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Relation and FunctionsQuestion and Answers: Page 14

Question Number 139029 Answers: 2 Comments: 0

Given f(x+(√(1+x^2 )))= (x/(x+1)) find f(x)=?

$$\mathrm{Given}\:\mathrm{f}\left(\mathrm{x}+\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\right)=\:\frac{\mathrm{x}}{\mathrm{x}+\mathrm{1}} \\ $$$$\mathrm{find}\:\mathrm{f}\left(\mathrm{x}\right)=? \\ $$

Question Number 138829 Answers: 1 Comments: 0

Question Number 138134 Answers: 0 Comments: 0

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

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

Question Number 137817 Answers: 1 Comments: 0

Let f(x)=x^2 −2x−3; x≥1 & g(x)=1+(√(x+4)) ; x≥−4 then the number of real solutions of equation f(x)=g(x) is ...

$${Let}\:{f}\left({x}\right)={x}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{3};\:{x}\geqslant\mathrm{1}\:\& \\ $$$${g}\left({x}\right)=\mathrm{1}+\sqrt{{x}+\mathrm{4}}\:;\:{x}\geqslant−\mathrm{4}\:{then} \\ $$$${the}\:{number}\:{of}\:{real}\:{solutions} \\ $$$${of}\:{equation}\:{f}\left({x}\right)={g}\left({x}\right)\:{is}\:... \\ $$

Question Number 137365 Answers: 2 Comments: 0

Given f(x^2 +x)+2f(x^2 −3x+2)= 9x^2 −15x find the value of f(2017).

$${Given}\:{f}\left({x}^{\mathrm{2}} +{x}\right)+\mathrm{2}{f}\left({x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}\right)=\:\mathrm{9}{x}^{\mathrm{2}} −\mathrm{15}{x} \\ $$$${find}\:{the}\:{value}\:{of}\:{f}\left(\mathrm{2017}\right). \\ $$

Question Number 137335 Answers: 1 Comments: 0

P(x) = 3x^75 + 2x^14 - 3x^2 - 1. What is the remainder when the above polynomial of s divided by x^2+x+1?

$$ \\ $$P(x) = 3x^75 + 2x^14 - 3x^2 - 1. What is the remainder when the above polynomial of s divided by x^2+x+1?

Question Number 137282 Answers: 2 Comments: 0

Question Number 137280 Answers: 2 Comments: 0

Question Number 136861 Answers: 1 Comments: 0

Given f((√(x+9)) )= 5x and f(a)=4a^2 find the possible value of a.

$$\mathrm{Given}\:\mathrm{f}\left(\sqrt{\mathrm{x}+\mathrm{9}}\:\right)=\:\mathrm{5x}\:\mathrm{and}\:\mathrm{f}\left(\mathrm{a}\right)=\mathrm{4a}^{\mathrm{2}} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{possible}\:\mathrm{value}\:\mathrm{of}\:\mathrm{a}. \\ $$$$ \\ $$

Question Number 136740 Answers: 1 Comments: 0

Given f(2f^(−1) (x))= (x/(2−x)) . what is f(x) ?

$$\:\mathrm{Given}\:\mathrm{f}\left(\mathrm{2f}^{−\mathrm{1}} \left(\mathrm{x}\right)\right)=\:\frac{\mathrm{x}}{\mathrm{2}−\mathrm{x}}\:. \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{f}\left(\mathrm{x}\right)\:? \\ $$

Question Number 136693 Answers: 2 Comments: 1

Question Number 136598 Answers: 1 Comments: 0

Question Number 136404 Answers: 1 Comments: 0

calculate Σ_(n=0) ^∞ ((n(−1)^n )/((2n+1)^2 (n+3)))

$$\mathrm{calculate}\:\sum_{\mathrm{n}=\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{n}\left(−\mathrm{1}\right)^{\mathrm{n}} }{\left(\mathrm{2n}+\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{n}+\mathrm{3}\right)} \\ $$

Question Number 136370 Answers: 1 Comments: 0

letf(x)=x^3 arctan((π/x)) 1) calculate f^((n)) (x) 2)calculate f^((n)) (1) 3) developp f at integer serie

$$\mathrm{letf}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{3}} \:\mathrm{arctan}\left(\frac{\pi}{\mathrm{x}}\right) \\ $$$$\left.\mathrm{1}\right)\:\mathrm{calculate}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{x}\right) \\ $$$$\left.\mathrm{2}\right)\mathrm{calculate}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{1}\right) \\ $$$$\left.\mathrm{3}\right)\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integer}\:\mathrm{serie} \\ $$

Question Number 136270 Answers: 1 Comments: 0

What is range of function f(x)=(x+1)(x+2)(x+3)(x+4)+1 where x ∈ [ −1, 1 ]

$$\mathrm{What}\:\mathrm{is}\:\mathrm{range}\:\mathrm{of}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)=\left(\mathrm{x}+\mathrm{1}\right)\left(\mathrm{x}+\mathrm{2}\right)\left(\mathrm{x}+\mathrm{3}\right)\left(\mathrm{x}+\mathrm{4}\right)+\mathrm{1} \\ $$$$\mathrm{where}\:\mathrm{x}\:\in\:\left[\:−\mathrm{1},\:\mathrm{1}\:\right] \\ $$

Question Number 136259 Answers: 1 Comments: 0

Given 2f(x)+f((1/x))=6x+(3/x) then ∫_1 ^( 2) f(x)dx=?

$${Given}\:\mathrm{2}{f}\left({x}\right)+{f}\left(\frac{\mathrm{1}}{{x}}\right)=\mathrm{6}{x}+\frac{\mathrm{3}}{{x}} \\ $$$${then}\:\int_{\mathrm{1}} ^{\:\mathrm{2}} {f}\left({x}\right){dx}=? \\ $$

Question Number 136124 Answers: 1 Comments: 0

Given a quadratic function f(x) =3-4k-(k+3) x-x^2, where k is a constant, is always negative when p

$$ \\ $$Given a quadratic function f(x) =3-4k-(k+3) x-x^2, where k is a constant, is always negative when p<k<q. What is the value of p and q?

Question Number 136033 Answers: 0 Comments: 0

explicite f(t)=∫_0 ^∞ (e^(−t(1+x^2 )) /(1+x^2 ))dx with t≥0

$$\mathrm{explicite}\:\mathrm{f}\left(\mathrm{t}\right)=\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{e}^{−\mathrm{t}\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)} }{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx}\:\:\mathrm{with}\:\mathrm{t}\geqslant\mathrm{0} \\ $$

Question Number 136032 Answers: 0 Comments: 0

proof the existence of x_1 ,x_2 ,....x_n integr natural / (1/x_1 )+(1/x_2 )+...+(1/x_n ) =1 with x_i ≠x_j for i≠j

$$\mathrm{proof}\:\mathrm{the}\:\mathrm{existence}\:\mathrm{of}\:\:\mathrm{x}_{\mathrm{1}} ,\mathrm{x}_{\mathrm{2}} ,....\mathrm{x}_{\mathrm{n}} \:\mathrm{integr}\:\mathrm{natural}\:/ \\ $$$$\frac{\mathrm{1}}{\mathrm{x}_{\mathrm{1}} }+\frac{\mathrm{1}}{\mathrm{x}_{\mathrm{2}} }+...+\frac{\mathrm{1}}{\mathrm{x}_{\mathrm{n}} }\:=\mathrm{1}\:\:\mathrm{with}\:\mathrm{x}_{\mathrm{i}} \neq\mathrm{x}_{\mathrm{j}} \:\mathrm{for}\:\mathrm{i}\neq\mathrm{j} \\ $$

Question Number 136031 Answers: 2 Comments: 0

study the sequence U_n =(√((1+u_(n−1) )/2)) with u_0 =(1/2) and determine lim_(n→+∞) U_n

$$\mathrm{study}\:\mathrm{the}\:\mathrm{sequence}\:\:\mathrm{U}_{\mathrm{n}} =\sqrt{\frac{\mathrm{1}+\mathrm{u}_{\mathrm{n}−\mathrm{1}} }{\mathrm{2}}} \\ $$$$\mathrm{with}\:\mathrm{u}_{\mathrm{0}} =\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{and}\:\mathrm{determine}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \mathrm{U}_{\mathrm{n}} \\ $$

Question Number 136030 Answers: 1 Comments: 0

solve y^((3)) −2y^((2)) +y =x−sinx

$$\mathrm{solve}\:\mathrm{y}^{\left(\mathrm{3}\right)} −\mathrm{2y}^{\left(\mathrm{2}\right)} \:+\mathrm{y}\:=\mathrm{x}−\mathrm{sinx} \\ $$

Question Number 136029 Answers: 1 Comments: 0

calculate lim_(x→0) ((ln((x/(sinx))))/x^2 )

$$\mathrm{calculate}\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{0}} \:\frac{\mathrm{ln}\left(\frac{\mathrm{x}}{\mathrm{sinx}}\right)}{\mathrm{x}^{\mathrm{2}} } \\ $$

Question Number 136028 Answers: 0 Comments: 0

let f(x)=e^(−x) arctan(x−(1/x)) calculate f^((n)) (1)

$$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{e}^{−\mathrm{x}} \mathrm{arctan}\left(\mathrm{x}−\frac{\mathrm{1}}{\mathrm{x}}\right) \\ $$$$\mathrm{calculate}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{1}\right) \\ $$

Question Number 136025 Answers: 0 Comments: 0

sove y^(′′) +2y−2 =xe^(−x) sin(2x) with y(0)=1 and y^′ (0)=−1

$$\mathrm{sove}\:\mathrm{y}^{''} +\mathrm{2y}−\mathrm{2}\:=\mathrm{xe}^{−\mathrm{x}} \mathrm{sin}\left(\mathrm{2x}\right)\:\:\mathrm{with}\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{1}\:\mathrm{and}\:\mathrm{y}^{'} \left(\mathrm{0}\right)=−\mathrm{1} \\ $$

Question Number 136024 Answers: 0 Comments: 1

1) decompose F(x)=((x^2 −3)/((x^2 +1)^2 (x−2)^3 )) 2)determine ∫ F(x)dx

$$\left.\mathrm{1}\right)\:\mathrm{decompose}\:\mathrm{F}\left(\mathrm{x}\right)=\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{3}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{x}−\mathrm{2}\right)^{\mathrm{3}} } \\ $$$$\left.\mathrm{2}\right)\mathrm{determine}\:\int\:\mathrm{F}\left(\mathrm{x}\right)\mathrm{dx} \\ $$

Question Number 136022 Answers: 0 Comments: 0

1)decompose inside C(x) the fraction F(x)=(1/((x^2 +1)^n )) 2) find ∫_1 ^∞ (dx/((x^2 +1)^n ))

$$\left.\mathrm{1}\right)\mathrm{decompose}\:\mathrm{inside}\:\mathrm{C}\left(\mathrm{x}\right)\:\mathrm{the}\:\mathrm{fraction}\:\mathrm{F}\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{n}} } \\ $$$$\left.\mathrm{2}\right)\:\mathrm{find}\:\int_{\mathrm{1}} ^{\infty} \:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{n}} } \\ $$

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