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AllQuestion and Answers: Page 1128

Question Number 105609 Answers: 0 Comments: 0

Question Number 105605 Answers: 2 Comments: 0

prove by mathematical induction 2^3 +4^3 +6^3 +8^3 +...+(2n)^3 = 2n^2 (n+1)^2

$${prove}\:{by}\:{mathematical}\:{induction}\: \\ $$$$\mathrm{2}^{\mathrm{3}} +\mathrm{4}^{\mathrm{3}} +\mathrm{6}^{\mathrm{3}} +\mathrm{8}^{\mathrm{3}} +...+\left(\mathrm{2}{n}\right)^{\mathrm{3}} =\:\mathrm{2}{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)^{\mathrm{2}} \\ $$

Question Number 105603 Answers: 2 Comments: 0

(d^2 y/dx^2 )−4(dy/dx)+y = a sin 2x

$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }−\mathrm{4}\frac{{dy}}{{dx}}+{y}\:=\:{a}\:\mathrm{sin}\:\mathrm{2}{x} \\ $$

Question Number 105599 Answers: 1 Comments: 0

Question Number 105598 Answers: 1 Comments: 0

Question Number 105596 Answers: 0 Comments: 1

Question Number 105594 Answers: 0 Comments: 3

Question Number 105593 Answers: 2 Comments: 0

f(x)=(((√(2x+1))×(√(2x+1)))/(2x+1)) Dom_f =?

$${f}\left({x}\right)=\frac{\sqrt{\mathrm{2}{x}+\mathrm{1}}×\sqrt{\mathrm{2}{x}+\mathrm{1}}}{\mathrm{2}{x}+\mathrm{1}}\:\:\:\:\:\:{Dom}_{{f}} =? \\ $$

Question Number 105584 Answers: 1 Comments: 0

lim_(x→0) [csc^2 (2x)−(1/(4x^2 )) ]?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left[\mathrm{csc}^{\mathrm{2}} \left(\mathrm{2}{x}\right)−\frac{\mathrm{1}}{\mathrm{4}{x}^{\mathrm{2}} }\:\right]? \\ $$

Question Number 105575 Answers: 0 Comments: 0

Question Number 105574 Answers: 1 Comments: 0

∫ ((x−1)/(x+x^2 ln x)) dx ?

$$\int\:\frac{{x}−\mathrm{1}}{{x}+{x}^{\mathrm{2}} \mathrm{ln}\:{x}}\:{dx}\:?\: \\ $$

Question Number 105571 Answers: 4 Comments: 0

Σ_(n = 1) ^∞ (n/((n+1)(n+2)(n+3))) =?

$$\underset{{n}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\frac{{n}}{\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)\left({n}+\mathrm{3}\right)}\:=? \\ $$

Question Number 105569 Answers: 1 Comments: 0

x^2 (dy/dx) −3xy−2y^2 = 0

$${x}^{\mathrm{2}} \:\frac{{dy}}{{dx}}\:−\mathrm{3}{xy}−\mathrm{2}{y}^{\mathrm{2}} \:=\:\mathrm{0}\: \\ $$

Question Number 105566 Answers: 0 Comments: 0

let f(x) =(x+1)^(2n) e^(−x) sin(x) 1) calculate f^((n)) (x)and f^((n)) (0) 2)developp f at integr serie 3) find ∫ f(x)dx

$$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2n}} \:\mathrm{e}^{−\mathrm{x}} \mathrm{sin}\left(\mathrm{x}\right) \\ $$$$\left.\mathrm{1}\right)\:\mathrm{calculate}\:\mathrm{f}^{\left(\mathrm{n}\right)} \:\left(\mathrm{x}\right)\mathrm{and}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integr}\:\mathrm{serie} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{find}\:\int\:\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx} \\ $$

Question Number 105565 Answers: 1 Comments: 0

let f(x) =x^2 ln(1−x^3 ) 1) calculate f^((n)) (x) and f^((n)) (0) 2) developp f at integr serie 3)calculate ∫ f(x)dx

$$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{x}^{\mathrm{2}} \mathrm{ln}\left(\mathrm{1}−\mathrm{x}^{\mathrm{3}} \right) \\ $$$$\left.\mathrm{1}\right)\:\mathrm{calculate}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integr}\:\mathrm{serie} \\ $$$$\left.\mathrm{3}\right)\mathrm{calculate}\:\int\:\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx} \\ $$

Question Number 105564 Answers: 1 Comments: 0

Solve the differential equation; y′′+4y′+5y=xe^(−2x) sinx

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation}; \\ $$$$\mathrm{y}''+\mathrm{4y}'+\mathrm{5y}=\mathrm{xe}^{−\mathrm{2x}} \mathrm{sinx} \\ $$

Question Number 105551 Answers: 2 Comments: 0

In how many different ways can 10 students be divided into 3 groups?

$${In}\:{how}\:{many}\:{different}\:{ways}\:{can}\:\mathrm{10} \\ $$$${students}\:{be}\:{divided}\:{into}\:\mathrm{3}\:{groups}? \\ $$

Question Number 105545 Answers: 3 Comments: 0

calculate ∫_0 ^∞ ((sin x)/x)dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{sin}\:{x}}{{x}}{dx} \\ $$

Question Number 105544 Answers: 0 Comments: 0

Question Number 105536 Answers: 1 Comments: 0

Question Number 105534 Answers: 1 Comments: 2

Question Number 105526 Answers: 1 Comments: 0

(1/(1+2))+(1/(1+2+3))+(1/(1+2+3+4))+...+(1/(1+2+3+4+...+29))

$$\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}+\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}}+...+\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+...+\mathrm{29}} \\ $$

Question Number 105506 Answers: 0 Comments: 3

(−(1/2))+(+(3/7))+(−(1/(10)))=?

$$\left(−\frac{\mathrm{1}}{\mathrm{2}}\right)+\left(+\frac{\mathrm{3}}{\mathrm{7}}\right)+\left(−\frac{\mathrm{1}}{\mathrm{10}}\right)=? \\ $$

Question Number 105504 Answers: 9 Comments: 0

(1)lim_(x→0) ((∫_( 0) ^( x^2 ) sec^2 t dt)/(x sin x)) ? (2) ∫_(−π/2) ^(π/2) (√(sec x−cos x)) dx ? (3)In a triangle if tan A=2sin 2C and 3cos A=2sin Bsin C. find C

$$\left(\mathrm{1}\right)\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\int_{\:\mathrm{0}} ^{\:{x}^{\mathrm{2}} } \mathrm{sec}\:^{\mathrm{2}} {t}\:{dt}}{{x}\:\mathrm{sin}\:{x}}\:? \\ $$$$\left(\mathrm{2}\right)\:\underset{−\pi/\mathrm{2}} {\overset{\pi/\mathrm{2}} {\int}}\sqrt{\mathrm{sec}\:{x}−\mathrm{cos}\:{x}}\:{dx}\:? \\ $$$$\left(\mathrm{3}\right){In}\:{a}\:{triangle}\:{if}\:\mathrm{tan}\:{A}=\mathrm{2sin}\:\mathrm{2}{C} \\ $$$${and}\:\mathrm{3cos}\:{A}=\mathrm{2sin}\:{B}\mathrm{sin}\:{C}.\:{find}\:{C} \\ $$

Question Number 105498 Answers: 1 Comments: 3

lim_(n→∞) (Π_(k=1) ^n ((1/k)))^(2/n)

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}\left(\frac{\mathrm{1}}{{k}}\right)\right)^{\frac{\mathrm{2}}{{n}}} \\ $$

Question Number 105493 Answers: 0 Comments: 0

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