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Relation and FunctionsQuestion and Answers: Page 4

Question Number 174469 Answers: 1 Comments: 0

f(x)=(x+1)(x+2)....(x+n) 1)calculate f^′ (x) (n≥1) 2)decompose F=(1/f)

$${f}\left({x}\right)=\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)....\left({x}+{n}\right) \\ $$$$\left.\mathrm{1}\right){calculate}\:{f}^{'} \left({x}\right)\:\:\:\left({n}\geqslant\mathrm{1}\right) \\ $$$$\left.\mathrm{2}\right){decompose}\:{F}=\frac{\mathrm{1}}{{f}} \\ $$

Question Number 174373 Answers: 0 Comments: 1

find ∫(√(x+(√(1−x))))dx

$${find}\:\int\sqrt{{x}+\sqrt{\mathrm{1}−{x}}}{dx} \\ $$

Question Number 173678 Answers: 3 Comments: 0

if f(x) is 2^(nd) digre function f(x−1)+f(x)+f(x+1)=x^2 +1 then faind f(2)=?

$${if}\:{f}\left({x}\right)\:{is}\:\mathrm{2}^{{nd}} \:{digre}\:{function}\:\:\: \\ $$$${f}\left({x}−\mathrm{1}\right)+{f}\left({x}\right)+{f}\left({x}+\mathrm{1}\right)={x}^{\mathrm{2}} +\mathrm{1} \\ $$$${then}\:{faind}\:\:{f}\left(\mathrm{2}\right)=? \\ $$

Question Number 173132 Answers: 0 Comments: 5

U_n = ((((−4)^(n+1) −1)/(1−(−4)^n )))U_(n−1) with U_0 =1 find U_(n ) in terms of n

$${U}_{{n}} \:=\:\left(\frac{\left(−\mathrm{4}\right)^{{n}+\mathrm{1}} −\mathrm{1}}{\mathrm{1}−\left(−\mathrm{4}\right)^{{n}} }\right){U}_{{n}−\mathrm{1}} \:{with}\:{U}_{\mathrm{0}} =\mathrm{1} \\ $$$${find}\:{U}_{{n}\:} \:{in}\:{terms}\:{of}\:{n}\:\: \\ $$

Question Number 173007 Answers: 0 Comments: 1

Question Number 171955 Answers: 2 Comments: 0

f(x)+ f((1/(1−x))) = 1+(1/(x(1−x))) f(x) = ??

$$\:\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)+\:\boldsymbol{{f}}\left(\frac{\mathrm{1}}{\mathrm{1}−\boldsymbol{{x}}}\right)\:=\:\mathrm{1}+\frac{\mathrm{1}}{\boldsymbol{{x}}\left(\mathrm{1}−\boldsymbol{{x}}\right)} \\ $$$$\:\:\:\:\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)\:=\:\:??\:\:\:\:\:\:\:\:\: \\ $$

Question Number 171546 Answers: 0 Comments: 1

f(x)=((−ln∣x∣)/x)+x−2 , g(x)=−x^2 +1−ln∣x∣ Calculate the derivative of f(x) as a function of g(x)

$${f}\left({x}\right)=\frac{−{ln}\mid{x}\mid}{{x}}+{x}−\mathrm{2}\:\:,\:\:\:{g}\left({x}\right)=−{x}^{\mathrm{2}} +\mathrm{1}−{ln}\mid{x}\mid \\ $$$$ \\ $$Calculate the derivative of f(x) as a function of g(x)

Question Number 171484 Answers: 3 Comments: 1

let f(x) = x+(2/(1.3))x^3 +((2.4)/(1.3.5))x^5 +((2.4.6)/(1.3.5.7))x^7 +......... ∀x∈(0,1) the value of f((1/( (√2)))) = ?

$$ \\ $$$$\:\:\:\:{let}\:{f}\left({x}\right)\:=\:{x}+\frac{\mathrm{2}}{\mathrm{1}.\mathrm{3}}{x}^{\mathrm{3}} +\frac{\mathrm{2}.\mathrm{4}}{\mathrm{1}.\mathrm{3}.\mathrm{5}}{x}^{\mathrm{5}} +\frac{\mathrm{2}.\mathrm{4}.\mathrm{6}}{\mathrm{1}.\mathrm{3}.\mathrm{5}.\mathrm{7}}{x}^{\mathrm{7}} +......... \\ $$$$\:\:\:\:\forall{x}\in\left(\mathrm{0},\mathrm{1}\right)\:\:{the}\:{value}\:{of}\:\:{f}\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\right)\:=\:? \\ $$

Question Number 171435 Answers: 1 Comments: 7

Let f:R→R be polynomial function satisfying f(x) f((1/x))=f(x)+f((1/x)) and f(3)=28, then f(x) is

$$\:\:{Let}\:{f}:{R}\rightarrow{R}\:{be}\:{polynomial} \\ $$$$\:{function}\:{satisfying}\: \\ $$$$\:{f}\left({x}\right)\:{f}\left(\frac{\mathrm{1}}{{x}}\right)={f}\left({x}\right)+{f}\left(\frac{\mathrm{1}}{{x}}\right)\:{and} \\ $$$$\:{f}\left(\mathrm{3}\right)=\mathrm{28},\:{then}\:{f}\left({x}\right)\:{is} \\ $$

Question Number 170473 Answers: 0 Comments: 0

Question Number 169987 Answers: 1 Comments: 0

Question Number 169932 Answers: 0 Comments: 0

if x+(1/x)=cosθ find x^n +(1/x^n ) interm of θ

$${if}\:{x}+\frac{\mathrm{1}}{{x}}={cos}\theta\:\:{find} \\ $$$${x}^{{n}} +\frac{\mathrm{1}}{{x}^{{n}} }\:{interm}\:{of}\:\theta \\ $$

Question Number 169922 Answers: 1 Comments: 0

Let f(x)=((2x−7)/(x+1)) . Compute f^(1989) (x). note f^2 (x)= f(f(x))

$$\:\:{Let}\:{f}\left({x}\right)=\frac{\mathrm{2}{x}−\mathrm{7}}{{x}+\mathrm{1}}\:.\:{Compute}\:{f}^{\mathrm{1989}} \left({x}\right). \\ $$$$\:{note}\:{f}^{\mathrm{2}} \left({x}\right)=\:{f}\left({f}\left({x}\right)\right) \\ $$

Question Number 168800 Answers: 0 Comments: 1

If the function f is continuous in [a,b] express lim_(n→∞) (1/n)Σ_(k=1) ^n f((k/n)) as a definite integral.

$$\mathrm{If}\:\mathrm{the}\:\mathrm{function}\:{f}\:\mathrm{is}\:\mathrm{continuous}\:\mathrm{in}\:\left[{a},{b}\right] \\ $$$$\mathrm{express}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{{n}}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{f}\left(\frac{{k}}{{n}}\right)\:\mathrm{as}\:\mathrm{a}\:\mathrm{definite} \\ $$$$\mathrm{integral}. \\ $$

Question Number 167819 Answers: 0 Comments: 0

let f(x)=e^(−x) arctan(2x) find f^((n)) (0)

$${let}\:{f}\left({x}\right)={e}^{−{x}} {arctan}\left(\mathrm{2}{x}\right) \\ $$$${find}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$

Question Number 167003 Answers: 1 Comments: 0

Σ_(n=2) ^(n=∞) ((3/4))^n cos (180°n)= ?

$$\:\:\:\:\:\underset{\mathrm{n}=\mathrm{2}} {\overset{\mathrm{n}=\infty} {\sum}}\left(\frac{\mathrm{3}}{\mathrm{4}}\right)^{\mathrm{n}} \mathrm{cos}\:\left(\mathrm{180}°\mathrm{n}\right)=\:? \\ $$

Question Number 165870 Answers: 1 Comments: 0

f(x^2 − 3) = (√(x − 5)), f((√(21))) = ?

$$\: \\ $$$$\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:−\:\mathrm{3}\right)\:=\:\sqrt{\boldsymbol{\mathrm{x}}\:−\:\mathrm{5}},\:\:\boldsymbol{\mathrm{f}}\left(\sqrt{\mathrm{21}}\right)\:=\:? \\ $$$$\: \\ $$

Question Number 165848 Answers: 1 Comments: 0

f((1/x))+f(1−x)=x f(x)=?

$$\:{f}\left(\frac{\mathrm{1}}{{x}}\right)+{f}\left(\mathrm{1}−{x}\right)={x} \\ $$$$\:\:{f}\left({x}\right)=? \\ $$

Question Number 165160 Answers: 1 Comments: 0

f(x+f(x))=3f(x) and f(−1)=7 faind f(27)=?

$${f}\left({x}+{f}\left({x}\right)\right)=\mathrm{3}{f}\left({x}\right)\:\:\:{and}\:{f}\left(−\mathrm{1}\right)=\mathrm{7} \\ $$$${faind}\:\:{f}\left(\mathrm{27}\right)=? \\ $$

Question Number 164874 Answers: 1 Comments: 0

Question Number 164770 Answers: 2 Comments: 0

{ ((f(3x−1)+g(6x−1)=3x)),((f(x+1)+x g(2x+3)=2x^2 +x)) :} f(x)=?

$$\begin{cases}{{f}\left(\mathrm{3}{x}−\mathrm{1}\right)+{g}\left(\mathrm{6}{x}−\mathrm{1}\right)=\mathrm{3}{x}}\\{{f}\left({x}+\mathrm{1}\right)+{x}\:{g}\left(\mathrm{2}{x}+\mathrm{3}\right)=\mathrm{2}{x}^{\mathrm{2}} +{x}}\end{cases} \\ $$$$\:{f}\left({x}\right)=? \\ $$

Question Number 164176 Answers: 2 Comments: 0

Question Number 163720 Answers: 1 Comments: 0

∫_2 ^( 4) ((√(ln(9−x)))/( (√(ln(9−x)))+(√(ln(3+x))))) dx

$$\int_{\mathrm{2}} ^{\:\mathrm{4}} \frac{\sqrt{{ln}\left(\mathrm{9}−{x}\right)}}{\:\sqrt{{ln}\left(\mathrm{9}−{x}\right)}+\sqrt{{ln}\left(\mathrm{3}+{x}\right)}}\:{dx} \\ $$$$ \\ $$

Question Number 163508 Answers: 0 Comments: 0

etudier la continuite de [ x ] − (√(x − [ x ]))

$${etudier}\:{la}\:{continuite}\:{de}\:\left[\:{x}\:\right]\:−\:\sqrt{{x}\:−\:\left[\:{x}\:\right]} \\ $$

Question Number 162823 Answers: 2 Comments: 0

Given: x.p(x−1)=(x−5).p(x) and p(−1)=1. Find p((1/2)).

$$\:\:{Given}:\:\:{x}.{p}\left({x}−\mathrm{1}\right)=\left({x}−\mathrm{5}\right).{p}\left({x}\right) \\ $$$$\:\:{and}\:{p}\left(−\mathrm{1}\right)=\mathrm{1}.\: \\ $$$$\:\:{Find}\:{p}\left(\frac{\mathrm{1}}{\mathrm{2}}\right). \\ $$

Question Number 162509 Answers: 0 Comments: 0

find Σ_(n=1) ^∞ (((−1)^n )/(n^3 (2n+1)^4 ))

$$\mathrm{find}\:\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{n}^{\mathrm{3}} \left(\mathrm{2n}+\mathrm{1}\right)^{\mathrm{4}} } \\ $$

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