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AllQuestion and Answers: Page 177

Question Number 196489 Answers: 0 Comments: 0

Question Number 196487 Answers: 1 Comments: 0

∫(sec^4 x−cot^4 x)dx

$$\int\left(\mathrm{sec}\:^{\mathrm{4}} {x}−\mathrm{cot}\:^{\mathrm{4}} {x}\right){dx} \\ $$

Question Number 196486 Answers: 0 Comments: 0

Question Number 196485 Answers: 1 Comments: 1

Σ_(k=o) ^n (−1)^k =?

$$\underset{{k}={o}} {\overset{{n}} {\sum}}\left(−\mathrm{1}\right)^{{k}} \:=? \\ $$

Question Number 196483 Answers: 0 Comments: 0

Question Number 196471 Answers: 1 Comments: 0

lim_(n→∞) (1/n)((1/(2 + (1/n))) + (1/(2 + (2/n))) + (1/(2 + (3/n))) + .. + (1/(2 + (n/n))))

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}}{\mathrm{n}}\left(\frac{\mathrm{1}}{\mathrm{2}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{n}}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{2}\:\:+\:\:\frac{\mathrm{2}}{\mathrm{n}}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{2}\:\:+\:\:\frac{\mathrm{3}}{\mathrm{n}}}\:\:+\:\:..\:\:+\:\:\frac{\mathrm{1}}{\mathrm{2}\:\:+\:\:\frac{\mathrm{n}}{\mathrm{n}}}\right) \\ $$

Question Number 196467 Answers: 1 Comments: 0

Question Number 196490 Answers: 0 Comments: 1

Know: xf(x)−f′(x)=x^2 Find f(x)=¿

$${Know}:\:{xf}\left({x}\right)−{f}'\left({x}\right)={x}^{\mathrm{2}} \\ $$$${Find}\:{f}\left({x}\right)=¿ \\ $$

Question Number 196464 Answers: 1 Comments: 0

if f(x)= x^3 +x^2 , g(x)= f^(−1) (x) , find g^′ (3) ?

$${if}\:{f}\left({x}\right)=\:{x}^{\mathrm{3}} +{x}^{\mathrm{2}} \:\:,\:{g}\left({x}\right)=\:{f}^{−\mathrm{1}} \left({x}\right)\:,\:{find}\:{g}^{'} \left(\mathrm{3}\right)\:?\:\: \\ $$

Question Number 196460 Answers: 1 Comments: 5

Question Number 196459 Answers: 1 Comments: 0

Question Number 196458 Answers: 1 Comments: 0

Question Number 196447 Answers: 2 Comments: 0

n! = 2^(25) ×3^(13) ×5^6 ×7^4 ×11^2 ×13^2 ×17×19×23 n=?

$$\:\:\:\:\mathrm{n}!\:=\:\mathrm{2}^{\mathrm{25}} ×\mathrm{3}^{\mathrm{13}} ×\mathrm{5}^{\mathrm{6}} ×\mathrm{7}^{\mathrm{4}} ×\mathrm{11}^{\mathrm{2}} ×\mathrm{13}^{\mathrm{2}} ×\mathrm{17}×\mathrm{19}×\mathrm{23} \\ $$$$\:\:\:\mathrm{n}=? \\ $$

Question Number 196444 Answers: 0 Comments: 1

Question Number 196440 Answers: 1 Comments: 0

prove ∣v−w∣≥∣v∣−∣w∣

$${prove}\:\mid{v}−{w}\mid\geqslant\mid{v}\mid−\mid{w}\mid \\ $$

Question Number 196436 Answers: 1 Comments: 0

∫(dx/(x(x^n −1)))

$$\int\frac{{dx}}{{x}\left({x}^{{n}} −\mathrm{1}\right)} \\ $$

Question Number 196435 Answers: 0 Comments: 2

Question Number 196429 Answers: 1 Comments: 0

Question Number 196427 Answers: 2 Comments: 0

If f(x)=∫^( x) _( 0) (dt/(t+e^(−f(t)) )), determine f(x)

$$\mathrm{If}\:\:{f}\left({x}\right)=\underset{\:\mathrm{0}} {\int}^{\:{x}} \frac{{dt}}{{t}+{e}^{−{f}\left({t}\right)} },\:\mathrm{determine}\:{f}\left({x}\right) \\ $$

Question Number 196423 Answers: 0 Comments: 2

Consider a complex 4x4 full-rank matrix H. The QR decomposition and singular value decomposition of H are given by H=QR and H=ABC, respectively. The diagonal elements of B are (4,3,2,1). Find the diagonal elements of R if they are all non-negative and equal.

$$ \\ $$Consider a complex 4x4 full-rank matrix H. The QR decomposition and singular value decomposition of H are given by H=QR and H=ABC, respectively. The diagonal elements of B are (4,3,2,1). Find the diagonal elements of R if they are all non-negative and equal.

Question Number 196413 Answers: 0 Comments: 3

determiner a et b

$$\mathrm{determiner}\:\:\boldsymbol{\mathrm{a}}\:\mathrm{et}\:\boldsymbol{\mathrm{b}} \\ $$$$ \\ $$

Question Number 196450 Answers: 3 Comments: 0

one solution of the equation (x−a)(x−b)(x−c)(x−d) = 9 is x=2. If a,b,c,d are different integers then a+b+c+d =?

$$\mathrm{one}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\:\left(\mathrm{x}−\mathrm{a}\right)\left(\mathrm{x}−\mathrm{b}\right)\left(\mathrm{x}−\mathrm{c}\right)\left(\mathrm{x}−\mathrm{d}\right)\:=\:\mathrm{9}\: \\ $$$$\:\mathrm{is}\:\mathrm{x}=\mathrm{2}.\:\mathrm{If}\:\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d}\:\mathrm{are}\:\mathrm{different}\: \\ $$$$\:\mathrm{integers}\:\mathrm{then}\:\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}\:=?\: \\ $$

Question Number 196412 Answers: 1 Comments: 1

Prove that ∫^( +∞) _( i) (cos2t+isin2t)e^(−t^2 ) dt= ((√π)/(2e))

$$\mathrm{Prove}\:\mathrm{that}\:\underset{\:{i}} {\int}^{\:+\infty} \left(\mathrm{cos2t}+\mathrm{isin2t}\right)\mathrm{e}^{−\mathrm{t}^{\mathrm{2}} } \mathrm{dt}=\:\frac{\sqrt{\pi}}{\mathrm{2e}} \\ $$

Question Number 196419 Answers: 1 Comments: 1

calcul lim_(x→+∞) (1+(1/(f(x))))^(f(x))