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Question Number 195414 Answers: 1 Comments: 0

x^n +(1/x^n )=¿

$${x}^{{n}} +\frac{\mathrm{1}}{{x}^{{n}} }=¿ \\ $$

Question Number 195413 Answers: 0 Comments: 5

Question Number 195412 Answers: 2 Comments: 0

Question Number 195411 Answers: 1 Comments: 0

Question Number 195407 Answers: 2 Comments: 0

f′(2)=g′(2)=g(2)=2 then find the (fog)′(2)=?

$$\mathrm{f}'\left(\mathrm{2}\right)=\mathrm{g}'\left(\mathrm{2}\right)=\mathrm{g}\left(\mathrm{2}\right)=\mathrm{2} \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\left(\mathrm{fog}\right)'\left(\mathrm{2}\right)=? \\ $$

Question Number 195404 Answers: 1 Comments: 0

Question Number 195401 Answers: 1 Comments: 0

calcu_⇓_⇓ late lim_( x→(π/2)) ( sin(x ))^( tan^( 2) (x )) = ? determinant ((),())

$$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{calc}\underset{\underset{\Downarrow} {\Downarrow}} {\mathrm{u}late} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{lim}_{\:\mathrm{x}\rightarrow\frac{\pi}{\mathrm{2}}} \:\left(\:\:\mathrm{sin}\left(\mathrm{x}\:\right)\right)^{\:\mathrm{tan}^{\:\mathrm{2}} \left(\mathrm{x}\:\right)} \:\:\:\:=\:?\:\:\:\:\:\:\:\:\begin{array}{|c|c|}\\\\\hline\end{array} \\ $$$$ \\ $$$$ \\ $$

Question Number 195385 Answers: 1 Comments: 0

lim_(x⇒a^+ ) (((√x) −(√a) −(√(x−a)))/( (√(x^2 −a^2 )))) ; a > 0

$$ \\ $$$$ \\ $$$$\mathrm{lim}_{{x}\Rightarrow\mathrm{a}^{+} } \:\:\:\:\frac{\sqrt{{x}}\:−\sqrt{\mathrm{a}}\:−\sqrt{{x}−\mathrm{a}}}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{a}^{\mathrm{2}} }}\:\:;\:\:\mathrm{a}\:>\:\mathrm{0} \\ $$

Question Number 195377 Answers: 0 Comments: 0

Question Number 195390 Answers: 1 Comments: 0

which prime number between the 20 and 1000

$${which}\:{prime}\:{number}\:{between} \\ $$$${the}\:\:\mathrm{20}\:\:{and}\:\:\:\:\mathrm{1000}\:\:\: \\ $$

Question Number 195391 Answers: 2 Comments: 0

f^2 (x)+2f(x)=x^2 −8x+15 f(x)=?

$${f}^{\mathrm{2}} \left({x}\right)+\mathrm{2}{f}\left({x}\right)={x}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{15} \\ $$$${f}\left({x}\right)=? \\ $$

Question Number 195370 Answers: 0 Comments: 0

Question Number 195369 Answers: 1 Comments: 0

Question Number 195368 Answers: 0 Comments: 0

Question Number 195365 Answers: 2 Comments: 0

_(x→y) ^(lim) ((tan x−tany)/(x−y))

$$\:\: \\ $$$$\:\underset{\mathrm{x}\rightarrow\mathrm{y}} {\overset{\mathrm{lim}} {\:}}\:\frac{\mathrm{tan}\:\mathrm{x}−\mathrm{tany}}{\mathrm{x}−\mathrm{y}} \\ $$$$ \\ $$

Question Number 195364 Answers: 1 Comments: 0

show that for any natural number n, the natural number (3−(√5))^n +(3+(√5))^n is divisible by 2^n .

$$ \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{for}\:\mathrm{any}\:\mathrm{natural}\:\mathrm{number}\:{n},\: \\ $$$$\mathrm{the}\:\mathrm{natural}\:\mathrm{number}\:\left(\mathrm{3}−\sqrt{\mathrm{5}}\right)^{{n}} +\left(\mathrm{3}+\sqrt{\mathrm{5}}\right)^{{n}} \:\mathrm{is}\:\mathrm{divisible} \\ $$$$\mathrm{by}\:\mathrm{2}^{{n}} . \\ $$

Question Number 195361 Answers: 0 Comments: 0

Question Number 195357 Answers: 2 Comments: 0

Question Number 195356 Answers: 2 Comments: 0

remark to question 195301 and similar ones x^2 +y=a x+y^2 =b a, b >0 how many solutions depending on a, b?

$$\mathrm{remark}\:\mathrm{to}\:\mathrm{question}\:\mathrm{195301}\:\mathrm{and}\:\mathrm{similar}\:\mathrm{ones} \\ $$$${x}^{\mathrm{2}} +{y}={a} \\ $$$${x}+{y}^{\mathrm{2}} ={b} \\ $$$${a},\:{b}\:>\mathrm{0} \\ $$$$\mathrm{how}\:\mathrm{many}\:\mathrm{solutions}\:\mathrm{depending}\:\mathrm{on}\:{a},\:{b}? \\ $$

Question Number 195352 Answers: 0 Comments: 0

Question Number 195349 Answers: 0 Comments: 0

Question Number 195344 Answers: 2 Comments: 0

Question Number 195393 Answers: 1 Comments: 0

prove that lim_(x→0) (((Σ_(k=1) ^n (1−(1/(2k)))^x )/n))^(1/( x )) = (1/4)(C_(2n) ^n )^(1/n)

$$\mathrm{prove}\:\mathrm{that}\: \\ $$$$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\sqrt[{\:\:\boldsymbol{{x}}\:\:}]{\frac{\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}{k}}\right)^{{x}} }{{n}}}\:=\:\frac{\mathrm{1}}{\mathrm{4}}\sqrt[{\boldsymbol{{n}}}]{\mathrm{C}_{\mathrm{2}\boldsymbol{\mathrm{n}}} ^{\boldsymbol{\mathrm{n}}} } \\ $$

Question Number 195395 Answers: 1 Comments: 0

Question Number 197578 Answers: 1 Comments: 1

Question Number 200284 Answers: 1 Comments: 0

Prove that for any set A containing n elements, ∣P(A)∣=2^n .

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{for}\:\mathrm{any}\:\mathrm{set}\:{A}\:\mathrm{containing}\:{n} \\ $$$$\mathrm{elements},\:\mid\mathcal{P}\left({A}\right)\mid=\mathrm{2}^{{n}} . \\ $$

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