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Question Number 106032 Answers: 0 Comments: 2

Version 2.127 is added. • automatically scroll hine in horizontal direction (requested by Mr W) • automatically scrolls to new line to bring newly added line in focus.

$$\mathrm{Version}\:\mathrm{2}.\mathrm{127}\:\mathrm{is}\:\mathrm{added}. \\ $$$$\bullet\:\mathrm{automatically}\:\mathrm{scroll}\:\mathrm{hine}\:\mathrm{in}\:\mathrm{horizontal} \\ $$$$\:\:\:\mathrm{direction}\:\left(\mathrm{requested}\:\mathrm{by}\:\mathrm{Mr}\:\mathrm{W}\right) \\ $$$$\bullet\:\mathrm{automatically}\:\mathrm{scrolls}\:\mathrm{to}\:\mathrm{new}\:\mathrm{line}\:\mathrm{to} \\ $$$$\:\:\:\mathrm{bring}\:\mathrm{newly}\:\mathrm{added}\:\mathrm{line}\:\mathrm{in}\:\mathrm{focus}. \\ $$

Question Number 106029 Answers: 1 Comments: 1

Question Number 106024 Answers: 2 Comments: 1

log _4 (5x−6).log _x (256)=8

$$\mathrm{log}\:_{\mathrm{4}} \left(\mathrm{5x}−\mathrm{6}\right).\mathrm{log}\:_{\mathrm{x}} \left(\mathrm{256}\right)=\mathrm{8} \\ $$

Question Number 106023 Answers: 1 Comments: 2

Given that f(0)≠0 for all x,y∈R; 2f(x)f(y)=f(x+y)+f(x−y), express f(2x) in term of f(x).

$$\mathrm{Given}\:\mathrm{that}\:\mathrm{f}\left(\mathrm{0}\right)\neq\mathrm{0}\:\mathrm{for}\:\mathrm{all}\:\mathrm{x},\mathrm{y}\in\mathbb{R}; \\ $$$$\mathrm{2f}\left(\mathrm{x}\right)\mathrm{f}\left(\mathrm{y}\right)=\mathrm{f}\left(\mathrm{x}+\mathrm{y}\right)+\mathrm{f}\left(\mathrm{x}−\mathrm{y}\right),\: \\ $$$$\mathrm{express}\:\mathrm{f}\left(\mathrm{2x}\right)\:\mathrm{in}\:\mathrm{term}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x}\right). \\ $$

Question Number 106022 Answers: 0 Comments: 0

Question Number 106019 Answers: 1 Comments: 0

Question Number 106010 Answers: 1 Comments: 0

∫ ((1+x+x^2 )/(x^2 (x+1))) dx

$$\int\:\frac{\mathrm{1}+{x}+{x}^{\mathrm{2}} }{{x}^{\mathrm{2}} \left({x}+\mathrm{1}\right)}\:{dx}\: \\ $$

Question Number 106017 Answers: 1 Comments: 0

Determine x & y, such that: lcm(x,y)−gcd(x,y)=x+y.

$$\mathcal{D}{etermine}\:{x}\:\&\:{y},\:{such}\:{that}: \\ $$$$\mathrm{lcm}\left({x},{y}\right)−\mathrm{gcd}\left({x},{y}\right)={x}+{y}. \\ $$

Question Number 106005 Answers: 3 Comments: 0

(1) y′ = ((y−2x)/(2y+x)) (2) lim_(x→0) ((2^x −cos x)/(sin x))

$$\left(\mathrm{1}\right)\:\mathrm{y}'\:=\:\frac{\mathrm{y}−\mathrm{2x}}{\mathrm{2y}+\mathrm{x}} \\ $$$$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2}^{\mathrm{x}} −\mathrm{cos}\:\mathrm{x}}{\mathrm{sin}\:\mathrm{x}} \\ $$

Question Number 106001 Answers: 2 Comments: 0

Question Number 105994 Answers: 1 Comments: 1

Given { ((2log _5 (x+2)−log _5 (y)+(1/2)=0)),((log _5 (x^2 +2x−2)=0 )) :} find the value of y

$$\mathbb{G}{iven}\:\begin{cases}{\mathrm{2log}\:_{\mathrm{5}} \left({x}+\mathrm{2}\right)−\mathrm{log}\:_{\mathrm{5}} \left({y}\right)+\frac{\mathrm{1}}{\mathrm{2}}=\mathrm{0}}\\{\mathrm{log}\:_{\mathrm{5}} \left({x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{2}\right)=\mathrm{0}\:}\end{cases} \\ $$$${find}\:{the}\:{value}\:{of}\:{y}\: \\ $$

Question Number 105992 Answers: 1 Comments: 0

Question Number 105990 Answers: 1 Comments: 0

lim_(x→0) (cosec^2 2x − (1/(4x^2 ))) = ?

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

Question Number 105985 Answers: 1 Comments: 0

Question Number 105983 Answers: 1 Comments: 1

∫ ((sin x dx)/(6−sin^2 x)) ?

$$\int\:\frac{\mathrm{sin}\:{x}\:{dx}}{\mathrm{6}−\mathrm{sin}\:^{\mathrm{2}} {x}}\:?\:\: \\ $$

Question Number 105969 Answers: 3 Comments: 0

∫((sinx+cosx)/(√(1+sin2x)))dx

$$\int\frac{\mathrm{sinx}+\mathrm{cosx}}{\sqrt{\mathrm{1}+\mathrm{sin2x}}}\mathrm{dx} \\ $$

Question Number 105952 Answers: 2 Comments: 0

Question Number 105951 Answers: 2 Comments: 0

Question Number 105949 Answers: 1 Comments: 0

∫arctan((t^2 −1)(√𝛃))dt=?

$$\int\boldsymbol{{arctan}}\left(\left(\boldsymbol{{t}}^{\mathrm{2}} −\mathrm{1}\right)\sqrt{\boldsymbol{\beta}}\right)\boldsymbol{{dt}}=? \\ $$

Question Number 105943 Answers: 3 Comments: 0

∫ln(1+𝛂(√(x^2 −1)))dx=?

$$\:\:\:\:\:\int\boldsymbol{{ln}}\left(\mathrm{1}+\boldsymbol{\alpha}\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}\right)\mathrm{dx}=? \\ $$

Question Number 105940 Answers: 1 Comments: 0

∫_0 ^1 log(tanθ)dθ

$$\int_{\mathrm{0}} ^{\mathrm{1}} {log}\left({tan}\theta\right){d}\theta \\ $$

Question Number 105934 Answers: 1 Comments: 0

A box contains 12 balls numbered from 1 to 12. 4 balls are selected successively without replacement. Given “X” the variable “the number of even numbered balls selected”. Determine the probability type/law of X.

$$\mathrm{A}\:\mathrm{box}\:\mathrm{contains}\:\mathrm{12}\:\mathrm{balls}\:\mathrm{numbered}\:\mathrm{from}\:\mathrm{1}\:\mathrm{to}\:\mathrm{12}.\:\mathrm{4}\:\mathrm{balls} \\ $$$$\mathrm{are}\:\mathrm{selected}\:\mathrm{successively}\:\mathrm{without}\:\mathrm{replacement}.\:\mathrm{Given} \\ $$$$``\mathrm{X}''\:\mathrm{the}\:\mathrm{variable}\:``\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{even}\:\mathrm{numbered}\:\mathrm{balls} \\ $$$$\mathrm{selected}''.\:\mathrm{Determine}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{type}/\mathrm{law}\:\mathrm{of}\:\mathrm{X}. \\ $$

Question Number 105929 Answers: 1 Comments: 0

Question Number 105927 Answers: 3 Comments: 2

((x/(x−2)))^2 +((x/(x+2)))^2 = 2

$$\left(\frac{{x}}{{x}−\mathrm{2}}\right)^{\mathrm{2}} +\left(\frac{{x}}{{x}+\mathrm{2}}\right)^{\mathrm{2}} =\:\mathrm{2}\: \\ $$

Question Number 105925 Answers: 0 Comments: 1

Question Number 105945 Answers: 1 Comments: 0

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