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Question Number 199520 Answers: 1 Comments: 0

n^4 +an^3 +bn^2 +cn+d=k^2 (k∈N) a,b,c,d=¿

$${n}^{\mathrm{4}} +{an}^{\mathrm{3}} +{bn}^{\mathrm{2}} +{cn}+{d}={k}^{\mathrm{2}} \:\left({k}\in{N}\right) \\ $$$${a},{b},{c},{d}=¿ \\ $$

Question Number 199511 Answers: 1 Comments: 1

∫_1 ^(+oo) ln(1+lnx)^(−lnx) dx

$$\int_{\mathrm{1}} ^{+{oo}} {ln}\left(\mathrm{1}+{lnx}\right)^{−{lnx}} \:{dx} \\ $$

Question Number 199510 Answers: 3 Comments: 0

Question Number 199509 Answers: 2 Comments: 2

Question Number 199498 Answers: 2 Comments: 1

Question Number 199486 Answers: 2 Comments: 0

Solve: 100^x = 200

$$\mathrm{Solve}:\:\:\:\mathrm{100}^{\boldsymbol{\mathrm{x}}} \:=\:\mathrm{200} \\ $$

Question Number 199482 Answers: 0 Comments: 3

can someone factor this (3x^3 y−7x^2 +5xy^3 −y^2 )

$$\mathrm{can}\:\mathrm{someone}\:\mathrm{factor}\:\mathrm{this}\:\left(\mathrm{3x}^{\mathrm{3}} \mathrm{y}−\mathrm{7x}^{\mathrm{2}} +\mathrm{5xy}^{\mathrm{3}} −\mathrm{y}^{\mathrm{2}} \right) \\ $$

Question Number 199480 Answers: 0 Comments: 1

Question Number 199471 Answers: 1 Comments: 0

Find the integral ∫_(−3) ^3 { ((x^3 −x),((x≤0))),(x^2 ,((x≥0))) :}dx

$${Find}\:{the}\:{integral} \\ $$$$\int_{−\mathrm{3}} ^{\mathrm{3}} \begin{cases}{{x}^{\mathrm{3}} −{x}}&{\left({x}\leq\mathrm{0}\right)}\\{{x}^{\mathrm{2}} }&{\left({x}\geq\mathrm{0}\right)}\end{cases}{dx} \\ $$

Question Number 199468 Answers: 1 Comments: 0

Question Number 199467 Answers: 1 Comments: 0

Question Number 199466 Answers: 1 Comments: 0

Question Number 199459 Answers: 2 Comments: 0

What minimum value f(x,y)=x^2 +y^2 −z^2 when x+2y+4z=21

$$\:\:\mathrm{What}\:\mathrm{minimum}\:\mathrm{value}\: \\ $$$$\:\:\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)=\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} −\mathrm{z}^{\mathrm{2}} \:\mathrm{when}\: \\ $$$$\:\:\mathrm{x}+\mathrm{2y}+\mathrm{4z}=\mathrm{21} \\ $$

Question Number 199458 Answers: 1 Comments: 0

Solve: log_3 p + log_r 8 =5 r+p=11. find r&p

$$\boldsymbol{{Solve}}:\:\boldsymbol{{log}}_{\mathrm{3}} \boldsymbol{{p}}\:+\:\boldsymbol{{log}}_{\boldsymbol{{r}}} \mathrm{8}\:=\mathrm{5} \\ $$$$\boldsymbol{{r}}+\boldsymbol{{p}}=\mathrm{11}.\:\:\boldsymbol{{find}}\:\boldsymbol{{r\&p}} \\ $$

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

$$\:\:\:\boldsymbol{{x}} \\ $$

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

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