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AllQuestion and Answers: Page 1318

Question Number 80733 Answers: 0 Comments: 3

x^2 =2^x ⇒x=?

$$\mathrm{x}^{\mathrm{2}} =\mathrm{2}^{\mathrm{x}} \Rightarrow\mathrm{x}=? \\ $$

Question Number 80731 Answers: 1 Comments: 1

Question Number 80718 Answers: 0 Comments: 2

Evaluate: lim_(x→0) (x/(∣x∣))

$$\mathrm{Evaluate}:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{\mathrm{x}}{\mid\mathrm{x}\mid} \\ $$

Question Number 80708 Answers: 1 Comments: 3

find sum of the series Σ_(n=0) ^∞ (((−1)^n )/((2n+1)(2n+3)))

$${find}\:{sum}\:{of}\:{the}\:{series} \\ $$$$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{3}\right)} \\ $$

Question Number 80706 Answers: 1 Comments: 0

Question Number 80702 Answers: 1 Comments: 4

{ (((1/x)+(1/y)=34)),(((1/(√x))+(1/(√y))=23−(1/(√(xy))) )) :} find the solution.

$$\begin{cases}{\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{y}}=\mathrm{34}}\\{\frac{\mathrm{1}}{\sqrt{{x}}}+\frac{\mathrm{1}}{\sqrt{{y}}}=\mathrm{23}−\frac{\mathrm{1}}{\sqrt{{xy}}}\:}\end{cases} \\ $$$${find}\:{the}\:{solution}. \\ $$

Question Number 80690 Answers: 0 Comments: 2

Question Number 80689 Answers: 0 Comments: 1

Question Number 80688 Answers: 0 Comments: 1

Question Number 80687 Answers: 0 Comments: 2

Question Number 80682 Answers: 0 Comments: 3

Question Number 80675 Answers: 2 Comments: 1

Question Number 80670 Answers: 1 Comments: 2

lim_(x→π) ((e^(sin x) −1)/(x−π))=?

$$\underset{{x}\rightarrow\pi} {\mathrm{lim}}\:\frac{{e}^{\mathrm{sin}\:{x}} −\mathrm{1}}{{x}−\pi}=? \\ $$

Question Number 80653 Answers: 0 Comments: 5

lim_(x→0) (((sin x)/x))^(3/x^2 )

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{sin}\:{x}}{{x}}\right)^{\frac{\mathrm{3}}{{x}^{\mathrm{2}} }} \\ $$

Question Number 80650 Answers: 2 Comments: 2

lim_(x→a) (((∣x∣−a)^3 −(∣a∣−a)^3 )/(x−a)) = P , a <0 lim_(x→a) (((∣x∣−a)^2 −(∣a∣−a)^2 )/(x^2 −ax))=?

$$\underset{{x}\rightarrow{a}} {\mathrm{lim}}\frac{\left(\mid{x}\mid−{a}\right)^{\mathrm{3}} −\left(\mid{a}\mid−{a}\right)^{\mathrm{3}} }{{x}−{a}}\:=\:{P}\:,\:{a}\:<\mathrm{0} \\ $$$$\underset{{x}\rightarrow{a}} {\mathrm{lim}}\:\frac{\left(\mid{x}\mid−{a}\right)^{\mathrm{2}} −\left(\mid{a}\mid−{a}\right)^{\mathrm{2}} }{{x}^{\mathrm{2}} −{ax}}=? \\ $$

Question Number 80648 Answers: 0 Comments: 9

Question Number 80645 Answers: 0 Comments: 11

if a_1 =2 a_(n+1) =a_n ^2 −1 find a_n =?

$${if} \\ $$$${a}_{\mathrm{1}} =\mathrm{2} \\ $$$${a}_{{n}+\mathrm{1}} ={a}_{{n}} ^{\mathrm{2}} −\mathrm{1} \\ $$$${find}\:{a}_{{n}} =? \\ $$

Question Number 80643 Answers: 2 Comments: 0

Prove that there is no solution for 7^n ≡1 mod(35) with n∈N.

$${Prove}\:{that}\:{there}\:{is}\:{no}\:{solution}\:{for} \\ $$$$\mathrm{7}^{{n}} \equiv\mathrm{1}\:{mod}\left(\mathrm{35}\right)\:{with}\:{n}\in\mathbb{N}. \\ $$

Question Number 80642 Answers: 0 Comments: 0

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Question Number 80639 Answers: 0 Comments: 2

((log_2 ^2 (x−4)−log_2 (4−x)^8 +16)/(30−3x−(4−x)^2 )) ≥ 0

$$\frac{\mathrm{log}_{\mathrm{2}} ^{\mathrm{2}} \:\left({x}−\mathrm{4}\right)−\mathrm{log}_{\mathrm{2}} \left(\mathrm{4}−{x}\right)^{\mathrm{8}} +\mathrm{16}}{\mathrm{30}−\mathrm{3}{x}−\left(\mathrm{4}−{x}\right)^{\mathrm{2}} }\:\geqslant\:\mathrm{0} \\ $$

Question Number 80620 Answers: 0 Comments: 1

Question Number 80614 Answers: 0 Comments: 1

Question Number 80613 Answers: 1 Comments: 2

Q.find (d/dx)(x!)

$${Q}.{find}\:\:\:\frac{{d}}{{dx}}\left({x}!\right) \\ $$

Question Number 80612 Answers: 0 Comments: 3

Ψ(x)=∫_1 ^x (1/(√(1−e^t ))) dt ∀x∈R prove that Ψ(x)=2ln(((1−(√(1−e^x )))/(1−(√(1−e)))))−x+1

$$\:\Psi\left({x}\right)=\int_{\mathrm{1}} ^{{x}} \frac{\mathrm{1}}{\sqrt{\mathrm{1}−{e}^{{t}} }}\:{dt}\:\:\:\:\:\forall{x}\in\mathbb{R} \\ $$$${prove}\:{that} \\ $$$$\Psi\left({x}\right)=\mathrm{2}{ln}\left(\frac{\mathrm{1}−\sqrt{\mathrm{1}−{e}^{{x}} }}{\mathrm{1}−\sqrt{\mathrm{1}−{e}}}\right)−{x}+\mathrm{1} \\ $$

Question Number 80607 Answers: 0 Comments: 0

Question Number 80595 Answers: 1 Comments: 2

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