}{x}^{\mathrm{3}} +\mathrm{4}{x}^{\mathrm{2}} −\mathrm{55}\right)^{\mathrm{2023}} \:=? \\ $$

Question Number 194844 Answers: 1 Comments: 0

(x^2 +1)^2 +(x+3)^2 =(x^2 +ax+b)(x^2 +cx+d) Find a,b,c,d.

$$\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} +\left({x}+\mathrm{3}\right)^{\mathrm{2}} =\left({x}^{\mathrm{2}} +{ax}+{b}\right)\left({x}^{\mathrm{2}} +{cx}+{d}\right) \\ $$$${Find}\:{a},{b},{c},{d}. \\ $$

Question Number 194837 Answers: 2 Comments: 0

for x>0 find the minimum of the function f(x)=x^3 +(5/x).

$${for}\:{x}>\mathrm{0}\:{find}\:{the}\:{minimum}\:{of}\:{the} \\ $$$${function}\:{f}\left({x}\right)={x}^{\mathrm{3}} +\frac{\mathrm{5}}{{x}}. \\ $$

Question Number 194836 Answers: 0 Comments: 1

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