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Question Number 184877 Answers: 1 Comments: 0

Find the sum of the last ten digits: 5^(23) ∙ 2^(2022) − 2023

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{last}\:\mathrm{ten}\:\mathrm{digits}: \\ $$$$\mathrm{5}^{\mathrm{23}} \:\centerdot\:\mathrm{2}^{\mathrm{2022}} \:−\:\mathrm{2023} \\ $$

Question Number 184875 Answers: 1 Comments: 0

Question Number 184873 Answers: 1 Comments: 0

Find the real number satisfying x=(√(1+(√(1+(√(1+x))))))

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{real}\:\mathrm{number}\:\mathrm{satisfying} \\ $$$$\:\mathrm{x}=\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\mathrm{x}}}} \\ $$

Question Number 184872 Answers: 0 Comments: 0

An odd function f(x) whose domain is R satisfies f(x)=f(x+2). When x ∈ (0, 1), f(x)=−2x^2 +ax−2. If f has 2023 zeros in [0, 1011]. Then the range of a can be ? A. [−6, −2(√2)] B. [−4, −2(√2)] C. [−8, −6] D. [−6, −4]

$$\mathrm{An}\:\mathrm{odd}\:\mathrm{function}\:{f}\left({x}\right)\:\mathrm{whose}\:\mathrm{domain}\:\mathrm{is}\:\mathbb{R} \\ $$$$\mathrm{satisfies}\:{f}\left({x}\right)={f}\left({x}+\mathrm{2}\right).\:\mathrm{When}\:{x}\:\in\:\left(\mathrm{0},\:\mathrm{1}\right), \\ $$$${f}\left({x}\right)=−\mathrm{2}{x}^{\mathrm{2}} +{ax}−\mathrm{2}. \\ $$$$\mathrm{If}\:{f}\:\mathrm{has}\:\mathrm{2023}\:\mathrm{zeros}\:\mathrm{in}\:\left[\mathrm{0},\:\mathrm{1011}\right].\:\mathrm{Then}\:\mathrm{the} \\ $$$$\mathrm{range}\:\mathrm{of}\:{a}\:\mathrm{can}\:\mathrm{be}\:? \\ $$$$\mathrm{A}.\:\left[−\mathrm{6},\:−\mathrm{2}\sqrt{\mathrm{2}}\right]\:\:\:\:\:\:\:\:\mathrm{B}.\:\left[−\mathrm{4},\:−\mathrm{2}\sqrt{\mathrm{2}}\right] \\ $$$$\mathrm{C}.\:\left[−\mathrm{8},\:−\mathrm{6}\right]\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{D}.\:\left[−\mathrm{6},\:−\mathrm{4}\right] \\ $$

Question Number 184869 Answers: 1 Comments: 0

Question Number 184866 Answers: 1 Comments: 1

Question Number 184861 Answers: 0 Comments: 0

x ∈ [−0,5 ; 0,5] find the product of all x′s 3(cos^2 πx + sinπy) + 2 = 9 + 3 ∣sinπx ∙ sinπy∣−sinπy

$$\mathrm{x}\:\in\:\left[−\mathrm{0},\mathrm{5}\:\:;\:\:\mathrm{0},\mathrm{5}\right] \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{product}\:\mathrm{of}\:\mathrm{all}\:\:\boldsymbol{\mathrm{x}}'\mathrm{s} \\ $$$$\mathrm{3}\left(\mathrm{cos}^{\mathrm{2}} \pi\mathrm{x}\:+\:\mathrm{sin}\pi\mathrm{y}\right)\:+\:\mathrm{2}\:=\:\mathrm{9}\:+\:\mathrm{3}\:\mid\mathrm{sin}\pi\mathrm{x}\:\centerdot\:\mathrm{sin}\pi\mathrm{y}\mid−\mathrm{sin}\pi\mathrm{y} \\ $$

Question Number 184859 Answers: 2 Comments: 0

Lim_( x→∞) x^( 4) ( 1− cos (1− cos((2/x))))=?

$$ \\ $$$$\:\mathrm{Lim}_{\:{x}\rightarrow\infty} \:{x}^{\:\mathrm{4}} \:\left(\:\mathrm{1}−\:{cos}\:\left(\mathrm{1}−\:{cos}\left(\frac{\mathrm{2}}{{x}}\right)\right)\right)=? \\ $$$$ \\ $$

Question Number 184858 Answers: 1 Comments: 0

Σ_(n=o) ^(+oo) (((−1)^n x^(2n+1) )/(4n^2 −1))

$$\underset{{n}={o}} {\overset{+{oo}} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} {x}^{\mathrm{2}{n}+\mathrm{1}} }{\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}} \\ $$

Question Number 184856 Answers: 0 Comments: 0

f(x)= (√( ∣ x_ ^ ∣ −∣ x−_ ^ ⌊ax⌋ ∣)) ; a ∈ [ 3 , 4 ) find : { (( D_( f) =? (domain ))),(( R_( f) =? (range ))) :}

$$ \\ $$$$\:\:\:\:\:{f}\left({x}\right)=\:\sqrt{\:\mid\:\underset{} {\overset{} {{x}}}\:\:\mid\:−\mid\:\:{x}\underset{} {\overset{} {−}}\lfloor{ax}\rfloor\:\mid} \\ $$$$\:\:\:\:\:\:;\:\:\:{a}\:\in\:\left[\:\mathrm{3}\:,\:\mathrm{4}\:\right) \\ $$$$\:\:\:\:\:{find}\::\:\:\:\begin{cases}{\:\:{D}_{\:{f}} \:=?\:\left({domain}\:\right)}\\{\:\:\mathcal{R}_{\:{f}} \:=?\:\left({range}\:\right)}\end{cases} \\ $$$$ \\ $$

Question Number 184845 Answers: 0 Comments: 0

x ∈ [−0,5 ; 0,5] find the product of all x′s 1. 4sin^2 πx−4sinπx + 2 = 2sin^2 πy−1 2. 4sinπx = 4sinπy − 7 − (1/(sin^2 πx))

$$\mathrm{x}\:\in\:\left[−\mathrm{0},\mathrm{5}\:;\:\mathrm{0},\mathrm{5}\right] \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{product}\:\mathrm{of}\:\mathrm{all}\:\:\boldsymbol{\mathrm{x}}'\mathrm{s} \\ $$$$\mathrm{1}.\:\mathrm{4sin}^{\mathrm{2}} \pi\mathrm{x}−\mathrm{4sin}\pi\mathrm{x}\:+\:\mathrm{2}\:=\:\mathrm{2sin}^{\mathrm{2}} \pi\mathrm{y}−\mathrm{1} \\ $$$$\mathrm{2}.\:\mathrm{4sin}\pi\mathrm{x}\:=\:\mathrm{4sin}\pi\mathrm{y}\:−\:\mathrm{7}\:−\:\frac{\mathrm{1}}{\mathrm{sin}^{\mathrm{2}} \pi\mathrm{x}} \\ $$

Question Number 184843 Answers: 0 Comments: 0

Question Number 184841 Answers: 1 Comments: 0

Question Number 184839 Answers: 3 Comments: 0

xy − 3x = 27 −5y find all (x , y) in Z^2

$${xy}\:−\:\mathrm{3}{x}\:=\:\mathrm{27}\:−\mathrm{5}{y} \\ $$$${find}\:{all}\:\left({x}\:,\:{y}\right)\:{in}\:\mathbb{Z}^{\mathrm{2}} \\ $$

Question Number 184832 Answers: 4 Comments: 1

Given the acceleration a=−4sin2t, initial velocity v(0)=2, and the initial position of the body as s(0)=−3, find the body′s position at time t. Hi

$$\mathrm{Given}\:\mathrm{the}\:\mathrm{acceleration}\: \\ $$$$\mathrm{a}=−\mathrm{4sin2t},\:\mathrm{initial}\:\mathrm{velocity}\: \\ $$$$\mathrm{v}\left(\mathrm{0}\right)=\mathrm{2},\:\mathrm{and}\:\mathrm{the}\:\mathrm{initial}\:\mathrm{position}\: \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{body}\:\mathrm{as}\:\mathrm{s}\left(\mathrm{0}\right)=−\mathrm{3},\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{body}'\mathrm{s}\:\mathrm{position}\:\mathrm{at}\:\mathrm{time}\:\mathrm{t}. \\ $$$$ \\ $$$$\mathrm{Hi} \\ $$

Question Number 184828 Answers: 0 Comments: 1

Find x in terms of c ∀ 0<c<(2/(3(√3))) (3x^2 −1)(3x^2 +36x−1)^2 ={4(x^3 −x−c)+9(7x^2 +1)}^2

$${Find}\:{x}\:{in}\:{terms}\:{of}\:\:\:{c}\:\:\forall\:\mathrm{0}<{c}<\frac{\mathrm{2}}{\mathrm{3}\sqrt{\mathrm{3}}} \\ $$$$\left(\mathrm{3}{x}^{\mathrm{2}} −\mathrm{1}\right)\left(\mathrm{3}{x}^{\mathrm{2}} +\mathrm{36}{x}−\mathrm{1}\right)^{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:=\left\{\mathrm{4}\left({x}^{\mathrm{3}} −{x}−{c}\right)+\mathrm{9}\left(\mathrm{7}{x}^{\mathrm{2}} +\mathrm{1}\right)\right\}^{\mathrm{2}} \\ $$

Question Number 184823 Answers: 1 Comments: 0

Lim_( x→ 0^( +) ) (( 1− cos ( 1− cos((√x) )))/x^( 4) )

$$ \\ $$$$\:\:\:\mathrm{Lim}_{\:{x}\rightarrow\:\mathrm{0}^{\:+} } \:\:\frac{\:\:\mathrm{1}−\:\:\mathrm{cos}\:\left(\:\mathrm{1}−\:\mathrm{cos}\left(\sqrt{{x}}\:\right)\right)}{{x}^{\:\mathrm{4}} } \\ $$

Question Number 184822 Answers: 1 Comments: 0

Question Number 184819 Answers: 2 Comments: 0

For 0≤x≤1 , maximum value of f(x)=x(√(1−x+(√(1−x)))) is __

$$\:\:{For}\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:,\:{maximum}\:{value} \\ $$$$\:\:{of}\:{f}\left({x}\right)={x}\sqrt{\mathrm{1}−{x}+\sqrt{\mathrm{1}−{x}}}\:{is}\:\_\_ \\ $$

Question Number 184798 Answers: 0 Comments: 1

Show that lim_(x→0) (x/(∣x∣)) does not exist

$${Show}\:{that}\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}}{\mid{x}\mid}\:\:{does}\:{not}\:{exist} \\ $$

Question Number 184797 Answers: 0 Comments: 1

Show that lim_(x→0) ((e^(1/x) −1)/(e^(1/x) +1)) does not exist

$${Show}\:{that}\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{e}^{\frac{\mathrm{1}}{{x}}} −\mathrm{1}}{{e}^{\frac{\mathrm{1}}{{x}}} +\mathrm{1}}\:\:\:{does}\:{not}\:{exist} \\ $$

Question Number 184796 Answers: 1 Comments: 2

Evaluate lim_(x→(π/6)) (((√3)sin x−cos x)/(x−(π/6)))

$${Evaluate}\: \\ $$$$\underset{{x}\rightarrow\frac{\pi}{\mathrm{6}}} {\mathrm{lim}}\frac{\sqrt{\mathrm{3}}\mathrm{sin}\:{x}−\mathrm{cos}\:{x}}{{x}−\frac{\pi}{\mathrm{6}}} \\ $$

Question Number 184795 Answers: 1 Comments: 1

Evaluate lim_(x→0) ((1−cos x(√(cos 2x)) )/x^2 )

$${Evaluate}\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−\mathrm{cos}\:{x}\sqrt{\mathrm{cos}\:\mathrm{2}{x}}\:}{{x}^{\mathrm{2}} } \\ $$

Question Number 184794 Answers: 4 Comments: 2

Evaluate lim_(x→2) ((x^5 −32)/(x^3 −8))

$${Evaluate}\: \\ $$$$\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{{x}^{\mathrm{5}} −\mathrm{32}}{{x}^{\mathrm{3}} −\mathrm{8}} \\ $$

Question Number 184793 Answers: 1 Comments: 0

Evaluate lim_(x→2) ((x^2 −4)/( (√(3x−2))−(√(x+2))))

$${Evaluate}\: \\ $$$$\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\:\frac{{x}^{\mathrm{2}} −\mathrm{4}}{\:\sqrt{\mathrm{3}{x}−\mathrm{2}}−\sqrt{{x}+\mathrm{2}}} \\ $$$$ \\ $$

Question Number 184792 Answers: 1 Comments: 2

Evaluate lim_(x→0) ((tan x−sin x)/(sin^3 x))

$${Evaluate}\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:{x}−\mathrm{sin}\:{x}}{\mathrm{sin}\:^{\mathrm{3}} {x}} \\ $$$$ \\ $$

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