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AllQuestion and Answers: Page 503

Question Number 169259 Answers: 0 Comments: 1

Question Number 169251 Answers: 1 Comments: 0

calculate C=∫(dt/(1+tan^2 (t))) using x=tan(t)

$${calculate}\:{C}=\int\frac{{dt}}{\mathrm{1}+{tan}^{\mathrm{2}} \left({t}\right)}\:{using}\:{x}={tan}\left({t}\right) \\ $$

Question Number 169250 Answers: 1 Comments: 1

Calculate B=∫(1/(1+sin(x)))dx using u=tan((x/2))

$${Calculate}\:{B}=\int\frac{\mathrm{1}}{\mathrm{1}+{sin}\left({x}\right)}{dx}\:{using}\:{u}={tan}\left(\frac{{x}}{\mathrm{2}}\right) \\ $$

Question Number 169249 Answers: 0 Comments: 1

calculate A=∫(dt/(sin(t))) by using u=cos(t)

$${calculate}\:{A}=\int\frac{{dt}}{{sin}\left({t}\right)}\:{by}\:{using} \\ $$$${u}={cos}\left({t}\right) \\ $$

Question Number 169242 Answers: 2 Comments: 0

Question Number 169239 Answers: 1 Comments: 4

Question Number 169230 Answers: 1 Comments: 0

Question Number 169226 Answers: 0 Comments: 0

Question Number 169211 Answers: 1 Comments: 5

Question Number 169210 Answers: 0 Comments: 0

Question Number 169235 Answers: 0 Comments: 4

Question Number 169233 Answers: 0 Comments: 0

Question Number 169205 Answers: 0 Comments: 0

(√(91))

$$\sqrt{\mathrm{91}} \\ $$

Question Number 169204 Answers: 1 Comments: 2

if lim_(x→1) ((x^2 −ax+b)/(x−1))=5 faind volve of a+b=?

$${if}\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{{x}^{\mathrm{2}} −{ax}+{b}}{{x}−\mathrm{1}}=\mathrm{5} \\ $$$${faind}\:{volve}\:{of}\:{a}+{b}=? \\ $$$$ \\ $$

Question Number 169200 Answers: 2 Comments: 0

Question Number 169196 Answers: 0 Comments: 3

Question Number 169195 Answers: 0 Comments: 0

Question Number 169191 Answers: 0 Comments: 0

Calculate :: lim_(x→−1^+ ) ((1/((π−arccos x)^2 ))−(1/(2(1+x))))=?

$$\mathrm{Calculate}\:\:::\:\underset{\mathrm{x}\rightarrow−\mathrm{1}^{+} } {\mathrm{lim}}\left(\frac{\mathrm{1}}{\left(\pi−\mathrm{arccos}\:\mathrm{x}\right)^{\mathrm{2}} }−\frac{\mathrm{1}}{\mathrm{2}\left(\mathrm{1}+\mathrm{x}\right)}\right)=? \\ $$

Question Number 169169 Answers: 0 Comments: 3

Question Number 169166 Answers: 1 Comments: 4

find for arbitrary α≥0 the limit lim_(n→+∞) (((1^α +2^α +3^α +......n^α )/n^α )−(n/(1+α)))

$$\:\:\:\:\:\:\:\:\mathrm{find}\:\mathrm{for}\:\mathrm{arbitrary}\:\alpha\geqslant\mathrm{0}\:\mathrm{the}\:\mathrm{limit}\: \\ $$$$\:\:\:\underset{\boldsymbol{\mathrm{n}}\rightarrow+\infty} {\mathrm{lim}}\:\left(\frac{\mathrm{1}^{\alpha} +\mathrm{2}^{\alpha} +\mathrm{3}^{\alpha} +......\mathrm{n}^{\alpha} }{\mathrm{n}^{\alpha} }−\frac{\mathrm{n}}{\mathrm{1}+\alpha}\right) \\ $$

Question Number 169164 Answers: 1 Comments: 2

Question Number 169159 Answers: 1 Comments: 1

The remainder of 13^(13) when divided by 99 is

$${The}\:{remainder}\:{of} \\ $$$$\mathrm{13}^{\mathrm{13}} {when}\: \\ $$$${divided}\:{by}\:\mathrm{99}\:{is} \\ $$

Question Number 169257 Answers: 0 Comments: 0

Question Number 169256 Answers: 0 Comments: 0

Question Number 169253 Answers: 1 Comments: 0

∫((−sinx)/e^x )dx Mastermind

$$\int\frac{−{sinx}}{{e}^{{x}} }{dx} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 169155 Answers: 0 Comments: 0

(3) Consider the boundary−value problem y′′+2y′+2y=0, y(a)=c, y(b)=d. (i) if this problem has a unique solution, how are a and b related? (ii) if this problem has no solution, how are a,b,c and d related?

$$\left(\mathrm{3}\right)\:\:{Consider}\:{the}\:{boundary}−{value}\: \\ $$$${problem}\:{y}''+\mathrm{2}{y}'+\mathrm{2}{y}=\mathrm{0},\:{y}\left({a}\right)={c}, \\ $$$${y}\left({b}\right)={d}.\:\left({i}\right)\:{if}\:{this}\:{problem}\:{has}\:{a}\: \\ $$$${unique}\:{solution},\:{how}\:{are}\:{a}\:{and}\:{b}\: \\ $$$${related}?\:\left({ii}\right)\:{if}\:{this}\:{problem}\:{has}\:{no} \\ $$$${solution},\:{how}\:{are}\:{a},{b},{c}\:{and}\:{d}\:{related}? \\ $$

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