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Question Number 32584 Answers: 1 Comments: 0

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Question Number 32543 Answers: 1 Comments: 0

The coefficient of x^4 in the expansion of (1+5x+9x^2 +.....∞)(1+x^2 )^(11) is a) 171 b) 172 c) 173 d) 176

$$\boldsymbol{{T}}{he}\:{coefficient}\:{of}\:{x}^{\mathrm{4}} \:{in}\:{the}\:{expansion} \\ $$$${of}\:\left(\mathrm{1}+\mathrm{5}{x}+\mathrm{9}{x}^{\mathrm{2}} +.....\infty\right)\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{11}} {is} \\ $$$$\left.{a}\right)\:\mathrm{171} \\ $$$$\left.{b}\right)\:\mathrm{172} \\ $$$$\left.{c}\right)\:\mathrm{173} \\ $$$$\left.{d}\right)\:\mathrm{176} \\ $$

Question Number 32541 Answers: 2 Comments: 0

Coefficient of x^5 in the expansion of (x^2 −x−2)^5 is

$${Coefficient}\:{of}\:{x}^{\mathrm{5}} \:{in}\:{the}\:{expansion} \\ $$$${of}\:\left({x}^{\mathrm{2}} −{x}−\mathrm{2}\right)^{\mathrm{5}} \:{is} \\ $$

Question Number 32538 Answers: 1 Comments: 1

Question Number 32535 Answers: 0 Comments: 0

k ≤ 2018 f (f (n) ) = 2n f (k) = 2018 how many the possible of k integers ?

$${k}\:\:\leqslant\:\:\mathrm{2018} \\ $$$${f}\:\left({f}\:\left({n}\right)\:\right)\:\:=\:\:\mathrm{2}{n} \\ $$$${f}\:\left({k}\right)\:\:=\:\:\mathrm{2018} \\ $$$${how}\:\:{many}\:\:\:{the}\:{possible}\:{of}\:\:\:\boldsymbol{{k}}\:\:{integers}\:? \\ $$

Question Number 32534 Answers: 1 Comments: 0

Question Number 32532 Answers: 0 Comments: 3

If a,b,c are 3 positive numbers in an A.P and T= ((a+8b)/(2b−a))+((8b+c)/(2b−c)). Then the value of T^( 2 ) is ? Ans. given is 361.

$$\boldsymbol{{I}}{f}\:{a},{b},{c}\:{are}\:\mathrm{3}\:{positive}\:{numbers}\:{in}\:{an} \\ $$$$\boldsymbol{{A}}.\boldsymbol{{P}}\:{and}\: \\ $$$${T}=\:\frac{{a}+\mathrm{8}{b}}{\mathrm{2}{b}−{a}}+\frac{\mathrm{8}{b}+{c}}{\mathrm{2}{b}−{c}}. \\ $$$${Then}\:{the}\:{value}\:{of}\:{T}^{\:\:\mathrm{2}\:} \:{is}\:? \\ $$$${Ans}.\:{given}\:{is}\:\mathrm{361}. \\ $$

Question Number 32529 Answers: 1 Comments: 2

Question Number 32517 Answers: 0 Comments: 1

calculatelim_(x→0^+ ) ((x^(sinx) −(sinx)^x )/x) .

$${calculatelim}_{{x}\rightarrow\mathrm{0}^{+} } \:\:\frac{{x}^{{sinx}} \:\:−\left({sinx}\right)^{{x}} }{{x}}\:. \\ $$

Question Number 32510 Answers: 2 Comments: 1

Question Number 32508 Answers: 1 Comments: 0

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Question Number 32503 Answers: 0 Comments: 0

algebra1ic

$${algebra}\mathrm{1}{ic} \\ $$

Question Number 32501 Answers: 1 Comments: 0

(x−2y+3)^2 +(3x+4y−1)^2 =100 what is the area of the ellipse?

$$\left(\mathrm{x}−\mathrm{2y}+\mathrm{3}\right)^{\mathrm{2}} +\left(\mathrm{3x}+\mathrm{4y}−\mathrm{1}\right)^{\mathrm{2}} =\mathrm{100} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{ellipse}? \\ $$

Question Number 32500 Answers: 1 Comments: 0

proof: (−a)(−b)=ab

$${proof}:\:\left(−{a}\right)\left(−{b}\right)={ab} \\ $$

Question Number 32499 Answers: 2 Comments: 0

proof: a(−b)=(−a)b=−(ab)

$${proof}:\:{a}\left(−{b}\right)=\left(−{a}\right){b}=−\left({ab}\right) \\ $$

Question Number 32496 Answers: 0 Comments: 0

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Question Number 32490 Answers: 1 Comments: 0

if f(x)=∣x∣ and g(x)=2x−3.Find the domain of gof

$${if}\:{f}\left({x}\right)=\mid{x}\mid\:{and}\:{g}\left({x}\right)=\mathrm{2}{x}−\mathrm{3}.{Find} \\ $$$${the}\:{domain}\:{of}\:{gof} \\ $$

Question Number 32489 Answers: 1 Comments: 1

find the range of f(x)=1+(√(2x−1))

$${find}\:{the}\:{range}\:{of}\:{f}\left({x}\right)=\mathrm{1}+\sqrt{\mathrm{2}{x}−\mathrm{1}} \\ $$

Question Number 32487 Answers: 0 Comments: 0

let x>1 and ξ(x) =Σ_(n=1) ^∞ (1/n^x ) (zeta function of Rieman) 1) calculate lim_(x→+∞) ξ(x) 2)let consider s(x)=Σ_(n=2) ^∞ ((ξ(n))/n) x^n study the convergence of s(x) and find a simple form of s(x).

$${let}\:{x}>\mathrm{1}\:{and}\:\xi\left({x}\right)\:=\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\mathrm{1}}{{n}^{{x}} }\:\left({zeta}\:{function}\:{of}\:{Rieman}\right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{lim}_{{x}\rightarrow+\infty} \xi\left({x}\right) \\ $$$$\left.\mathrm{2}\right){let}\:{consider}\:\:{s}\left({x}\right)=\sum_{{n}=\mathrm{2}} ^{\infty} \:\:\frac{\xi\left({n}\right)}{{n}}\:{x}^{{n}} \:{study}\:{the}\:{convergence} \\ $$$${of}\:{s}\left({x}\right)\:{and}\:{find}\:{a}\:{simple}\:{form}\:{of}\:{s}\left({x}\right). \\ $$

Question Number 32486 Answers: 0 Comments: 1

find lim_(n→∞) Σ_(k=n+1) ^(2n) sin((1/k)).

$${find}\:{lim}_{{n}\rightarrow\infty} \:\:\:\sum_{{k}={n}+\mathrm{1}} ^{\mathrm{2}{n}} \:{sin}\left(\frac{\mathrm{1}}{{k}}\right). \\ $$

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