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Question Number 87245 Answers: 0 Comments: 12

expand (1+x)^(−1) using maclaurins theorem and talyors formula

$${expand}\: \\ $$$$\left(\mathrm{1}+{x}\right)^{−\mathrm{1}} \\ $$$${using}\:{maclaurins} \\ $$$${theorem}\:{and}\:{talyors} \\ $$$${formula} \\ $$

Question Number 87194 Answers: 2 Comments: 6

find the solution of ((∣ log_2 (x)+2∣)/(x−3)) < 2

$$\mathrm{find}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{of}\: \\ $$$$\frac{\mid\:\mathrm{log}_{\mathrm{2}} \left(\mathrm{x}\right)+\mathrm{2}\mid}{\mathrm{x}−\mathrm{3}}\:<\:\mathrm{2}\: \\ $$

Question Number 87179 Answers: 0 Comments: 2

Question Number 87175 Answers: 1 Comments: 2

if in the expansion of (1+x)^n the coefficient of x^9 is the aritmetic mean of the coeficients of x^8 and x^(10) . find the possible value of n where n is a positive integer

$$\mathrm{if}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{n}} \:\mathrm{the} \\ $$$$\mathrm{coefficient}\:\mathrm{of}\:\mathrm{x}^{\mathrm{9}} \:\mathrm{is}\:\mathrm{the}\:\mathrm{aritmetic}\: \\ $$$$\mathrm{mean}\:\mathrm{of}\:\mathrm{the}\:\mathrm{coeficients}\:\mathrm{of}\:\mathrm{x}^{\mathrm{8}} \:\mathrm{and}\: \\ $$$$\mathrm{x}^{\mathrm{10}} .\:\mathrm{find}\:\mathrm{the}\:\mathrm{possible}\:\mathrm{value}\: \\ $$$$\mathrm{of}\:\mathrm{n}\:\mathrm{where}\:\mathrm{n}\:\mathrm{is}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{integer} \\ $$

Question Number 87171 Answers: 0 Comments: 2

Given f(x) = 2 sin^2 x − sin x + 1 , 0 ≤ x ≤ 2π Find maximum and minumum value of f(x) without differential .

$${Given}\:\:{f}\left({x}\right)\:\:=\:\:\mathrm{2}\:\mathrm{sin}^{\mathrm{2}} \:{x}\:−\:\mathrm{sin}\:{x}\:+\:\mathrm{1}\:\:,\:\:\mathrm{0}\:\:\leqslant\:{x}\:\leqslant\:\mathrm{2}\pi \\ $$$${Find}\:\:{maximum}\:\:{and}\:\:{minumum}\:\:{value} \\ $$$${of}\:\:{f}\left({x}\right)\:\:{without}\:\:{differential}\:. \\ $$

Question Number 87168 Answers: 0 Comments: 15

Calculate these limits: Please sirs detail

$${Calculate}\:{these}\:{limits}: \\ $$$${Please}\:{sirs}\:{detail}\: \\ $$

Question Number 87185 Answers: 3 Comments: 0

∫((2x−1)/(x(x^2 +3)))dx

$$\int\frac{\mathrm{2}{x}−\mathrm{1}}{{x}\left({x}^{\mathrm{2}} +\mathrm{3}\right)}{dx} \\ $$

Question Number 87153 Answers: 1 Comments: 2

lim_(x→0) ((e^x +e^(−x) −2)/x^2 )

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{e}^{\mathrm{x}} +\mathrm{e}^{−\mathrm{x}} −\mathrm{2}}{\mathrm{x}^{\mathrm{2}} } \\ $$

Question Number 87146 Answers: 1 Comments: 0

find the area of the region enclosed by the polar curve r = 4 + 2 cos θ ?

$$\mathrm{find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{region}\: \\ $$$$\mathrm{enclosed}\:\mathrm{by}\:\mathrm{the}\:\mathrm{polar}\:\mathrm{curve}\: \\ $$$$\mathrm{r}\:=\:\mathrm{4}\:+\:\mathrm{2}\:\mathrm{cos}\:\theta\:? \\ $$

Question Number 87133 Answers: 0 Comments: 2

Question Number 87130 Answers: 0 Comments: 5

find the slope for the curve r = 3 sin 2θ at θ =(π/4) ?

$$\mathrm{find}\:\mathrm{the}\:\mathrm{slope}\:\mathrm{for}\:\mathrm{the}\:\mathrm{curve}\: \\ $$$$\mathrm{r}\:=\:\mathrm{3}\:\mathrm{sin}\:\mathrm{2}\theta\:\mathrm{at}\:\theta\:=\frac{\pi}{\mathrm{4}}\:? \\ $$

Question Number 87125 Answers: 0 Comments: 3

Question Number 87121 Answers: 3 Comments: 0

∫_0 ^(π/2) ((1−x^4 )/(1+x^4 ))dx

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{1}−{x}^{\mathrm{4}} }{\mathrm{1}+{x}^{\mathrm{4}} }{dx} \\ $$

Question Number 87116 Answers: 1 Comments: 0

(d^2 y/dx^2 )+x^2 y=0

$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }+{x}^{\mathrm{2}} {y}=\mathrm{0} \\ $$

Question Number 87105 Answers: 2 Comments: 1

Question Number 87103 Answers: 2 Comments: 2

∫(dx/((1+x)(√(x−x^2 ))))

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

Question Number 87093 Answers: 0 Comments: 6

⌊((x−1)/4)⌋+⌊((x−2)/3)⌋=⌊((x−3)/2)⌋

$$\lfloor\frac{{x}−\mathrm{1}}{\mathrm{4}}\rfloor+\lfloor\frac{{x}−\mathrm{2}}{\mathrm{3}}\rfloor=\lfloor\frac{{x}−\mathrm{3}}{\mathrm{2}}\rfloor \\ $$

Question Number 87089 Answers: 0 Comments: 5

Question Number 87088 Answers: 1 Comments: 0

Question Number 87086 Answers: 1 Comments: 0

Question Number 87074 Answers: 1 Comments: 4

what is coefficient of t^3 in the expanssion {((1−t^6 )/(1−t))}^3

$$\mathrm{what}\:\mathrm{is}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{t}^{\mathrm{3}} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{expanssion}\:\left\{\frac{\mathrm{1}−\mathrm{t}^{\mathrm{6}} }{\mathrm{1}−\mathrm{t}}\right\}^{\mathrm{3}} \: \\ $$

Question Number 87069 Answers: 0 Comments: 1

((cos x−sin x)/(√(1+sin 2x))) = sec 2x−tan 2x prove it

$$\frac{\mathrm{cos}\:\mathrm{x}−\mathrm{sin}\:\mathrm{x}}{\sqrt{\mathrm{1}+\mathrm{sin}\:\mathrm{2x}}}\:=\:\mathrm{sec}\:\mathrm{2x}−\mathrm{tan}\:\mathrm{2x} \\ $$$$\mathrm{prove}\:\mathrm{it}\: \\ $$

Question Number 87065 Answers: 0 Comments: 2

Question Number 87061 Answers: 1 Comments: 2

lim_(x→0) ((cos^3 (2x)−cos (x))/(cos^2 (2x)−cos (x))) =

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:^{\mathrm{3}} \left(\mathrm{2x}\right)−\mathrm{cos}\:\left(\mathrm{x}\right)}{\mathrm{cos}\:^{\mathrm{2}} \left(\mathrm{2x}\right)−\mathrm{cos}\:\left(\mathrm{x}\right)}\:=\: \\ $$

Question Number 87059 Answers: 1 Comments: 0

(y ′)^2 −xy′ +y = 0 find the solution

$$\left(\mathrm{y}\:'\right)^{\mathrm{2}} −\mathrm{xy}'\:+\mathrm{y}\:=\:\mathrm{0} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{solution} \\ $$

Question Number 87052 Answers: 0 Comments: 4

f(x)=∫_0 ^(π/2) ((sin^2 (t))/(1+xsin^2 (t)))dt

$${f}\left({x}\right)=\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \frac{{sin}^{\mathrm{2}} \left({t}\right)}{\mathrm{1}+{xsin}^{\mathrm{2}} \left({t}\right)}{dt} \\ $$

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