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AllQuestion and Answers: Page 273

Question Number 193542 Answers: 1 Comments: 2

f(x) = x^3 +3x^2 −1 1) calcul h(X) = f(a+X) −b 2) determine a and b such that h is odd

$$\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{x}^{\mathrm{3}} +\mathrm{3x}^{\mathrm{2}} −\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{calcul}\:\:\:\:\mathrm{h}\left(\mathrm{X}\right)\:=\:\mathrm{f}\left(\mathrm{a}+\mathrm{X}\right)\:−\mathrm{b} \\ $$2) determine a and b such that h is odd

Question Number 193538 Answers: 2 Comments: 0

∫ (dx/(x^6 +1)) =?

$$\:\:\:\int\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{6}} +\mathrm{1}}\:=? \\ $$

Question Number 193540 Answers: 0 Comments: 0

Question Number 193533 Answers: 2 Comments: 0

If cot x−tan x=4 then cot^2 +(2/(sin 2x)) −tan^2 x =?

$$\:\:\:\mathrm{If}\:\mathrm{cot}\:\mathrm{x}−\mathrm{tan}\:\mathrm{x}=\mathrm{4}\:\mathrm{then} \\ $$$$\:\:\:\:\mathrm{cot}\:^{\mathrm{2}} +\frac{\mathrm{2}}{\mathrm{sin}\:\mathrm{2x}}\:−\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}\:=? \\ $$

Question Number 193532 Answers: 2 Comments: 0

lim_(x→2) ((1−cos πx)/((2−x)^2 )) =?

$$\:\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:\pi\mathrm{x}}{\left(\mathrm{2}−\mathrm{x}\right)^{\mathrm{2}} }\:=? \\ $$

Question Number 193526 Answers: 2 Comments: 0

Question Number 193525 Answers: 2 Comments: 0

((27t73)/(11)) and R=0 then t=? how is explontry solution

$$\:\:\:\:\:\frac{\mathrm{27t73}}{\mathrm{11}} \\ $$$$\:\:\:\:\:\mathrm{and}\:\mathrm{R}=\mathrm{0}\:\:\:\mathrm{then}\:\mathrm{t}=? \\ $$$$\:\:\:\:\:\:\mathrm{how}\:\mathrm{is}\:\mathrm{explontry}\:\mathrm{solution} \\ $$

Question Number 193521 Answers: 0 Comments: 0

Question Number 193522 Answers: 1 Comments: 0

Question Number 193513 Answers: 1 Comments: 0

Evaluate I=∫_s ∫x^3 dydz + x^2 ydzdx. where S is the closed surface consis− ting of the cylinder x^2 +y^2 =a^2 , 0≤z≤b and the cylinder disks z=0 and z=b, x^2 +y^2 =b, x^2 +y^2 ≤a. Help!

$$\mathrm{Evaluate}\:\mathrm{I}=\underset{\mathrm{s}} {\int}\int\mathrm{x}^{\mathrm{3}} \mathrm{dydz}\:+\:\mathrm{x}^{\mathrm{2}} \mathrm{ydzdx}. \\ $$$$\mathrm{where}\:\mathrm{S}\:\mathrm{is}\:\mathrm{the}\:\mathrm{closed}\:\mathrm{surface}\:\mathrm{consis}− \\ $$$$\mathrm{ting}\:\mathrm{of}\:\mathrm{the}\:\mathrm{cylinder}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} =\mathrm{a}^{\mathrm{2}} ,\:\mathrm{0}\leqslant\mathrm{z}\leqslant\mathrm{b} \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{cylinder}\:\:\mathrm{disks}\:\mathrm{z}=\mathrm{0}\:\mathrm{and}\:\mathrm{z}=\mathrm{b}, \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} =\mathrm{b},\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \leqslant\mathrm{a}. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 193512 Answers: 1 Comments: 0

Question Number 193511 Answers: 1 Comments: 0

Question Number 193504 Answers: 0 Comments: 1

lim_(x→0) x^x^x =?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}x}^{\mathrm{x}^{\mathrm{x}} } =? \\ $$

Question Number 193502 Answers: 2 Comments: 0

olve cos 2x .tan (((7π)/(19)))=tan (((17π)/(23)))+tan (((6π)/(23)))+tan (((12π)/(19)))

$$ \mathrm{olve}\: \\ $$$$\:\:\mathrm{cos}\:\mathrm{2x}\:.\mathrm{tan}\:\left(\frac{\mathrm{7}\pi}{\mathrm{19}}\right)=\mathrm{tan}\:\left(\frac{\mathrm{17}\pi}{\mathrm{23}}\right)+\mathrm{tan}\:\left(\frac{\mathrm{6}\pi}{\mathrm{23}}\right)+\mathrm{tan}\:\left(\frac{\mathrm{12}\pi}{\mathrm{19}}\right) \\ $$

Question Number 193492 Answers: 1 Comments: 0

Question Number 193494 Answers: 3 Comments: 1

Let n be a fixed positive integer such that sin((π/(2n)))+cos((𝛑/(2n)))=((√n)/2) Then find n

$$\boldsymbol{\mathrm{Let}}\:\boldsymbol{\mathrm{n}}\:\boldsymbol{\mathrm{be}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{fixed}}\:\boldsymbol{\mathrm{positive}}\:\boldsymbol{\mathrm{integer}}\:\boldsymbol{\mathrm{such}}\:\boldsymbol{\mathrm{that}} \\ $$$$\mathrm{sin}\left(\frac{\pi}{\mathrm{2n}}\right)+\mathrm{cos}\left(\frac{\boldsymbol{\pi}}{\mathrm{2n}}\right)=\frac{\sqrt{\mathrm{n}}}{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{Then}}\:\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{n}} \\ $$

Question Number 193490 Answers: 0 Comments: 0

Question Number 193486 Answers: 1 Comments: 0

Question Number 193485 Answers: 2 Comments: 0

Show that 2^n −(−1)^n is divisible by 3 for all positive integers n.

$$\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\boldsymbol{\mathrm{Show}}\:\boldsymbol{\mathrm{that}}\:\mathrm{2}^{\boldsymbol{\mathrm{n}}} −\left(−\mathrm{1}\right)^{\boldsymbol{\mathrm{n}}} \:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{divisible}}\:\boldsymbol{\mathrm{by}} \\ $$$$\:\:\:\:\:\:\:\mathrm{3}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{all}}\:\boldsymbol{\mathrm{positive}}\:\boldsymbol{\mathrm{integers}}\:\boldsymbol{\mathrm{n}}. \\ $$

Question Number 193484 Answers: 0 Comments: 0

Nice problem: Find 8 distinctive numbers ∈N\{0} such that these are simultaniously true: (1) a+b+c+d = e+f+g+h (2) a^2 +b^2 +c^2 +d^2 = e^2 +f^2 +g^2 +h^2 (3) a^3 +b^3 +c^3 +d^3 = e^3 +f^3 +g^3 +h^3 [Find a method to generate such numbers]

$$\mathrm{Nice}\:\mathrm{problem}: \\ $$$$\mathrm{Find}\:\mathrm{8}\:\mathrm{distinctive}\:\mathrm{numbers}\:\in\mathbb{N}\backslash\left\{\mathrm{0}\right\}\:\mathrm{such} \\ $$$$\mathrm{that}\:\mathrm{these}\:\mathrm{are}\:\mathrm{simultaniously}\:\mathrm{true}: \\ $$$$\left(\mathrm{1}\right)\:\:\:\:\:\:\:\:\:\:\:\:{a}+{b}+{c}+{d}\:=\:{e}+{f}+{g}+{h} \\ $$$$\left(\mathrm{2}\right)\:\:\:\:\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} +{d}^{\mathrm{2}} \:=\:{e}^{\mathrm{2}} +{f}^{\mathrm{2}} +{g}^{\mathrm{2}} +{h}^{\mathrm{2}} \\ $$$$\left(\mathrm{3}\right)\:\:\:\:\:{a}^{\mathrm{3}} +{b}^{\mathrm{3}} +{c}^{\mathrm{3}} +{d}^{\mathrm{3}} \:=\:{e}^{\mathrm{3}} +{f}^{\mathrm{3}} +{g}^{\mathrm{3}} +{h}^{\mathrm{3}} \\ $$$$\left[\mathrm{Find}\:\mathrm{a}\:\mathrm{method}\:\mathrm{to}\:\mathrm{generate}\:\mathrm{such}\:\mathrm{numbers}\right] \\ $$

Question Number 193469 Answers: 0 Comments: 0

Question Number 193467 Answers: 3 Comments: 3

Proof : cot^(−1) ((((√(1+sint))+(√(1−sint)))/( (√(1+sint))−(√(1−sint)))))=(t/2)

$$\mathrm{Proof}\:: \\ $$$$\mathrm{cot}^{−\mathrm{1}} \left(\frac{\sqrt{\mathrm{1}+\mathrm{sint}}+\sqrt{\mathrm{1}−\mathrm{sint}}}{\:\sqrt{\mathrm{1}+\mathrm{sint}}−\sqrt{\mathrm{1}−\mathrm{sint}}}\right)=\frac{\mathrm{t}}{\mathrm{2}}\: \\ $$

Question Number 193464 Answers: 1 Comments: 3

Question Number 193461 Answers: 2 Comments: 0

lim_(x→0) ((((√(1+sin x))−1)/(sin 2x))) = ??

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\sqrt{\mathrm{1}+\mathrm{sin}\:\mathrm{x}}−\mathrm{1}}{\mathrm{sin}\:\mathrm{2x}}\right)\:=\:?? \\ $$

Question Number 193458 Answers: 1 Comments: 1

lim_(x→0) (((1−cos(x))/(x sin(x)))) = ???

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\mathrm{1}−\mathrm{cos}\left(\mathrm{x}\right)}{\mathrm{x}\:\mathrm{sin}\left(\mathrm{x}\right)}\right)\:=\:\:\:??? \\ $$

Question Number 193449 Answers: 1 Comments: 4

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