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AllQuestion and Answers: Page 717

Question Number 142017 Answers: 3 Comments: 3

Question Number 142103 Answers: 2 Comments: 0

∫_(−∞) ^∞ ((tan^(−1) ((√(x^2 +2))))/((x^2 +1)(√(x^2 +2))))dx

$$\int_{−\infty} ^{\infty} \frac{{tan}^{−\mathrm{1}} \left(\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}\right)}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}}{dx} \\ $$

Question Number 142010 Answers: 0 Comments: 0

find x 2cosh 2x +10sinh 2x=5

$$\mathrm{find}\:\mathrm{x}\:\mathrm{2cosh}\:\mathrm{2x}\:+\mathrm{10sinh}\:\mathrm{2x}=\mathrm{5} \\ $$

Question Number 141998 Answers: 2 Comments: 0

∫_0 ^(π/2) ((sin (40x))/(sin (5x))) dx

$$\:\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\frac{\mathrm{sin}\:\left(\mathrm{40}{x}\right)}{\mathrm{sin}\:\left(\mathrm{5}{x}\right)}\:{dx}\: \\ $$

Question Number 141997 Answers: 2 Comments: 0

find two irrational numbers between 0.333.... and 0.444...

$$\mathrm{find}\:\mathrm{two}\:\mathrm{irrational}\:\mathrm{numbers}\: \\ $$$$\mathrm{between}\:\mathrm{0}.\mathrm{333}....\:\mathrm{and}\:\mathrm{0}.\mathrm{444}... \\ $$$$ \\ $$

Question Number 141994 Answers: 1 Comments: 0

factorise x−(√(xy )) +(√(2y)) −(√(2x ))

$$\mathrm{factorise}\:\:\mathrm{x}−\sqrt{\mathrm{xy}\:}\:+\sqrt{\mathrm{2y}}\:−\sqrt{\mathrm{2x}\:}\: \\ $$

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)=?

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

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