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Question Number 29794 Answers: 0 Comments: 9

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Question Number 29831 Answers: 0 Comments: 0

let give f(x)= (1/(1+x^2 )) 1)prove that prove that f^((n)) (x)=((p_n (x))/((1+x^2 )^(n+1) )) with p_n is a polynomial 2) prove that p_(n+1) (x)=(1+x^2 )p_n ^′ (x) −2(n+1)p_n (x) 3) calculate p_0 (x) ,p_1 (x) ,p_2 (x) ,p_3 (x) .

$$\left.{let}\:{give}\:{f}\left({x}\right)=\:\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} }\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}\right){prove}\:{that}\:\:\:{prove}\:{that} \\ $$$${f}^{\left({n}\right)} \left({x}\right)=\frac{{p}_{{n}} \left({x}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{{n}+\mathrm{1}} }\:{with}\:{p}_{{n}} {is}\:{a}\:{polynomial} \\ $$$$\left.\mathrm{2}\right)\:{prove}\:{that}\:{p}_{{n}+\mathrm{1}} \left({x}\right)=\left(\mathrm{1}+{x}^{\mathrm{2}} \right){p}_{{n}} ^{'} \left({x}\right)\:−\mathrm{2}\left({n}+\mathrm{1}\right){p}_{{n}} \left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:{p}_{\mathrm{0}} \left({x}\right)\:,{p}_{\mathrm{1}} \left({x}\right)\:,{p}_{\mathrm{2}} \left({x}\right)\:\:,{p}_{\mathrm{3}} \left({x}\right)\:\:. \\ $$

Question Number 29786 Answers: 0 Comments: 0

Question Number 29785 Answers: 0 Comments: 0

Question Number 29778 Answers: 1 Comments: 0

Question Number 29803 Answers: 0 Comments: 3

Question Number 29773 Answers: 0 Comments: 0

lim_(x→0,y→∞) xy=?

$$\underset{\mathrm{x}\rightarrow\mathrm{0},\mathrm{y}\rightarrow\infty} {\mathrm{lim}xy}=? \\ $$

Question Number 29753 Answers: 0 Comments: 0

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Question Number 29752 Answers: 0 Comments: 0

pls elp with dis... ∫(((1−x)dx)/((1+x)(√(1+x^2 +x^3 ))))

$$\mathrm{pls}\:\mathrm{elp}\:\mathrm{with}\:\mathrm{dis}... \\ $$$$ \\ $$$$\int\frac{\left(\mathrm{1}−\mathrm{x}\right)\boldsymbol{{dx}}}{\left(\mathrm{1}+\mathrm{x}\right)\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} +\mathrm{x}^{\mathrm{3}} }} \\ $$

Question Number 29770 Answers: 2 Comments: 0

find the equation of a pair of straight lines represented by given equation 2x^(2 ) −5xy−3y^2 +3x+19y−20=0

$${find}\:{the}\:{equation}\:{of}\:{a}\:{pair}\:{of}\:{straight}\:{lines}\:{represented}\:{by}\:{given}\:{equation}\:\mathrm{2}{x}^{\mathrm{2}\:} −\mathrm{5}{xy}−\mathrm{3}{y}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{19}{y}−\mathrm{20}=\mathrm{0} \\ $$

Question Number 29728 Answers: 0 Comments: 8

Question Number 29727 Answers: 1 Comments: 4

Question Number 29776 Answers: 0 Comments: 0

Question Number 29777 Answers: 2 Comments: 5

f(x) = (x − 1)(x − 2)(x − 3)...(x − 50) Find coefficient of x^(49)

$${f}\left({x}\right)\:=\:\left({x}\:−\:\mathrm{1}\right)\left({x}\:−\:\mathrm{2}\right)\left({x}\:−\:\mathrm{3}\right)...\left({x}\:−\:\mathrm{50}\right) \\ $$$$\mathrm{Find}\:\mathrm{coefficient}\:\mathrm{of}\:{x}^{\mathrm{49}} \\ $$

Question Number 29726 Answers: 0 Comments: 2

Question Number 29887 Answers: 1 Comments: 3

Question Number 29723 Answers: 1 Comments: 1

Question Number 29700 Answers: 1 Comments: 0

32^(32^(32) ) /7...find remainder

$$\mathrm{32}^{\mathrm{32}^{\mathrm{32}} } \:/\mathrm{7}...\mathrm{find}\:\mathrm{remainder} \\ $$

Question Number 29689 Answers: 1 Comments: 2

find lim_(x→0) ((2/(1+a^x )))^(1/x) =?

$${find}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\mathrm{2}}{\mathrm{1}+{a}^{{x}} }\right)^{\frac{\mathrm{1}}{{x}}} =? \\ $$

Question Number 29680 Answers: 1 Comments: 0

i^(i ) what is iota to power iota

$$\mathrm{i}^{\mathrm{i}\:} \:\:\mathrm{what}\:\mathrm{is}\:\mathrm{iota}\:\mathrm{to}\:\mathrm{power}\:\mathrm{iota} \\ $$

Question Number 29658 Answers: 1 Comments: 0

tanθ+tan2θ+(√3) tanθ.tan2θ=(√3) (0^(o ) ≤θ≤360)

$${tan}\theta+{tan}\mathrm{2}\theta+\sqrt{\mathrm{3}}\:{tan}\theta.{tan}\mathrm{2}\theta=\sqrt{\mathrm{3}}\:\:\:\:\:\left(\mathrm{0}^{{o}\:} \leqslant\theta\leqslant\mathrm{360}\right) \\ $$

Question Number 29648 Answers: 1 Comments: 5

How many arrangements are there of 4 letters chosen from the word COMMUNICATION

$$\mathrm{How}\:\mathrm{many}\:\mathrm{arrangements}\:\mathrm{are} \\ $$$$\mathrm{there}\:\mathrm{of}\:\mathrm{4}\:\mathrm{letters}\:\mathrm{chosen}\:\mathrm{from}\: \\ $$$$\mathrm{the}\:\mathrm{word}\:{COMMUNICATION} \\ $$

Question Number 29647 Answers: 0 Comments: 1

Question Number 29645 Answers: 1 Comments: 0

if the sum of first 5 terms of a G.P. is 155, sum of last 5 terms is 39680,first term is 5 and last term is 20480. find the number of terms of the sequence.

$${if}\:{the}\:{sum}\:{of}\:{first}\:\mathrm{5}\:{terms}\:{of}\:\:{a}\:{G}.{P}.\:{is}\:\mathrm{155},\:{sum}\:{of}\:{last}\:\mathrm{5}\:{terms}\:{is}\:\mathrm{39680},{first}\:{term}\:{is}\:\mathrm{5}\:{and}\:{last}\:{term}\:\:{is}\:\mathrm{20480}.\:{find}\:{the}\:{number}\:{of}\:{terms}\:{of}\:{the}\:{sequence}. \\ $$

Question Number 29646 Answers: 0 Comments: 0

Question Number 29643 Answers: 0 Comments: 0

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