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Question Number 31562 Answers: 1 Comments: 0

Question Number 31560 Answers: 1 Comments: 1

Question Number 31907 Answers: 0 Comments: 0

Question Number 31906 Answers: 1 Comments: 0

Question Number 31549 Answers: 1 Comments: 0

witout using calculator, simpify cos22.5°

$${witout}\:{using}\:{calculator},\:{simpify} \\ $$$${cos}\mathrm{22}.\mathrm{5}° \\ $$

Question Number 31548 Answers: 1 Comments: 0

simplify cosx + (√3)sinx as a single trigonometry ratio

$${simplify}\:{cosx}\:+\:\sqrt{\mathrm{3}}{sinx}\:{as}\:{a}\: \\ $$$${single}\:{trigonometry}\:{ratio} \\ $$

Question Number 31546 Answers: 1 Comments: 0

let consider the numrtical function f(x)= (1/(x^2 +x+1)) calculate f^((n)) (x) then give f^((n)) (0).

$${let}\:{consider}\:{the}\:{numrtical}\:{function} \\ $$$${f}\left({x}\right)=\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} \:+{x}+\mathrm{1}}\:\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right)\:{then}\:{give} \\ $$$${f}^{\left({n}\right)} \left(\mathrm{0}\right). \\ $$

Question Number 31543 Answers: 0 Comments: 2

∫((x^3 +x+1)/(x^2 +1)) dx

$$\int\frac{{x}^{\mathrm{3}} +{x}+\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}\:{dx} \\ $$$$ \\ $$$$ \\ $$

Question Number 31542 Answers: 0 Comments: 0

let p(x)=(1+x+x^2 )^n −(1−x+x^2 )^n ∈C[x] 1) find the roots of p(x) 2) factorize p(x) inside C[x].

$${let}\:{p}\left({x}\right)=\left(\mathrm{1}+{x}+{x}^{\mathrm{2}} \right)^{{n}} \:−\left(\mathrm{1}−{x}+{x}^{\mathrm{2}} \right)^{{n}} \:\in{C}\left[{x}\right] \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{roots}\:{of}\:{p}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{factorize}\:{p}\left({x}\right)\:{inside}\:{C}\left[{x}\right]. \\ $$

Question Number 31538 Answers: 1 Comments: 0

If f(x)= a e^(2x) +b e^x +cx satisfies the condition f(0)= −1, f ′(log 2)=31, ∫_( 0) ^(log 4) (f(x)−cx) dx = ((39)/2), then

$$\mathrm{If}\:{f}\left({x}\right)=\:{a}\:{e}^{\mathrm{2}{x}} +{b}\:{e}^{{x}} +{cx}\:\mathrm{satisfies}\:\mathrm{the} \\ $$$$\mathrm{condition}\:{f}\left(\mathrm{0}\right)=\:−\mathrm{1},\:{f}\:'\left(\mathrm{log}\:\mathrm{2}\right)=\mathrm{31}, \\ $$$$\:\underset{\:\mathrm{0}} {\overset{\mathrm{log}\:\mathrm{4}} {\int}}\left({f}\left({x}\right)−{cx}\right)\:{dx}\:=\:\frac{\mathrm{39}}{\mathrm{2}},\:\mathrm{then} \\ $$

Question Number 31533 Answers: 0 Comments: 0

let put S(x)=Σ_(n=0) ^∞ (((−1)^n )/(n+x)) 1) prove that S is C^1 on]0′+∞[ 2)give the variation of S(x) 3)prove that ∀x>0 S(x+1)+S(x)=(1/x) 4)give a equivalent for S at 0 5)find a equivalent for S at +∞.

$${let}\:{put}\:{S}\left({x}\right)=\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}+{x}} \\ $$$$\left.\mathrm{1}\left.\right)\:{prove}\:{that}\:{S}\:{is}\:{C}^{\mathrm{1}} \:{on}\right]\mathrm{0}'+\infty\left[\right. \\ $$$$\left.\mathrm{2}\right){give}\:{the}\:{variation}\:{of}\:{S}\left({x}\right) \\ $$$$\left.\mathrm{3}\right){prove}\:{that}\:\forall{x}>\mathrm{0}\:{S}\left({x}+\mathrm{1}\right)+{S}\left({x}\right)=\frac{\mathrm{1}}{{x}} \\ $$$$\left.\mathrm{4}\right){give}\:{a}\:{equivalent}\:{for}\:{S}\:{at}\:\mathrm{0} \\ $$$$\left.\mathrm{5}\right){find}\:{a}\:{equivalent}\:{for}\:{S}\:{at}\:+\infty. \\ $$

Question Number 31531 Answers: 0 Comments: 0

let give f(x)=(1/x) +Σ_(n=1) ^∞ ((1/(x+n)) +(1/(x−n))) with x∈R−Z 1) prove the existence of f(x) 2)prove that f is 1−periodic 3)prove that f((x/2)) +f(((x+1)/2))=2f(x).

$${let}\:{give}\:{f}\left({x}\right)=\frac{\mathrm{1}}{{x}}\:+\sum_{{n}=\mathrm{1}} ^{\infty} \:\left(\frac{\mathrm{1}}{{x}+{n}}\:+\frac{\mathrm{1}}{{x}−{n}}\right)\:{with}\:{x}\in{R}−{Z} \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{the}\:{existence}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){prove}\:{that}\:{f}\:{is}\:\mathrm{1}−{periodic} \\ $$$$\left.\mathrm{3}\right){prove}\:{that}\:{f}\left(\frac{{x}}{\mathrm{2}}\right)\:+{f}\left(\frac{{x}+\mathrm{1}}{\mathrm{2}}\right)=\mathrm{2}{f}\left({x}\right). \\ $$

Question Number 31529 Answers: 0 Comments: 1

find lim_(x→1^− ) lnx.ln(1−x) .

$${find}\:{lim}_{{x}\rightarrow\mathrm{1}^{−} } \:\:\:\:{lnx}.{ln}\left(\mathrm{1}−{x}\right)\:. \\ $$

Question Number 31528 Answers: 0 Comments: 1

find lim_(x→2) ((x^2 −2^x )/(arctanx −artan2)) .

$${find}\:{lim}_{{x}\rightarrow\mathrm{2}} \:\:\frac{{x}^{\mathrm{2}} \:\:−\mathrm{2}^{{x}} }{{arctanx}\:−{artan}\mathrm{2}}\:. \\ $$

Question Number 31526 Answers: 0 Comments: 2

1)find lim_(n→∞) ( ((a^(1/n) +b^(1/n) )/2))^n 2) let 0<θ<(π/2) calculate lim_(n→∞) (1/2^n )(^n (√(cosθ)) +^n (√(sinθ)) )^n

$$\left.\mathrm{1}\right){find}\:{lim}_{{n}\rightarrow\infty} \left(\:\frac{{a}^{\frac{\mathrm{1}}{{n}}} \:+{b}^{\frac{\mathrm{1}}{{n}}} }{\mathrm{2}}\right)^{{n}} \\ $$$$\left.\mathrm{2}\right)\:{let}\:\mathrm{0}<\theta<\frac{\pi}{\mathrm{2}}\:{calculate}\:{lim}_{{n}\rightarrow\infty} \:\frac{\mathrm{1}}{\mathrm{2}^{{n}} }\left(\:^{{n}} \sqrt{{cos}\theta}\:+^{{n}} \sqrt{{sin}\theta}\:\right)^{{n}} \\ $$

Question Number 31523 Answers: 0 Comments: 0

let give u_n =^(n+1) (√(n+1)) −^n (√n) 1) study the convergence of (u_n ) 2) find nature of serie Σ_(n=1) ^∞ u_n