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Question Number 77962 Answers: 1 Comments: 2

∫(dx/(1+(tan(x))^(√2) )) dx

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

Question Number 77960 Answers: 0 Comments: 3

∫ ((2x^3 −1)/(x^4 +x)) dx?

$$\int\:\frac{\mathrm{2}{x}^{\mathrm{3}} −\mathrm{1}}{{x}^{\mathrm{4}} +{x}}\:{dx}? \\ $$

Question Number 77959 Answers: 2 Comments: 0

solve tan ((1/(1+x^2 )))>1

$${solve}\:\mathrm{tan}\:\left(\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} }\right)>\mathrm{1}\: \\ $$

Question Number 77953 Answers: 2 Comments: 0

Given that Σ_(r=0) ^4 6r =2Σ_(r=1) ^n 5r, work out the value of n.

$$\mathrm{Given}\:\mathrm{that}\:\underset{\mathrm{r}=\mathrm{0}} {\overset{\mathrm{4}} {\sum}}\mathrm{6r}\:=\mathrm{2}\underset{\mathrm{r}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{5r},\:\mathrm{work}\:\mathrm{out}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:\mathrm{n}. \\ $$

Question Number 78012 Answers: 1 Comments: 3

prove that lim_(x→1) ((sin(𝛑cos𝛑x))/((x−1)^2 )) = − (𝛑^3 /2)

$$\boldsymbol{{prove}}\:\boldsymbol{{that}} \\ $$$$\underset{\boldsymbol{{x}}\rightarrow\mathrm{1}} {\boldsymbol{{lim}}}\frac{\boldsymbol{{sin}}\left(\boldsymbol{\pi{cos}\pi{x}}\right)}{\left(\boldsymbol{{x}}−\mathrm{1}\right)^{\mathrm{2}} }\:=\:−\:\frac{\boldsymbol{\pi}^{\mathrm{3}} }{\mathrm{2}} \\ $$

Question Number 77918 Answers: 1 Comments: 1

∫ _0 ^π e^(−2x) sin x dx ?

$$\int\underset{\mathrm{0}} {\overset{\pi} {\:}}\:{e}^{−\mathrm{2}{x}} \:\mathrm{sin}\:{x}\:{dx}\:?\: \\ $$

Question Number 77915 Answers: 1 Comments: 0

Find prime factor of 4^8 − 3^8

$${Find}\:\:{prime}\:\:{factor}\:\:{of}\:\:\mathrm{4}^{\mathrm{8}} \:−\:\mathrm{3}^{\mathrm{8}} \:\: \\ $$

Question Number 77902 Answers: 0 Comments: 8

Question Number 77897 Answers: 1 Comments: 5

calculateU_n = Σ_(k=1) ^n k(−1)^k and v_n =Σ_(k=1) ^n k^2 (−1)^k

$${calculateU}_{{n}} =\:\sum_{{k}=\mathrm{1}} ^{{n}} {k}\left(−\mathrm{1}\right)^{{k}} \:\:\:{and}\:{v}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} {k}^{\mathrm{2}} \left(−\mathrm{1}\right)^{{k}} \\ $$

Question Number 77891 Answers: 0 Comments: 0

Question Number 77890 Answers: 0 Comments: 0

Question Number 77887 Answers: 1 Comments: 0

∫(e^(sinh(x)) /(cosh(x))) dx

$$\int\frac{{e}^{{sinh}\left({x}\right)} }{{cosh}\left({x}\right)}\:{dx} \\ $$

Question Number 77886 Answers: 0 Comments: 1

calculate ∫_0 ^∞ ((arctan(x^2 +x^(−2) ))/(x^2 +a^2 ))dx with a>0 2) find the value of ∫_0 ^∞ ((arctan(x^2 +x^(−2) ))/(x^2 +1))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left({x}^{\mathrm{2}} \:+{x}^{−\mathrm{2}} \right)}{{x}^{\mathrm{2}} \:+{a}^{\mathrm{2}} }{dx}\:\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left({x}^{\mathrm{2}} \:+{x}^{−\mathrm{2}} \right)}{{x}^{\mathrm{2}} \:+\mathrm{1}}{dx} \\ $$

Question Number 77885 Answers: 2 Comments: 0

solve for : x 1.(√((x−a)(x−b)))+(√((x−b)(x−c)))+(√((x−c)(x−a)))=d [a,b,c,d∈R try for: a=4,b=3,c=2,d=1] 2. (x−a^2 )(√(x−a))+(x−a)(√(x−a^2 ))=a^2 +a+1 3. (x−a^2 )(√(x^2 −a))+(x^2 −a)(√(x−a^2 ))=a^2 +a+1 [a∈R try for: a=(1/2) ]

$$\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\::\:\boldsymbol{\mathrm{x}} \\ $$$$\mathrm{1}.\sqrt{\left(\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{a}}\right)\left(\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{b}}\right)}+\sqrt{\left(\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{b}}\right)\left(\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{c}}\right)}+\sqrt{\left(\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{c}}\right)\left(\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{a}}\right)}=\boldsymbol{\mathrm{d}} \\ $$$$\left[\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}},\boldsymbol{\mathrm{c}},\boldsymbol{\mathrm{d}}\in\boldsymbol{\mathrm{R}}\right. \\ $$$$\left.\mathrm{try}\:\mathrm{for}:\:\:\mathrm{a}=\mathrm{4},\mathrm{b}=\mathrm{3},\mathrm{c}=\mathrm{2},\mathrm{d}=\mathrm{1}\right] \\ $$$$\mathrm{2}.\:\left(\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{a}}^{\mathrm{2}} \right)\sqrt{\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{a}}}+\left(\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{a}}\right)\sqrt{\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{a}}^{\mathrm{2}} }=\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\boldsymbol{\mathrm{a}}+\mathrm{1} \\ $$$$\mathrm{3}.\:\left(\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{a}}^{\mathrm{2}} \right)\sqrt{\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\boldsymbol{\mathrm{a}}}+\left(\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\boldsymbol{\mathrm{a}}\right)\sqrt{\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{a}}^{\mathrm{2}} }=\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\boldsymbol{\mathrm{a}}+\mathrm{1} \\ $$$$\left[\boldsymbol{\mathrm{a}}\in\boldsymbol{\mathrm{R}}\right. \\ $$$$\left.\mathrm{try}\:\mathrm{for}:\:\mathrm{a}=\frac{\mathrm{1}}{\mathrm{2}}\:\right] \\ $$$$ \\ $$

Question Number 77883 Answers: 1 Comments: 7

Question Number 77881 Answers: 0 Comments: 5

Question Number 77879 Answers: 0 Comments: 0

∫_1 ^∞ (1/(√(x^3 +5))) dx

$$\int_{\mathrm{1}} ^{\infty} \frac{\mathrm{1}}{\sqrt{{x}^{\mathrm{3}} +\mathrm{5}}}\:{dx} \\ $$

Question Number 77872 Answers: 2 Comments: 6

show that f(x)=2r^3 +5x−1 has a zero in the interval [0.1].

$${show}\:{that}\:{f}\left({x}\right)=\mathrm{2}{r}^{\mathrm{3}} +\mathrm{5}{x}−\mathrm{1}\:{has}\:{a}\:{zero}\:{in}\:{the}\:{interval}\:\left[\mathrm{0}.\mathrm{1}\right]. \\ $$

Question Number 77889 Answers: 0 Comments: 2

Show that the capacitance of two concentric sphere that have a and b as respective radii of the inner and outer sphere is ((4π∈_o ab)/(b−a))

$${Show}\:{that}\:{the}\:{capacitance} \\ $$$${of}\:{two}\:{concentric}\:{sphere} \\ $$$${that}\:{have}\:{a}\:{and}\:{b}\:{as} \\ $$$${respective}\:{radii}\:{of}\:{the} \\ $$$${inner}\:{and}\:{outer}\:{sphere} \\ $$$${is}\:\frac{\mathrm{4}\pi\in_{{o}} {ab}}{{b}−{a}} \\ $$

Question Number 77864 Answers: 1 Comments: 1

Question Number 77859 Answers: 2 Comments: 1

y = ∣x∣^(∣x∣) (dy/dx) = ?

$${y}\:=\:\mid{x}\mid\:^{\mid{x}\mid} \:\: \\ $$$$\frac{{dy}}{{dx}}\:=\:? \\ $$

Question Number 77856 Answers: 1 Comments: 1

l_(x→0) im(((e^x −x−1)/x))

$$\underset{{x}\rightarrow\mathrm{0}} {{l}im}\left(\frac{{e}^{{x}} −{x}−\mathrm{1}}{{x}}\right) \\ $$

Question Number 77855 Answers: 0 Comments: 0

Question Number 77854 Answers: 1 Comments: 1

a circle offends the y axis at point(0,b) and through the intersection of the curve y = x −2(√x)+(1/4). value of b = ?

$${a}\:{circle}\: \\ $$$${offends}\:{the}\:{y}\:{axis}\:{at}\:{point}\left(\mathrm{0},{b}\right)\: \\ $$$${and}\:{through}\:{the}\:{intersection} \\ $$$${of}\:{the}\:{curve}\:{y}\:=\:{x}\:−\mathrm{2}\sqrt{{x}}+\frac{\mathrm{1}}{\mathrm{4}}.\: \\ $$$${value}\:{of}\:{b}\:=\:? \\ $$

Question Number 77852 Answers: 0 Comments: 0

5245

$$\mathrm{5245} \\ $$

Question Number 77848 Answers: 0 Comments: 3

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