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Question Number 110075 Answers: 2 Comments: 2

△((be)/(math))▽ (1)lim_(x→0) ((x.cos x−sin x)/(x^2 .sin x)) ? (2) find (dy/dx) from ((x+y)/(x−y)) = x^2 +y^2

$$\:\:\bigtriangleup\frac{{be}}{{math}}\bigtriangledown \\ $$$$\:\left(\mathrm{1}\right)\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}.\mathrm{cos}\:{x}−\mathrm{sin}\:{x}}{{x}^{\mathrm{2}} .\mathrm{sin}\:{x}}\:? \\ $$$$\left(\mathrm{2}\right)\:{find}\:\frac{{dy}}{{dx}}\:{from}\:\frac{{x}+{y}}{{x}−{y}}\:=\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \\ $$

Question Number 110072 Answers: 2 Comments: 0

△((be)/(math))▽ lim_(x→0) ((sin 2x+sin 6x+sin 10x−sin 18x)/(3sin x−sin 3x))=?

$$\:\:\:\bigtriangleup\frac{{be}}{{math}}\bigtriangledown \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:\mathrm{2}{x}+\mathrm{sin}\:\mathrm{6}{x}+\mathrm{sin}\:\mathrm{10}{x}−\mathrm{sin}\:\mathrm{18}{x}}{\mathrm{3sin}\:{x}−\mathrm{sin}\:\mathrm{3}{x}}=? \\ $$

Question Number 110027 Answers: 2 Comments: 0

Question Number 110018 Answers: 1 Comments: 0

find the domain f(x,y)=x^2 −y^2

$${find}\:{the}\:{domain}\:{f}\left({x},{y}\right)={x}^{\mathrm{2}} −{y}^{\mathrm{2}} \\ $$

Question Number 110016 Answers: 3 Comments: 0

The solution of the equation (x+1)+(x+4)+(x+7)+...+(x+28)=155 is given by x = _____.

$$\mathrm{The}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\left({x}+\mathrm{1}\right)+\left({x}+\mathrm{4}\right)+\left({x}+\mathrm{7}\right)+...+\left({x}+\mathrm{28}\right)=\mathrm{155} \\ $$$$\mathrm{is}\:\mathrm{given}\:\mathrm{by}\:{x}\:=\:\_\_\_\_\_. \\ $$

Question Number 110015 Answers: 2 Comments: 1

The cubes of the natural numbers are grouped as 1^3 , (2^3 , 3^3 ), (4^3 , 5^3 , 6^3 ), ...., then the sum of the numbers in the nth group is

$$\mathrm{The}\:\mathrm{cubes}\:\mathrm{of}\:\mathrm{the}\:\mathrm{natural}\:\mathrm{numbers}\:\mathrm{are} \\ $$$$\mathrm{grouped}\:\mathrm{as}\:\mathrm{1}^{\mathrm{3}} ,\:\left(\mathrm{2}^{\mathrm{3}} ,\:\mathrm{3}^{\mathrm{3}} \right),\:\left(\mathrm{4}^{\mathrm{3}} ,\:\mathrm{5}^{\mathrm{3}} ,\:\mathrm{6}^{\mathrm{3}} \right),\:...., \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{numbers}\:\mathrm{in}\:\mathrm{the}\:{n}\mathrm{th} \\ $$$$\mathrm{group}\:\mathrm{is} \\ $$

Question Number 109989 Answers: 1 Comments: 1

Question Number 109988 Answers: 0 Comments: 0

Question Number 109985 Answers: 0 Comments: 2

Question Number 109978 Answers: 1 Comments: 0

Question Number 109963 Answers: 1 Comments: 0

Question Number 138470 Answers: 1 Comments: 0

Given (Γ): x^4 −16(y^2 −2y)^2 =0 Show that (Γ) is a reunion of and Ellipsis and an hyperbole then give their equations.

$${Given}\:\left(\Gamma\right):\:{x}^{\mathrm{4}} −\mathrm{16}\left({y}^{\mathrm{2}} −\mathrm{2}{y}\right)^{\mathrm{2}} =\mathrm{0} \\ $$$${Show}\:{that}\:\left(\Gamma\right)\:{is}\:{a}\:{reunion}\:{of}\:\:{and}\: \\ $$$${Ellipsis}\:{and}\:{an}\:{hyperbole}\:{then}\:{give} \\ $$$${their}\:{equations}. \\ $$

Question Number 109955 Answers: 3 Comments: 0

what is the minimal period of cosx+cos3x

$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{minimal}\:\mathrm{period}\:\mathrm{of}\:\mathrm{cosx}+\mathrm{cos3x} \\ $$

Question Number 109954 Answers: 1 Comments: 0

!3=????

$$!\mathrm{3}=???? \\ $$

Question Number 109952 Answers: 1 Comments: 0

Question Number 109950 Answers: 2 Comments: 0

Question Number 109949 Answers: 1 Comments: 0

Question Number 109948 Answers: 1 Comments: 0

Question Number 109947 Answers: 0 Comments: 0

Question Number 109946 Answers: 0 Comments: 0

Question Number 109929 Answers: 0 Comments: 1

△((♭e)/(Math))▽ lim_(x→∞) (√(81x^2 −10x+1))−4x+3−(√(25x^2 −10x+1)) =?

$$\:\:\:\bigtriangleup\frac{\flat{e}}{\mathcal{M}{ath}}\bigtriangledown \\ $$$$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\sqrt{\mathrm{81}{x}^{\mathrm{2}} −\mathrm{10}{x}+\mathrm{1}}−\mathrm{4}{x}+\mathrm{3}−\sqrt{\mathrm{25}{x}^{\mathrm{2}} −\mathrm{10}{x}+\mathrm{1}}\:=? \\ $$

Question Number 110181 Answers: 0 Comments: 2

Given the equation of two circles C_1 : x^2 + y^2 −6x−4y + 9 = 0 andC_2 : x^2 +y^2 −2x−6y + 9 =0 find the equation of the common tangent to both circles.

$$\mathrm{Given}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{two}\:\mathrm{circles} \\ $$$${C}_{\mathrm{1}} :\:{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:−\mathrm{6}{x}−\mathrm{4}{y}\:+\:\mathrm{9}\:=\:\mathrm{0}\:\mathrm{and}{C}_{\mathrm{2}} \::\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{6}{y}\:+\:\mathrm{9}\:=\mathrm{0} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{common}\:\mathrm{tangent}\:\mathrm{to}\:\mathrm{both}\:\mathrm{circles}. \\ $$

Question Number 109922 Answers: 1 Comments: 0

Question Number 109923 Answers: 1 Comments: 0

find sin3 in surd form

$${find}\: \\ $$$${sin}\mathrm{3}\:\:\: \\ $$$${in}\:{surd}\:{form} \\ $$

Question Number 109914 Answers: 1 Comments: 0

Prove that tan142°30′+(√6)+(√3)−(√2) is an integer.

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{tan142}°\mathrm{30}'+\sqrt{\mathrm{6}}+\sqrt{\mathrm{3}}−\sqrt{\mathrm{2}} \\ $$$$\mathrm{is}\:\mathrm{an}\:\mathrm{integer}. \\ $$

Question Number 109913 Answers: 1 Comments: 0

((16))^(1/(x−1)) −5 (4)^(1/(x−1)) +2=0 find x?

$$\sqrt[{{x}−\mathrm{1}}]{\mathrm{16}}−\mathrm{5}\:\:\sqrt[{{x}−\mathrm{1}}]{\mathrm{4}}+\mathrm{2}=\mathrm{0}\:{find}\:{x}? \\ $$

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