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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)))

$${calculate}\:{lim}_{{x}\rightarrow+\infty} \:\:\:\:\:\:\frac{\mathrm{1}}{{x}}\:{tan}\left(\frac{\pi{x}}{\mathrm{2}{x}+\mathrm{3}}\right) \\ $$

Question Number 40091 Answers: 0 Comments: 1

find a equivalent to f(x)=cos(sinx) for x∈v(0) 2) find a equivalent to g(x)= tan((π/(2x+1))) (x→0)

$${find}\:{a}\:{equivalent}\:{to}\:{f}\left({x}\right)={cos}\left({sinx}\right)\:{for}\:{x}\in{v}\left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{a}\:{equivalent}\:{to}\:{g}\left({x}\right)=\:{tan}\left(\frac{\pi}{\mathrm{2}{x}+\mathrm{1}}\right)\:\left({x}\rightarrow\mathrm{0}\right) \\ $$

Question Number 40090 Answers: 0 Comments: 1

let f(x)= 1−[x]−[1−x] 1) prove that f is periodic with period 1 2) give a expression of f(x) when x∈[0,1[

$${let}\:{f}\left({x}\right)=\:\mathrm{1}−\left[{x}\right]−\left[\mathrm{1}−{x}\right] \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:{f}\:{is}\:{periodic}\:{with}\:{period}\:\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{give}\:{a}\:{expression}\:{of}\:{f}\left({x}\right)\:{when}\:\:{x}\in\left[\mathrm{0},\mathrm{1}\left[\right.\right. \\ $$

Question Number 40089 Answers: 0 Comments: 0

find lim _(x→−∞) ((x^4 +1)/(cotan((1/x))))

$${find}\:\:{lim}\:_{{x}\rightarrow−\infty} \:\:\:\:\:\frac{{x}^{\mathrm{4}} \:+\mathrm{1}}{{cotan}\left(\frac{\mathrm{1}}{{x}}\right)} \\ $$

Question Number 40088 Answers: 0 Comments: 0

calculate lim_(x→+∞) x^2 sin((1/x))

$${calculate}\:\:\:{lim}_{{x}\rightarrow+\infty} \:\:\:{x}^{\mathrm{2}} {sin}\left(\frac{\mathrm{1}}{{x}}\right) \\ $$

Question Number 40087 Answers: 0 Comments: 0

find lim_(x→0) sinx{x−[(1/x)]}

$${find}\:\:\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:{sinx}\left\{{x}−\left[\frac{\mathrm{1}}{{x}}\right]\right\} \\ $$

Question Number 40086 Answers: 0 Comments: 0

find lim_(x→0) x [(1/x)]

$${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\:{x}\:\left[\frac{\mathrm{1}}{{x}}\right] \\ $$

Question Number 40085 Answers: 0 Comments: 0

calculate lim_(x→(π/3)) ((tan(x)tan(x−(π/3)))/(1−2cosx))

$${calculate}\:{lim}_{{x}\rightarrow\frac{\pi}{\mathrm{3}}} \:\:\:\:\:\frac{{tan}\left({x}\right){tan}\left({x}−\frac{\pi}{\mathrm{3}}\right)}{\mathrm{1}−\mathrm{2}{cosx}} \\ $$

Question Number 40084 Answers: 0 Comments: 0

calculate lim_(x→(π/4)) ((sin(2x)sin(x−(π/4)))/(sinx −cosx))

$${calculate}\:{lim}_{{x}\rightarrow\frac{\pi}{\mathrm{4}}} \:\:\:\:\frac{{sin}\left(\mathrm{2}{x}\right){sin}\left({x}−\frac{\pi}{\mathrm{4}}\right)}{{sinx}\:−{cosx}} \\ $$

Question Number 40083 Answers: 1 Comments: 2

solve for x: 5^x + 5x = 140

$$\mathrm{solve}\:\mathrm{for}\:\mathrm{x}:\:\:\:\:\:\mathrm{5}^{\mathrm{x}} \:+\:\mathrm{5x}\:=\:\mathrm{140} \\ $$

Question Number 40166 Answers: 1 Comments: 0

Question Number 40067 Answers: 0 Comments: 2

let S_n = Σ_(k=1) ^n (((−1)^k )/k) 1) calculate S_n interms of H_n 2) find lim_(n→+∞) S_n 3) let W_n = Σ_(1≤i<j≤n) (((−1)^(i+j) )/(i.j)) prove that (W_n ) is convergent and calculste its limit.

$${let}\:\:{S}_{{n}} =\:\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{\left(−\mathrm{1}\right)^{{k}} }{{k}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{S}_{{n}} \:{interms}\:{of}\:{H}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{S}_{{n}} \\ $$$$\left.\mathrm{3}\right)\:{let}\:{W}_{{n}} =\:\sum_{\mathrm{1}\leqslant{i}<{j}\leqslant{n}} \frac{\left(−\mathrm{1}\right)^{{i}+{j}} }{{i}.{j}} \\ $$$${prove}\:{that}\:\left({W}_{{n}} \right)\:{is}\:{convergent}\:{and}\:{calculste}\:{its} \\ $$$${limit}. \\ $$

Question Number 40063 Answers: 1 Comments: 0

Question Number 40060 Answers: 0 Comments: 0

Mr John bought a four roomed house for 2520000bucks. these rooms are rented out to four students ,at 9000 buck per month for each room. a) find the rents collected at the end of each year.if each year 72000 bucks is spent on repairs. b) find the real annual income on the house

$${Mr}\:{John}\:{bought}\:{a}\:{four}\:{roomed} \\ $$$${house}\:{for}\:\mathrm{2520000}{bucks}. \\ $$$${these}\:{rooms}\:{are}\:{rented}\:{out} \\ $$$${to}\:{four}\:{students}\:,{at}\:\mathrm{9000}\:{buck} \\ $$$${per}\:{month}\:{for}\:{each}\:{room}. \\ $$$$\left.{a}\right)\:{find}\:{the}\:{rents}\:{collected}\:{at}\:{the}\:{end} \\ $$$${of}\:{each}\:{year}.{if}\:{each}\:{year}\:\mathrm{72000}\:{bucks} \\ $$$${is}\:{spent}\:{on}\:{repairs}. \\ $$$$\left.{b}\right)\:{find}\:{the}\:{real}\:{annual}\:{income}\:{on}\:{the}\:{house} \\ $$$$ \\ $$

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