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Question Number 169319 Answers: 1 Comments: 2

if f(2x−1)=x^2 −3x+2, find f(2)

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

Question Number 169317 Answers: 2 Comments: 3

Question Number 169315 Answers: 1 Comments: 1

lim_(x→∞) (((1+(√(x+2)))/(1−(√(x+2))))) Mastermind

$${lim}_{{x}\rightarrow\infty} \left(\frac{\mathrm{1}+\sqrt{{x}+\mathrm{2}}}{\mathrm{1}−\sqrt{{x}+\mathrm{2}}}\right) \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 169308 Answers: 0 Comments: 0

Question Number 169305 Answers: 4 Comments: 2

Differentiate the following wrt x 1) y=x^x 2) y=sin^(−1) (2x+1) Mastermind

$${Differentiate}\:{the}\:{following}\:{wrt}\:{x} \\ $$$$\left.\mathrm{1}\right)\:{y}={x}^{{x}} \\ $$$$\left.\mathrm{2}\right)\:{y}={sin}^{−\mathrm{1}} \left(\mathrm{2}{x}+\mathrm{1}\right) \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 169304 Answers: 1 Comments: 4

3^x =4 4^y =12 ^(faind value of (((x+1)/(2xy)))=?)

$$\mathrm{3}^{{x}} =\mathrm{4} \\ $$$$\mathrm{4}^{{y}} =\mathrm{12}\:\:\:\:\:\overset{{faind}\:{value}\:{of}\:\left(\frac{{x}+\mathrm{1}}{\mathrm{2}{xy}}\right)=?} {\:} \\ $$

Question Number 169303 Answers: 1 Comments: 1

Given that: x cos y=sin(x+y), find (dy/dx) Mastermind

$${Given}\:{that}: \\ $$$${x}\:{cos}\:{y}={sin}\left({x}+{y}\right),\:{find}\:\frac{{dy}}{{dx}} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 169295 Answers: 0 Comments: 0

Prove without using Mathematical Induction that: cos^n x=(1/2^(n−1) )Σ_(k=0) ^((n−1)/2) C_k ^n cos (n−2k)x where x is any real number and n is any positive odd integer.

$$\mathrm{Prove}\:\mathrm{without}\:\mathrm{using}\:\mathrm{Mathematical}\: \\ $$$$\mathrm{Induction}\:\mathrm{that}: \\ $$$$\mathrm{cos}^{{n}} {x}=\frac{\mathrm{1}}{\mathrm{2}^{{n}−\mathrm{1}} }\underset{{k}=\mathrm{0}} {\overset{\left({n}−\mathrm{1}\right)/\mathrm{2}} {\sum}}{C}_{{k}} ^{{n}} \mathrm{cos}\:\left({n}−\mathrm{2}{k}\right){x}\: \\ $$$$\mathrm{where}\:\:{x}\:\mathrm{is}\:\mathrm{any}\:\mathrm{real}\:\mathrm{number}\:\mathrm{and}\:{n}\:\mathrm{is}\:\mathrm{any} \\ $$$$\mathrm{positive}\:\mathrm{odd}\:\mathrm{integer}. \\ $$

Question Number 169294 Answers: 1 Comments: 2

Question Number 169291 Answers: 0 Comments: 6

lim_(x→1) ((x^x^.^.^x −x!)/(x!^(x!) −1)) = ??

$$ \\ $$$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{{x}^{{x}^{.^{.^{{x}} } } } −{x}!}{{x}!^{{x}!} −\mathrm{1}}\:=\:?? \\ $$$$ \\ $$

Question Number 169287 Answers: 0 Comments: 2

solve : x^3 (d^3 y/dx^3 ) + 2x^2 (d^2 y/dx^2 ) +2y = 10(x+(1/x))

$$\:\:{solve}\::\:{x}^{\mathrm{3}} \:\frac{{d}^{\mathrm{3}} {y}}{{dx}^{\mathrm{3}} }\:+\:\mathrm{2}{x}^{\mathrm{2}} \:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\mathrm{2}{y}\:=\:\mathrm{10}\left({x}+\frac{\mathrm{1}}{{x}}\right) \\ $$

Question Number 169281 Answers: 0 Comments: 2

Question Number 169280 Answers: 1 Comments: 0

a^2 +b^2 −25a^2 b^2 =0 b^2 +c^2 −36b^2 c^2 =0 a^2 +c^2 −49a^2 c^2 =0 a^2 +b^2 +c^2 =?

$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} −\mathrm{25}{a}^{\mathrm{2}} {b}^{\mathrm{2}} =\mathrm{0} \\ $$$${b}^{\mathrm{2}} +{c}^{\mathrm{2}} −\mathrm{36}{b}^{\mathrm{2}} {c}^{\mathrm{2}} =\mathrm{0} \\ $$$${a}^{\mathrm{2}} +{c}^{\mathrm{2}} −\mathrm{49}{a}^{\mathrm{2}} {c}^{\mathrm{2}} =\mathrm{0} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} =? \\ $$

Question Number 169273 Answers: 2 Comments: 0

lim_(x→∞) ((∫_1 ^( x) ((√(4x^2 +6x−2))−2x)dx)/(5x)) =?

$$\:\:\:\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\int_{\mathrm{1}} ^{\:{x}} \left(\sqrt{\mathrm{4}{x}^{\mathrm{2}} +\mathrm{6}{x}−\mathrm{2}}−\mathrm{2}{x}\right){dx}}{\mathrm{5}{x}}\:=? \\ $$

Question Number 169272 Answers: 0 Comments: 3

Question Number 169271 Answers: 1 Comments: 0

Question Number 169268 Answers: 1 Comments: 0

𝛀=∫((cos^2 (ln(tan(x/2))))/(tan((x/2))))dx=?

$$\boldsymbol{\Omega}=\int\frac{\boldsymbol{\mathrm{cos}}^{\mathrm{2}} \left(\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{tan}}\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}\right)\right)}{\boldsymbol{\mathrm{tan}}\left(\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}\right)}\boldsymbol{\mathrm{dx}}=? \\ $$

Question Number 169260 Answers: 1 Comments: 0

Question Number 169259 Answers: 0 Comments: 1

Question Number 169251 Answers: 1 Comments: 0

calculate C=∫(dt/(1+tan^2 (t))) using x=tan(t)

$${calculate}\:{C}=\int\frac{{dt}}{\mathrm{1}+{tan}^{\mathrm{2}} \left({t}\right)}\:{using}\:{x}={tan}\left({t}\right) \\ $$

Question Number 169250 Answers: 1 Comments: 1

Calculate B=∫(1/(1+sin(x)))dx using u=tan((x/2))

$${Calculate}\:{B}=\int\frac{\mathrm{1}}{\mathrm{1}+{sin}\left({x}\right)}{dx}\:{using}\:{u}={tan}\left(\frac{{x}}{\mathrm{2}}\right) \\ $$

Question Number 169249 Answers: 0 Comments: 1

calculate A=∫(dt/(sin(t))) by using u=cos(t)

$${calculate}\:{A}=\int\frac{{dt}}{{sin}\left({t}\right)}\:{by}\:{using} \\ $$$${u}={cos}\left({t}\right) \\ $$

Question Number 169242 Answers: 2 Comments: 0

Question Number 169239 Answers: 1 Comments: 4

Question Number 169230 Answers: 1 Comments: 0

Question Number 169226 Answers: 0 Comments: 0

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