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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?

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

Question Number 169182    Answers: 2   Comments: 1

lim_(x→π) ((πcos2x−x)/(1+cosx))=?

$$\underset{{x}\rightarrow\pi} {\mathrm{lim}}\frac{\pi{cos}\mathrm{2}{x}−{x}}{\mathrm{1}+{cosx}}=? \\ $$

Question Number 169148    Answers: 0   Comments: 2

lim_(x→π) ((πcos2x−1)/(1+cosx))=?

$$\underset{{x}\rightarrow\pi} {\mathrm{lim}}\frac{\pi{cos}\mathrm{2}{x}−\mathrm{1}}{\mathrm{1}+{cosx}}=? \\ $$

Question Number 169147    Answers: 0   Comments: 2

lim_(x→(π/3)) ((1−2cosx)/(sin(x−(π/3))))=?

$$\underset{{x}\rightarrow\frac{\pi}{\mathrm{3}}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{2}{cosx}}{{sin}\left({x}−\frac{\pi}{\mathrm{3}}\right)}=? \\ $$

Question Number 169145    Answers: 1   Comments: 0

ABC is a triangle in which the bisector of angle at B meet the side AC at D, and the bisector of the angle BDC is parallel to the side AB. Prove that the △ABC is issoceles triangle.

$$\boldsymbol{{ABC}}\:\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{triangle}}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{which}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{bisector}} \\ $$$$\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{angle}}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{{B}}\:\boldsymbol{\mathrm{meet}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{side}}\:\boldsymbol{{AC}}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{{D}}, \\ $$$$\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{bisector}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{angle}}\:\boldsymbol{{BDC}}\:\boldsymbol{\mathrm{is}} \\ $$$$\:\boldsymbol{\mathrm{parallel}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{side}}\:\boldsymbol{{AB}}.\:\boldsymbol{\mathrm{Prove}}\:\boldsymbol{\mathrm{that}} \\ $$$$\:\boldsymbol{\mathrm{the}}\:\bigtriangleup\boldsymbol{{ABC}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{issoceles}}\:\boldsymbol{\mathrm{triangle}}. \\ $$$$ \\ $$

Question Number 169142    Answers: 2   Comments: 1

Question Number 169140    Answers: 0   Comments: 0

Question Number 169139    Answers: 0   Comments: 3

Question Number 169138    Answers: 0   Comments: 0

Hello, please help me. calculate P= Π_(k=0) ^n cos(θk)

$${Hello},\:{please}\:{help}\:{me}. \\ $$$${calculate}\:{P}=\:\underset{{k}=\mathrm{0}} {\overset{{n}} {\prod}}{cos}\left(\theta{k}\right) \\ $$

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