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Question Number 199451 Answers: 3 Comments: 0

Find: 1. lim_(n→∞) (((5n − 25)/(3n + 15)))^(1/(5n)) 2. lim_(x→∞) (((x^3 + 3x^2 + 1))^(1/3) − ((x^3 − 3x^2 + 1))^(1/3) ) 3. lim_(x→0) ((cos 4x^3 − 1)/(sin^6 2x))

$$\mathrm{Find}: \\ $$$$\mathrm{1}.\:\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\sqrt[{\mathrm{5}\boldsymbol{\mathrm{n}}}]{\frac{\mathrm{5n}\:−\:\mathrm{25}}{\mathrm{3n}\:+\:\mathrm{15}}} \\ $$$$\mathrm{2}.\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\infty} {\mathrm{lim}}\:\left(\sqrt[{\mathrm{3}}]{\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{3x}^{\mathrm{2}} \:+\:\mathrm{1}}\:−\:\sqrt[{\mathrm{3}}]{\mathrm{x}^{\mathrm{3}} \:−\:\mathrm{3x}^{\mathrm{2}} \:+\:\mathrm{1}}\:\right) \\ $$$$\mathrm{3}.\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\mathrm{4x}^{\mathrm{3}} \:−\:\mathrm{1}}{\mathrm{sin}^{\mathrm{6}} \:\mathrm{2x}} \\ $$

Question Number 199481 Answers: 1 Comments: 0

Give △ABC is acute triangle. M is a midpoint of BC Prove that AB+AC>2AM

$${Give}\:\bigtriangleup{ABC}\:{is}\:{acute}\:{triangle}. \\ $$$${M}\:\:{is}\:{a}\:{midpoint}\:{of}\:{BC} \\ $$$${Prove}\:{that}\:{AB}+{AC}>\mathrm{2}{AM} \\ $$

Question Number 199447 Answers: 1 Comments: 0

b_n =sin(a_1 +(n−1)d)⇒ S_n =?

$${b}_{{n}} ={sin}\left({a}_{\mathrm{1}} +\left({n}−\mathrm{1}\right){d}\right)\Rightarrow\:{S}_{{n}} =? \\ $$

Question Number 199446 Answers: 0 Comments: 0

53bxnx

$$\mathrm{53bxnx} \\ $$

Question Number 199433 Answers: 1 Comments: 1

Question Number 199432 Answers: 2 Comments: 0

without using calculator: what is larger? log_2 3 or log_3 5?

$${without}\:{using}\:{calculator}: \\ $$$${what}\:{is}\:{larger}?\:\mathrm{log}_{\mathrm{2}} \:\mathrm{3}\:{or}\:\mathrm{log}_{\mathrm{3}} \:\mathrm{5}? \\ $$

Question Number 199424 Answers: 1 Comments: 0

f(x)=(1/2)sin 2x−(1/4)sin 4x+(1/3)cos 3x for 0<x<π

$$\:\: \\ $$$$ \\ $$$$ \mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin}\:\mathrm{2x}−\frac{\mathrm{1}}{\mathrm{4}}\mathrm{sin}\:\mathrm{4x}+\frac{\mathrm{1}}{\mathrm{3}}\mathrm{cos}\:\mathrm{3x} \\ $$$$\:\:\mathrm{for}\:\mathrm{0}<\mathrm{x}<\pi\: \\ $$

Question Number 199413 Answers: 2 Comments: 0

Question Number 199405 Answers: 2 Comments: 0

calculate ... Q: If , f(x) =2 e^x −1 + ⌊e^x + (3/2) +⌊e^x ⌋ ⌋ ⇒ f^(−1) ( (π/4) ) =?

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{calculate}\:... \\ $$$$\:\:\mathrm{Q}:\:\:\:\:\:\:\mathrm{I}{f}\:\:,\:\:\:{f}\left({x}\right)\:=\mathrm{2}\:{e}^{{x}} \:−\mathrm{1}\:+\:\lfloor{e}^{{x}} +\:\frac{\mathrm{3}}{\mathrm{2}}\:+\lfloor{e}^{{x}} \rfloor\:\rfloor \\ $$$$\:\:\:\:\:\:\:\:\:\Rightarrow\:\:\:\:{f}\:^{−\mathrm{1}} \:\left(\:\frac{\pi}{\mathrm{4}}\:\right)\:=? \\ $$$$\:\:\:\:\: \\ $$

Question Number 199399 Answers: 1 Comments: 0

Solve: log_2 r+log_3 p=3 p+r=11 fund p and r.

$$\boldsymbol{{Solve}}:\:\boldsymbol{{log}}_{\mathrm{2}} \boldsymbol{{r}}+\boldsymbol{{log}}_{\mathrm{3}} \boldsymbol{{p}}=\mathrm{3} \\ $$$$\boldsymbol{{p}}+\boldsymbol{{r}}=\mathrm{11}\:\:\:\boldsymbol{{fund}}\:\boldsymbol{{p}}\:\boldsymbol{{and}}\:\boldsymbol{{r}}. \\ $$

Question Number 199393 Answers: 2 Comments: 0

Question Number 199392 Answers: 1 Comments: 0

Question Number 199391 Answers: 1 Comments: 0

Question Number 199389 Answers: 2 Comments: 0

log_(12) 60=? log_6 30=a log_(15) 24=b

$$\mathrm{log}_{\mathrm{12}} \mathrm{60}=? \\ $$$$\mathrm{log}_{\mathrm{6}} \mathrm{30}={a} \\ $$$$\mathrm{log}_{\mathrm{15}} \mathrm{24}={b} \\ $$

Question Number 199385 Answers: 2 Comments: 0

Find: Ω = ∫_0 ^( 1) x^(15) (√(1 + 3x^8 )) dx = ?

$$\mathrm{Find}: \\ $$$$\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\mathrm{x}^{\mathrm{15}} \:\sqrt{\mathrm{1}\:+\:\mathrm{3x}^{\mathrm{8}} }\:\mathrm{dx}\:=\:? \\ $$

Question Number 199382 Answers: 2 Comments: 0

if A = [((cosh(x) sinh(x) )),((sinh(x) cosh(x))) ]find A^k ?

$${if}\:{A}\:=\:\begin{bmatrix}{{cosh}\left({x}\right)\:\:\:\:\:\:{sinh}\left({x}\right)\:}\\{{sinh}\left({x}\right)\:\:\:\:\:\:{cosh}\left({x}\right)}\end{bmatrix}{find}\:{A}^{{k}} \:? \\ $$

Question Number 199381 Answers: 1 Comments: 0

Question Number 199380 Answers: 0 Comments: 0

Question Number 199377 Answers: 1 Comments: 0

∫∫_R cos (max{x^3 , y^(3/2) })dx dy , where R = [0,1]×[0,1]

$$\:\:\int\underset{\mathrm{R}} {\int}\mathrm{cos}\:\left(\mathrm{max}\left\{\mathrm{x}^{\mathrm{3}} ,\:\mathrm{y}^{\mathrm{3}/\mathrm{2}} \right\}\right)\mathrm{dx}\:\mathrm{dy}\:,\:\mathrm{where}\:\mathrm{R}\:=\:\left[\mathrm{0},\mathrm{1}\right]×\left[\mathrm{0},\mathrm{1}\right] \\ $$

Question Number 199374 Answers: 3 Comments: 3

Question Number 199371 Answers: 0 Comments: 1

Question Number 199370 Answers: 0 Comments: 0

lim_(x→0) ((4e^(3x) −9e^(2x) +6x+5)/x^3 )=?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{4}{e}^{\mathrm{3}{x}} −\mathrm{9}{e}^{\mathrm{2}{x}} +\mathrm{6}{x}+\mathrm{5}}{{x}^{\mathrm{3}} }=? \\ $$

Question Number 199369 Answers: 0 Comments: 0

∫_(−1) ^1 ∫_(−(√(1−x^2 ))) ^(√(1−x^2 )) ∫_(1−(√(1−x^2 −y^2 ))) ^(1+(√(1−y^2 ))) (x^2 +y^2 +z^2 )^(5/2) dx dy dz is

$$\int_{−\mathrm{1}} ^{\mathrm{1}} \:\int_{−\sqrt{\mathrm{1}−{x}^{\mathrm{2}} \:}} ^{\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }} \:\int_{\mathrm{1}−\sqrt{\mathrm{1}−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} }} ^{\mathrm{1}+\sqrt{\mathrm{1}−{y}^{\mathrm{2}} }} \left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \right)^{\mathrm{5}/\mathrm{2}} {dx}\:{dy}\:{dz}\:\:{is} \\ $$

Question Number 199368 Answers: 2 Comments: 0

Question Number 199349 Answers: 0 Comments: 0

Question Number 199339 Answers: 1 Comments: 2

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