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AllQuestion and Answers: Page 170

Question Number 204701    Answers: 3   Comments: 0

Question Number 204717    Answers: 1   Comments: 0

((3^0 +3^1 +3^2 +.........+ 3^(200) )/(13)) =^(Remainder) ?

$$\frac{\mathrm{3}^{\mathrm{0}} +\mathrm{3}^{\mathrm{1}} +\mathrm{3}^{\mathrm{2}} \:+.........+\:\mathrm{3}^{\mathrm{200}} }{\mathrm{13}}\:\overset{\mathrm{Remainder}} {=}\:? \\ $$

Question Number 204691    Answers: 1   Comments: 0

(√(a÷(√(a÷(√(a÷∙∙∙÷(√a)))))))=?

$$\sqrt{{a}\boldsymbol{\div}\sqrt{{a}\boldsymbol{\div}\sqrt{{a}\boldsymbol{\div}\centerdot\centerdot\centerdot\boldsymbol{\div}\sqrt{{a}}}}}=? \\ $$

Question Number 204690    Answers: 1   Comments: 0

((a^x ÷((b^y ÷(c^z )^(1/r) ))^(1/q) ))^(1/p) =?

$$\sqrt[{{p}}]{{a}^{{x}} \boldsymbol{\div}\sqrt[{{q}}]{{b}^{{y}} \boldsymbol{\div}\sqrt[{{r}}]{{c}^{{z}} }}}=? \\ $$

Question Number 204689    Answers: 1   Comments: 0

y=∣f(x)∣ ; (dy/dx)=?

$${y}=\mid{f}\left({x}\right)\mid\:\:;\:\:\:\:\frac{{dy}}{{dx}}=? \\ $$

Question Number 204688    Answers: 1   Comments: 0

f(x)=sgn(x); f^′ (x)=(d/dx)[f(x)]=?

$${f}\left({x}\right)={sgn}\left({x}\right);\:\:\:\:\:{f}^{'} \left({x}\right)=\frac{{d}}{{dx}}\left[{f}\left({x}\right)\right]=? \\ $$

Question Number 204687    Answers: 0   Comments: 0

(√(a−(√(b−(√c)))))=?

$$\sqrt{{a}−\sqrt{{b}−\sqrt{{c}}}}=? \\ $$

Question Number 204684    Answers: 0   Comments: 2

Question Number 204674    Answers: 1   Comments: 1

Question Number 204671    Answers: 3   Comments: 0

if f(f(x))=x^2 −3x+4, find f(1)=?

$${if}\:{f}\left({f}\left({x}\right)\right)={x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{4},\:{find}\:{f}\left(\mathrm{1}\right)=? \\ $$

Question Number 204666    Answers: 0   Comments: 0

this is a closed curve: f(θ)=(e^(iθ) )^((e^(iθ) )) =e^(−θsin θ) e^(iθcos θ) ; −π<θ≤π f: { ((x(θ)=e^(−θsin θ) cos (θcos θ))),((y(θ)=e^(−θsin θ) sin (θcos θ))) :} find the area

$$\mathrm{this}\:\mathrm{is}\:\mathrm{a}\:\mathrm{closed}\:\mathrm{curve}: \\ $$$${f}\left(\theta\right)=\left(\mathrm{e}^{\mathrm{i}\theta} \right)^{\left(\mathrm{e}^{\mathrm{i}\theta} \right)} =\mathrm{e}^{−\theta\mathrm{sin}\:\theta} \mathrm{e}^{\mathrm{i}\theta\mathrm{cos}\:\theta} ;\:−\pi<\theta\leqslant\pi \\ $$$${f}:\:\begin{cases}{{x}\left(\theta\right)=\mathrm{e}^{−\theta\mathrm{sin}\:\theta} \mathrm{cos}\:\left(\theta\mathrm{cos}\:\theta\right)}\\{{y}\left(\theta\right)=\mathrm{e}^{−\theta\mathrm{sin}\:\theta} \mathrm{sin}\:\left(\theta\mathrm{cos}\:\theta\right)}\end{cases} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{area} \\ $$

Question Number 204664    Answers: 2   Comments: 0

8+(√(8^2 +(√(8^4 +(√(8^8 +(√(8^(16) +(√(...)))))))))) = ?

$$\:\:\mathrm{8}+\sqrt{\mathrm{8}^{\mathrm{2}} +\sqrt{\mathrm{8}^{\mathrm{4}} +\sqrt{\mathrm{8}^{\mathrm{8}} +\sqrt{\mathrm{8}^{\mathrm{16}} +\sqrt{...}}}}}\:=\:?\: \\ $$

Question Number 204663    Answers: 1   Comments: 0

Question Number 204658    Answers: 2   Comments: 0

If a = (9)^(1/3) − (3)^(1/3) + 1 Find (((4 − a)/a))^6 = ?

$$\mathrm{If}\:\:\:\mathrm{a}\:=\:\sqrt[{\mathrm{3}}]{\mathrm{9}}\:−\:\sqrt[{\mathrm{3}}]{\mathrm{3}}\:+\:\mathrm{1} \\ $$$$\mathrm{Find}\:\:\:\left(\frac{\mathrm{4}\:−\:\mathrm{a}}{\mathrm{a}}\right)^{\mathrm{6}} =\:? \\ $$

Question Number 204657    Answers: 1   Comments: 0

Consider point A inside a triangle with sides 3,4 and 5. if d is the sum of the distances of this point from the sides.what is the smallest value of d?

$${Consider}\:{point}\:{A}\:{inside}\:{a}\:{triangle} \\ $$$${with}\:{sides}\:\mathrm{3},\mathrm{4}\:{and}\:\mathrm{5}.\:{if}\:{d}\:\:{is}\:{the}\:{sum} \\ $$$$\:{of}\:{the}\:{distances}\:\:{of}\:{this}\:{point}\:{from} \\ $$$${the}\:{sides}.{what}\:{is}\:{the}\:{smallest} \\ $$$${value}\:{of}\:{d}? \\ $$$$ \\ $$

Question Number 204686    Answers: 0   Comments: 1

(√(a−(√(a−(√(a−∙∙∙))))))=?

$$\sqrt{{a}−\sqrt{{a}−\sqrt{{a}−\centerdot\centerdot\centerdot}}}=? \\ $$

Question Number 204647    Answers: 4   Comments: 0

Question Number 204645    Answers: 1   Comments: 1

Let f : [ 1^ ∞) →R be a differentiable function such that f(1)= (1/3) and 3∫_1 ^x f(t) dt = x f(x)−(x^3 /3) ,x∈[1,∞) find tbe value of f(e)

$$\:\:\mathrm{Let}\:{f}\::\:\left[\:\bar {\mathrm{1}}\infty\right)\:\rightarrow\mathrm{R}\:\mathrm{be}\:\mathrm{a}\:\mathrm{differentiable}\: \\ $$$$\:\mathrm{function}\:\mathrm{such}\:\mathrm{that}\:{f}\left(\mathrm{1}\right)=\:\frac{\mathrm{1}}{\mathrm{3}}\:\mathrm{and}\: \\ $$$$\:\mathrm{3}\underset{\mathrm{1}} {\overset{\mathrm{x}} {\int}}\:{f}\left({t}\right)\:{dt}\:=\:{x}\:{f}\left({x}\right)−\frac{{x}^{\mathrm{3}} }{\mathrm{3}}\:,\mathrm{x}\in\left[\mathrm{1},\infty\right)\: \\ $$$$\:\mathrm{find}\:\mathrm{tbe}\:\mathrm{value}\:\mathrm{of}\:{f}\left({e}\right)\: \\ $$

Question Number 204642    Answers: 1   Comments: 0

If (1/1^2 )+(1/2^2 )+(1/3^2 )+ (1/4^2 )+(1/5^2 ) + ............. = (π^2 /6) then (1/1^2 )+(1/3^2 )+(1/5^2 ) + ............. = ?

$$\mathrm{If}\:\:\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }+\:\frac{\mathrm{1}}{\mathrm{4}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{5}^{\mathrm{2}} }\:+\:.............\:=\:\frac{\pi^{\mathrm{2}} }{\mathrm{6}} \\ $$$$\mathrm{then}\:\:\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{5}^{\mathrm{2}} }\:+\:.............\:=\:? \\ $$$$ \\ $$

Question Number 204640    Answers: 1   Comments: 0

f(x)=(1/( (√(1+x))))+(1/( (√(1+a))))+(√((ax)/(ax+8))) a>0 x>0 prove 1<f(x)<2

$${f}\left({x}\right)=\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{x}}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{a}}}+\sqrt{\frac{{ax}}{{ax}+\mathrm{8}}} \\ $$$${a}>\mathrm{0}\:{x}>\mathrm{0} \\ $$$${prove}\:\mathrm{1}<{f}\left({x}\right)<\mathrm{2} \\ $$

Question Number 204632    Answers: 3   Comments: 0

Question Number 204628    Answers: 2   Comments: 0

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Question Number 204621    Answers: 3   Comments: 0

a , b , c ∈ R^+ If (√a) + (√b) + (√c) = 1 Prove that: a + b + c ≥ (1/3)

$$\mathrm{a}\:,\:\mathrm{b}\:,\:\mathrm{c}\:\in\:\mathbb{R}^{+} \\ $$$$\mathrm{If}\:\:\:\sqrt{\mathrm{a}}\:+\:\sqrt{\mathrm{b}}\:+\:\sqrt{\mathrm{c}}\:=\:\mathrm{1} \\ $$$$\mathrm{Prove}\:\mathrm{that}:\:\:\:\mathrm{a}\:+\:\mathrm{b}\:+\:\mathrm{c}\:\geqslant\:\frac{\mathrm{1}}{\mathrm{3}} \\ $$

Question Number 204618    Answers: 1   Comments: 0

if 7x=(π/2)→((cosxsin2xtan3x)/(cot4xcos5xsin6x))=?

$${if}\:\:\mathrm{7}{x}=\frac{\pi}{\mathrm{2}}\rightarrow\frac{{cosxsin}\mathrm{2}{xtan}\mathrm{3}{x}}{{cot}\mathrm{4}{xcos}\mathrm{5}{xsin}\mathrm{6}{x}}=? \\ $$

Question Number 204617    Answers: 0   Comments: 1

Question Number 204615    Answers: 0   Comments: 2

((exercice )/) prouver ∫_0 ^𝛑 ∫_0 ^x sin((x^2 /𝛑))dxdy=𝛑 ...............prof cedric junior...........

$$\:\:\:\:\:\:\:\:\frac{\boldsymbol{\mathrm{exercice}}\:}{} \\ $$$$\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{prouver}}\:\int_{\mathrm{0}} ^{\boldsymbol{\pi}} \int_{\mathrm{0}} ^{\boldsymbol{\mathrm{x}}} \boldsymbol{{sin}}\left(\frac{\boldsymbol{\mathrm{x}}^{\mathrm{2}} }{\boldsymbol{\pi}}\right)\boldsymbol{{d}\mathrm{x}{d}\mathrm{y}}=\boldsymbol{\pi} \\ $$$$\: \\ $$$$\:\:...............\boldsymbol{{prof}}\:\boldsymbol{{cedric}}\:\boldsymbol{{junior}}........... \\ $$$$ \\ $$

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