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AllQuestion and Answers: Page 768

Question Number 141987 Answers: 1 Comments: 1

Question Number 141983 Answers: 0 Comments: 1

Question Number 142025 Answers: 1 Comments: 0

Question Number 141975 Answers: 0 Comments: 0

Question Number 141974 Answers: 0 Comments: 0

Question Number 141972 Answers: 0 Comments: 2

Question Number 141966 Answers: 0 Comments: 3

find lim_(x→0) ((log x^n −[x])/([x])), n∈N where [x] represents greatest integer less than or equal to x.

$${find}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{log}\:{x}^{{n}} −\left[{x}\right]}{\left[{x}\right]},\:{n}\in{N}\:{where}\: \\ $$$$\left[{x}\right]\:{represents}\:{greatest}\:{integer}\:{less}\:{than}\:{or}\:{equal}\:{to}\:{x}. \\ $$

Question Number 141961 Answers: 4 Comments: 0

lim_(x→1) ((x^(50) −8x+7)/(x^(20) +5x−6)) =?

$$\:\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{{x}^{\mathrm{50}} −\mathrm{8}{x}+\mathrm{7}}{{x}^{\mathrm{20}} +\mathrm{5}{x}−\mathrm{6}}\:=? \\ $$

Question Number 141947 Answers: 2 Comments: 0

Ω:=∫_0 ^( 1) (((√(1−x)) arcsin(x))/( (√(1+x))))dx=??

$$ \\ $$$$\:\:\:\:\:\:\Omega:=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\sqrt{\mathrm{1}−{x}}\:{arcsin}\left({x}\right)}{\:\sqrt{\mathrm{1}+{x}}}{dx}=?? \\ $$

Question Number 141946 Answers: 1 Comments: 0

....nice calculus... lim_(n→∞) n∫_0 ^( 1) (((2x)/(1+x)))^n =???

$$\:\:\:\:\:\:\:\:\:\:....{nice}\:\:\:{calculus}... \\ $$$$\:\:\:\:{lim}_{{n}\rightarrow\infty} {n}\int_{\mathrm{0}} ^{\:\mathrm{1}} \left(\frac{\mathrm{2}{x}}{\mathrm{1}+{x}}\right)^{{n}} =??? \\ $$

Question Number 141945 Answers: 1 Comments: 0

f(x)=(((∣x∣−1)(∣x∣−2)^2 ))^(1/3) find the domain of f

$$\mathrm{f}\left(\mathrm{x}\right)=\sqrt[{\mathrm{3}}]{\left(\mid\mathrm{x}\mid−\mathrm{1}\right)\left(\mid\mathrm{x}\mid−\mathrm{2}\right)^{\mathrm{2}} } \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{domain}\:\mathrm{of}\:\mathrm{f} \\ $$

Question Number 141944 Answers: 4 Comments: 0

∫x^2 (√(9x^2 +25))dx

$$\int{x}^{\mathrm{2}} \sqrt{\mathrm{9}{x}^{\mathrm{2}} +\mathrm{25}}{dx} \\ $$

Question Number 141943 Answers: 2 Comments: 0

∫(dx/(x(√(16−4x^2 ))))

$$\int\frac{{dx}}{{x}\sqrt{\mathrm{16}−\mathrm{4}{x}^{\mathrm{2}} }} \\ $$

Question Number 141935 Answers: 0 Comments: 0

Determine if the numbers 1, 5, 8 are in the range of the fuctions f(x)= { ((2x if −2≤x<2)),((3 if x=2)) :}

$${Determine}\:{if}\:{the}\:{numbers}\:\mathrm{1},\:\mathrm{5},\:\mathrm{8}\: \\ $$$${are}\:{in}\:{the}\:{range}\:{of}\:{the}\:{fuctions} \\ $$$$ \\ $$$${f}\left({x}\right)=\begin{cases}{\mathrm{2}{x}\:\:\:\:\:\:{if}\:\:−\mathrm{2}\leqslant{x}<\mathrm{2}}\\{\mathrm{3}\:\:\:\:\:\:\:\:\:{if}\:\:\:\:{x}=\mathrm{2}}\end{cases} \\ $$$$ \\ $$

Question Number 141933 Answers: 0 Comments: 1

let f(t) =∫_0 ^∞ ((logx)/(x^2 +t^2 ))dx (t>0) 1)calculate f^((n)) (t) and f^((n)) (0) 2) developp f at integr serie

$$\mathrm{let}\:\mathrm{f}\left(\mathrm{t}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{logx}}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{t}^{\mathrm{2}} }\mathrm{dx}\:\:\:\left(\mathrm{t}>\mathrm{0}\right) \\ $$$$\left.\mathrm{1}\right)\mathrm{calculate}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{t}\right)\:\:\mathrm{and}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integr}\:\mathrm{serie} \\ $$

Question Number 141932 Answers: 2 Comments: 0

calculate lim_(x→0) ((sin(sin(sinx))+1−cos(x^2 ))/x^3 )

$$\mathrm{calculate}\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{0}} \:\frac{\mathrm{sin}\left(\mathrm{sin}\left(\mathrm{sinx}\right)\right)+\mathrm{1}−\mathrm{cos}\left(\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{x}^{\mathrm{3}} } \\ $$

Question Number 141931 Answers: 2 Comments: 0

calculate ∫_0 ^∞ e^(−2x) ln(1+e^(3x) )dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\mathrm{e}^{−\mathrm{2x}} \mathrm{ln}\left(\mathrm{1}+\mathrm{e}^{\mathrm{3x}} \right)\mathrm{dx} \\ $$

Question Number 141930 Answers: 0 Comments: 0

calculate ∫_0 ^∞ e^(−(x^3 +(1/x^3 ))) dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\mathrm{e}^{−\left(\mathrm{x}^{\mathrm{3}} \:+\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} }\right)} \mathrm{dx} \\ $$

Question Number 141929 Answers: 1 Comments: 0

find ∫_0 ^∞ e^(−(t^2 +(1/t^2 ))) dt

$$\mathrm{find}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\mathrm{e}^{−\left(\mathrm{t}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{t}^{\mathrm{2}} }\right)} \mathrm{dt} \\ $$

Question Number 141924 Answers: 1 Comments: 1

cos(x−180)=?

$${cos}\left({x}−\mathrm{180}\right)=? \\ $$

Question Number 142263 Answers: 0 Comments: 0

(((0 sin(x))),((0 0)) )!+ (((0 sin(2x))),((0 0)) )!+ (((0 sin(3x))),((0 0)) )!+... n^(th) term

$$\begin{pmatrix}{\mathrm{0}\:{sin}\left({x}\right)}\\{\mathrm{0}\:\:\mathrm{0}}\end{pmatrix}!+\begin{pmatrix}{\mathrm{0}\:\:{sin}\left(\mathrm{2}{x}\right)}\\{\mathrm{0}\:\:\:\:\:\:\:\:\mathrm{0}}\end{pmatrix}!+\begin{pmatrix}{\mathrm{0}\:\:\:{sin}\left(\mathrm{3}{x}\right)}\\{\mathrm{0}\:\:\:\:\:\:\:\:\mathrm{0}}\end{pmatrix}!+...\:{n}^{{th}} \:{term} \\ $$

Question Number 141916 Answers: 1 Comments: 0

prove that:: I:=∫_0 ^( (π/2)) arccosh(sin(x)+cos(x))dx=(π/2)ln(2) ..

$$ \\ $$$$\:\:\:\:\:{prove}\:\:{that}:: \\ $$$$\:\:\:\mathrm{I}:=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {arccosh}\left({sin}\left({x}\right)+{cos}\left({x}\right)\right){dx}=\frac{\pi}{\mathrm{2}}{ln}\left(\mathrm{2}\right)\:.. \\ $$

Question Number 141914 Answers: 3 Comments: 0

prove that:: φ:=∫_0 ^( π) (x/((sin(x))^(1/2) ))dx=(√(π/8)) Γ^( 2) ((1/4))...✓ .........

$$\:\:\:\: \\ $$$$\:\:\:\:\:\:{prove}\:{that}:: \\ $$$$\:\:\:\:\:\phi:=\int_{\mathrm{0}} ^{\:\pi} \frac{{x}}{\left({sin}\left({x}\right)\right)^{\frac{\mathrm{1}}{\mathrm{2}}} }{dx}=\sqrt{\frac{\pi}{\mathrm{8}}}\:\Gamma^{\:\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{4}}\right)...\checkmark \\ $$$$\:\:\:\:\:\:\:\:\:......... \\ $$

Question Number 141912 Answers: 0 Comments: 0

Q138579

$${Q}\mathrm{138579} \\ $$

Question Number 141911 Answers: 0 Comments: 0

Q137956

$${Q}\mathrm{137956} \\ $$

Question Number 141910 Answers: 0 Comments: 0

Q137026

$${Q}\mathrm{137026} \\ $$

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