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Question Number 182648 Answers: 3 Comments: 0

∫_0 ^(π/4) ((sec^2 x)/(tan x−sec x)) dx =?

$$\:\:\underset{\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\:\frac{\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}}{\mathrm{tan}\:\mathrm{x}−\mathrm{sec}\:\mathrm{x}}\:\mathrm{dx}\:=? \\ $$

Question Number 182646 Answers: 0 Comments: 2

prove that lim_(n→∞) [((((n+1)!∙(2n+1)!!))^(1/(n+1)) /(n+1))−(((n!∙(2n−1)!!))^(1/n) /n)]=(2/e^2 )

$${prove}\:{that} \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left[\frac{\sqrt[{{n}+\mathrm{1}}]{\left({n}+\mathrm{1}\right)!\centerdot\left(\mathrm{2}{n}+\mathrm{1}\right)!!}}{{n}+\mathrm{1}}−\frac{\sqrt[{{n}}]{{n}!\centerdot\left(\mathrm{2}{n}−\mathrm{1}\right)!!}}{{n}}\right]=\frac{\mathrm{2}}{{e}^{\mathrm{2}} } \\ $$

Question Number 182644 Answers: 0 Comments: 5

solve for x>0 (1+(1/x))^x >(5/2)

$${solve}\:{for}\:{x}>\mathrm{0} \\ $$$$\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)^{{x}} >\frac{\mathrm{5}}{\mathrm{2}} \\ $$

Question Number 182640 Answers: 0 Comments: 0

which software is the best for mathematics problems solving by video edit maker?

$${which}\:{software}\:{is}\:{the}\:{best}\:{for} \\ $$$${mathematics}\:{problems}\:{solving}\:{by}\:{video} \\ $$$${edit}\:{maker}? \\ $$

Question Number 182636 Answers: 0 Comments: 2

∫_(−1) ^3 (1/x^2 ) dx=?

$$\underset{−\mathrm{1}} {\overset{\mathrm{3}} {\int}}\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\:{dx}=? \\ $$

Question Number 182632 Answers: 1 Comments: 0

If log _(11) (3p)=log _(13) (q+6p) = log _(143) (q^2 ) find (p/q).

$$\:\:\mathrm{If}\:\mathrm{log}\:_{\mathrm{11}} \left(\mathrm{3p}\right)=\mathrm{log}\:_{\mathrm{13}} \left(\mathrm{q}+\mathrm{6p}\right)\:=\:\mathrm{log}\:_{\mathrm{143}} \left(\mathrm{q}^{\mathrm{2}} \right) \\ $$$$\:\mathrm{find}\:\frac{\mathrm{p}}{\mathrm{q}}. \\ $$

Question Number 182629 Answers: 0 Comments: 0

Π_(n=2) ^∞ e(1−(1/n^2 ))^n^2 = ?

$$\:\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{2}} {\overset{\infty} {\prod}}\:\boldsymbol{\mathrm{e}}\left(\mathrm{1}−\frac{\mathrm{1}}{\boldsymbol{\mathrm{n}}^{\mathrm{2}} }\right)^{\boldsymbol{\mathrm{n}}^{\mathrm{2}} } \:=\:\:? \\ $$

Question Number 182627 Answers: 1 Comments: 0

(((1+(√5))/2))^(15) =((a+b(√5))/2) find a+b

$$\left(\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}\right)^{\mathrm{15}} =\frac{{a}+{b}\sqrt{\mathrm{5}}}{\mathrm{2}} \\ $$$${find}\:{a}+{b} \\ $$

Question Number 182623 Answers: 2 Comments: 1

Question Number 182620 Answers: 1 Comments: 0

Question Number 182613 Answers: 2 Comments: 0

Question Number 182608 Answers: 2 Comments: 1

Question Number 182600 Answers: 3 Comments: 0

Question Number 182595 Answers: 0 Comments: 1

Question Number 182593 Answers: 1 Comments: 1

Question Number 182586 Answers: 0 Comments: 0

Question Number 182584 Answers: 1 Comments: 0

Transform into factorial form the following A = 1×3×5×7×9×...×(2n−1) . Example: 4×3×2×1=4!

$$\:\:{Transform}\:{into}\:{factorial}\:{form}\:{the}\:{following} \\ $$$$\:\:{A}\:=\:\mathrm{1}×\mathrm{3}×\mathrm{5}×\mathrm{7}×\mathrm{9}×...×\left(\mathrm{2}{n}−\mathrm{1}\right)\:.\: \\ $$$${Example}:\:\mathrm{4}×\mathrm{3}×\mathrm{2}×\mathrm{1}=\mathrm{4}! \\ $$

Question Number 182582 Answers: 2 Comments: 0

Question Number 182581 Answers: 1 Comments: 0

f(x)=((x^2 +4x−3)/(x^2 −3)) f^(−1) (x)=?

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

Question Number 182576 Answers: 0 Comments: 0

Question Number 182575 Answers: 1 Comments: 0

((x+1))^(1/x) >(e)^(1/e) 1) Solve for x(x∈N^+ ). 2) Solve for x(x>0).

$$\sqrt[{{x}}]{{x}+\mathrm{1}}>\sqrt[{{e}}]{{e}} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{Solve}\:\mathrm{for}\:{x}\left({x}\in\mathbb{N}^{+} \right). \\ $$$$\left.\mathrm{2}\right)\:\mathrm{Solve}\:\mathrm{for}\:{x}\left({x}>\mathrm{0}\right). \\ $$

Question Number 182571 Answers: 1 Comments: 0

Question Number 182566 Answers: 0 Comments: 0

Solve (x^2 +( xy^2 )^(1/3) )(dy/dx) = y^2

$$\mathrm{Solve} \\ $$$$\left(\mathrm{x}^{\mathrm{2}} \:+\left(\:\mathrm{xy}^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{3}}} \right)\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{y}^{\mathrm{2}} \\ $$

Question Number 182560 Answers: 1 Comments: 0

lim_(x→0) (1/x^2 ) − cot^2 x = ?

$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\:−\:\mathrm{cot}^{\mathrm{2}} {x}\:=\:\:? \\ $$

Question Number 182552 Answers: 0 Comments: 0

Find the period of the following: a• sin 4x sin 3x b• sin πx+ cos x c• ((2 sin^2 3x− 3 tan 4x+ 4 cot 6x)/(∣cosec 8x∣− sec^3 10x+ (√(cot 12x))))

$${Find}\:{the}\:{period}\:{of}\:{the}\:{following}: \\ $$$$\:{a}\bullet\:\mathrm{sin}\:\mathrm{4}{x}\:\mathrm{sin}\:\mathrm{3}{x} \\ $$$$\:{b}\bullet\:\mathrm{sin}\:\pi{x}+\:\mathrm{cos}\:{x} \\ $$$$\:{c}\bullet\:\frac{\mathrm{2}\:\mathrm{sin}^{\mathrm{2}} \:\mathrm{3}{x}−\:\mathrm{3}\:\mathrm{tan}\:\mathrm{4}{x}+\:\mathrm{4}\:\mathrm{cot}\:\mathrm{6}{x}}{\mid\mathrm{cosec}\:\mathrm{8}{x}\mid−\:\mathrm{sec}^{\mathrm{3}} \:\mathrm{10}{x}+\:\sqrt{\mathrm{cot}\:\mathrm{12}{x}}} \\ $$

Question Number 182546 Answers: 2 Comments: 1

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