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Question Number 40108 Answers: 0 Comments: 0

calculate lim_(x→(π/2)) (sinx)^(ln∣x−(π/2)∣)

$${calculate}\:\:{lim}_{{x}\rightarrow\frac{\pi}{\mathrm{2}}} \:\:\:\:\:\left({sinx}\right)^{{ln}\mid{x}−\frac{\pi}{\mathrm{2}}\mid} \\ $$

Question Number 40107 Answers: 1 Comments: 0

prove the relations 1) ∀t ∈]0,1] arctan(((√(1−t^2 ))/t))=arccost 2) ∀ t∈[−1,1] 2 arccos(√((1+t)/2)) =arccost

$${prove}\:{the}\:{relations} \\ $$$$\left.\mathrm{1}\left.\right)\left.\:\forall{t}\:\in\right]\mathrm{0},\mathrm{1}\right]\:\:\:{arctan}\left(\frac{\sqrt{\mathrm{1}−{t}^{\mathrm{2}} }}{{t}}\right)={arccost} \\ $$$$\left.\mathrm{2}\right)\:\forall\:{t}\in\left[−\mathrm{1},\mathrm{1}\right]\:\:\:\:\mathrm{2}\:{arccos}\sqrt{\frac{\mathrm{1}+{t}}{\mathrm{2}}}\:={arccost} \\ $$

Question Number 40106 Answers: 1 Comments: 0

study and give the graph for the function f(x)= (x/(x−1)) e^(1/x)

$${study}\:{and}\:{give}\:{the}\:{graph}\:{for}\:{the}\:{function} \\ $$$${f}\left({x}\right)=\:\frac{{x}}{{x}−\mathrm{1}}\:{e}^{\frac{\mathrm{1}}{{x}}} \\ $$

Question Number 40105 Answers: 0 Comments: 1

let f(x) = x^n e^(−2nx) with n integr natural calculate f^((n)) (0).

$${let}\:\:{f}\left({x}\right)\:=\:{x}^{{n}} \:{e}^{−\mathrm{2}{nx}} \:\:\:\:{with}\:{n}\:{integr}\:{natural} \\ $$$$\:{calculate}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right). \\ $$

Question Number 40104 Answers: 0 Comments: 0

find number of solution for the equation (e^x /(2(x+1)^2 )) =1 .

$${find}\:{number}\:{of}\:{solution}\:{for}\:{the}\:{equation} \\ $$$$\frac{{e}^{{x}} }{\mathrm{2}\left({x}+\mathrm{1}\right)^{\mathrm{2}} }\:=\mathrm{1}\:. \\ $$

Question Number 40103 Answers: 0 Comments: 0

let g(x)=(√(−x+(√(1+x^2 )))) 1) prove that g is solution for the differencial equation 4(1+x^2 )y^(′′) +4xy^′ −y =0 .prove that g is C^∞ on R 2) determine a relation between g^((n)) (0) and g^((n+2)) (0)

$${let}\:{g}\left({x}\right)=\sqrt{−{x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }} \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:{g}\:{is}\:{solution}\:{for}\:{the}\:{differencial}\:{equation} \\ $$$$\mathrm{4}\left(\mathrm{1}+{x}^{\mathrm{2}} \right){y}^{''} \:+\mathrm{4}{xy}^{'} \:−{y}\:=\mathrm{0}\:\:\:.{prove}\:{that}\:{g}\:{is}\:{C}^{\infty} {on}\:{R} \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{a}\:{relation}\:{between}\:{g}^{\left({n}\right)} \left(\mathrm{0}\right)\:{and}\:{g}^{\left({n}+\mathrm{2}\right)} \left(\mathrm{0}\right) \\ $$

Question Number 40102 Answers: 2 Comments: 0

let f(x) = ((∣x∣)/((1+∣1−x^2 ∣)^n )) study tbe derivability of f at points 0 and 1 (n natural integr)

$${let}\:{f}\left({x}\right)\:=\:\frac{\mid{x}\mid}{\left(\mathrm{1}+\mid\mathrm{1}−{x}^{\mathrm{2}} \mid\right)^{{n}} } \\ $$$${study}\:{tbe}\:{derivability}\:{of}\:{f}\:{at}\:{points}\:\mathrm{0}\:{and}\:\mathrm{1}\:\left({n}\:{natural}\:{integr}\right) \\ $$

Question Number 40101 Answers: 0 Comments: 0

study the variation of f(x)=arcsin(2x(√(1−x^2 )) ) and give its graph

$${study}\:\:{the}\:{variation}\:{of}\:{f}\left({x}\right)={arcsin}\left(\mathrm{2}{x}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\:\right)\:{and}\:{give}\:{its}\:{graph} \\ $$

Question Number 40100 Answers: 0 Comments: 1

solve arctan(2x) +arctan(3x)=(π/4)

$${solve}\:\:\:{arctan}\left(\mathrm{2}{x}\right)\:+{arctan}\left(\mathrm{3}{x}\right)=\frac{\pi}{\mathrm{4}} \\ $$

Question Number 40099 Answers: 0 Comments: 0

solve arcsin(((2x)/(1+x^2 ))) =(π/3)

$${solve}\:\:{arcsin}\left(\frac{\mathrm{2}{x}}{\mathrm{1}+{x}^{\mathrm{2}} }\right)\:=\frac{\pi}{\mathrm{3}} \\ $$

Question Number 40098 Answers: 0 Comments: 0

solve arcsin(sinx) =(π/9)

$${solve}\:\:{arcsin}\left({sinx}\right)\:=\frac{\pi}{\mathrm{9}} \\ $$

Question Number 40097 Answers: 0 Comments: 2

let f(x)=ln(√((2+x)/(2−x))) 1) find D_f and find the assymptotes to C_f 2) calculate f^′ (x) and give the variation of f 3) give the graph of f 4) give the equation of tangent to C_(f ) at point E((1/2),f((1/2))) 5) calculate ∫_0 ^1 f(x)dx .

$${let}\:{f}\left({x}\right)={ln}\sqrt{\frac{\mathrm{2}+{x}}{\mathrm{2}−{x}}} \\ $$$$\left.\mathrm{1}\right)\:\:{find}\:{D}_{{f}} \:\:\:\:{and}\:{find}\:{the}\:{assymptotes}\:{to}\:{C}_{{f}} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{f}^{'} \left({x}\right)\:{and}\:{give}\:{the}\:{variation}\:{of}\:{f} \\ $$$$\left.\mathrm{3}\right)\:{give}\:{the}\:{graph}\:{of}\:{f} \\ $$$$\left.\mathrm{4}\right)\:{give}\:{the}\:{equation}\:{of}\:{tangent}\:{to}\:{C}_{{f}\:} \:\:\:{at}\:{point}\:\:{E}\left(\frac{\mathrm{1}}{\mathrm{2}},{f}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)\right) \\ $$$$\left.\mathrm{5}\right)\:{calculate}\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({x}\right){dx}\:. \\ $$

Question Number 40095 Answers: 1 Comments: 0

let f(x) =cos(x)cos((1/x)) is f have a limit at point 0?

$${let}\:{f}\left({x}\right)\:={cos}\left({x}\right){cos}\left(\frac{\mathrm{1}}{{x}}\right)\:\:{is}\:{f}\:\:{have}\:{a}\:{limit}\:{at}\:{point}\:\mathrm{0}? \\ $$$$ \\ $$

Question Number 40094 Answers: 0 Comments: 0

find lim _(x→0^+ ) ln(x)tan{ln(1+x)}

$${find}\:\:{lim}\:_{{x}\rightarrow\mathrm{0}^{+} } \:\:\:\:\:\:{ln}\left({x}\right){tan}\left\{{ln}\left(\mathrm{1}+{x}\right)\right\} \\ $$

Question Number 40093 Answers: 0 Comments: 0

find lim _(x→0) ((ln(cosx))/(1−cos(2x)))

$${find}\:\:{lim}\:_{{x}\rightarrow\mathrm{0}} \:\:\frac{{ln}\left({cosx}\right)}{\mathrm{1}−{cos}\left(\mathrm{2}{x}\right)} \\ $$

Question Number 40092 Answers: 0 Comments: 1

calculate lim_(x→+∞) (1/x) tan(((πx)/(2x+3)))