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Question Number 88752 Answers: 1 Comments: 2

cos(𝛂)+cos(𝛃)+cos(𝛄)≤(3/2) prove the inequality

$$\boldsymbol{\mathrm{cos}}\left(\boldsymbol{\alpha}\right)+\boldsymbol{\mathrm{cos}}\left(\boldsymbol{\beta}\right)+\boldsymbol{\mathrm{cos}}\left(\boldsymbol{\gamma}\right)\leqslant\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{prove}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{inequality}} \\ $$

Question Number 88731 Answers: 0 Comments: 3

Question Number 88723 Answers: 1 Comments: 0

prove that Σ_(k=0) ^∞ (((k+2)^2 x^k )/((k+3)!))=(e^x /x^3 )(x^2 −x+1)−((x^2 +2)/(2x^3 ))

$${prove}\:{that} \\ $$$$ \\ $$$$\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left({k}+\mathrm{2}\right)^{\mathrm{2}} {x}^{{k}} }{\left({k}+\mathrm{3}\right)!}=\frac{{e}^{{x}} }{{x}^{\mathrm{3}} }\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)−\frac{{x}^{\mathrm{2}} +\mathrm{2}}{\mathrm{2}{x}^{\mathrm{3}} } \\ $$

Question Number 88710 Answers: 2 Comments: 1

∫_(−(√3) ) ^(√3) ∫_1 ^(√(4−x^2 )) (x^2 +y^2 )^(3/2) dydx

$$\underset{−\sqrt{\mathrm{3}}\:} {\overset{\sqrt{\mathrm{3}}} {\int}}\underset{\mathrm{1}} {\overset{\sqrt{\mathrm{4}−{x}^{\mathrm{2}} }} {\int}}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)^{\mathrm{3}/\mathrm{2}} \:{dydx} \\ $$

Question Number 88708 Answers: 2 Comments: 5

Question Number 88690 Answers: 1 Comments: 0

Question Number 88683 Answers: 2 Comments: 0

Question Number 88681 Answers: 0 Comments: 2

If f(x) is a periodic function, with period T, then

$$\mathrm{If}\:\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{periodic}\:\mathrm{function},\:\mathrm{with} \\ $$$$\mathrm{period}\:{T},\:\mathrm{then} \\ $$

Question Number 88678 Answers: 0 Comments: 8

Find (√i)+(√(−i))

$$\boldsymbol{\mathrm{F}}{ind}\:\:\:\sqrt{\boldsymbol{{i}}}+\sqrt{−\boldsymbol{\mathrm{i}}} \\ $$

Question Number 88673 Answers: 2 Comments: 2

Question Number 88663 Answers: 1 Comments: 0

{ ((log_2 x+log_4 y=4)),((x.y=8)) :}

$$\begin{cases}{{log}_{\mathrm{2}} {x}+{log}_{\mathrm{4}} {y}=\mathrm{4}}\\{{x}.{y}=\mathrm{8}}\end{cases} \\ $$

Question Number 88656 Answers: 1 Comments: 1

Question Number 88642 Answers: 1 Comments: 2

Question Number 88623 Answers: 2 Comments: 4

Question Number 88616 Answers: 1 Comments: 9

Question Number 88613 Answers: 1 Comments: 3

Question Number 88611 Answers: 0 Comments: 0

prove that ((1+p^2 +p^4 +......+p^(2n) )/(p+p^3 +p^5 +.....p^(2n−1) ))>((n+1)/(np))

$${prove}\:{that} \\ $$$$\frac{\mathrm{1}+{p}^{\mathrm{2}} +{p}^{\mathrm{4}} +......+{p}^{\mathrm{2}{n}} }{{p}+{p}^{\mathrm{3}} +{p}^{\mathrm{5}} +.....{p}^{\mathrm{2}{n}−\mathrm{1}} }>\frac{{n}+\mathrm{1}}{{np}} \\ $$

Question Number 88610 Answers: 0 Comments: 2

is 1×1×1×..........=1^∞ or 1×1×1×1×1×..........=1

$${is}\:\mathrm{1}×\mathrm{1}×\mathrm{1}×..........=\mathrm{1}^{\infty} \: \\ $$$${or} \\ $$$$\:\mathrm{1}×\mathrm{1}×\mathrm{1}×\mathrm{1}×\mathrm{1}×..........=\mathrm{1} \\ $$$$ \\ $$$$ \\ $$

Question Number 88607 Answers: 0 Comments: 0

chose the right option 1) if x,y ∈Q^c and x<y then ∃a∈Q such that x<a<y in case we say that a)Q^c is an ordered field b)Q dense inQ^c c)not ordered field 2)let Q≠A ∈ Q,A not necessary has least upper bound and greatest lower bound that mean (Q,+,.,≤)is....... a)not complete b)complete c)dense in R 3)the sequence a_n =(n/(n+1)) is convergent to...... a)0 b)1 3)∞ 4) let f:A→B be a real valued function and Q≠S⊆A such that f is not continuous on S then f is a)contiuous on A b) continuous at any points x_0 in A c) continuous on A/S 4)every set of natural numbers has a least element so the order set of natural number is...... a)bounded from above b)bounded from below c)well ordered

$${chose}\:{the}\:{right}\:{option} \\ $$$$\left.\mathrm{1}\right)\:{if}\:{x},{y}\:\in{Q}^{{c}} \:{and}\:{x}<{y}\:\:{then}\:\exists{a}\in{Q} \\ $$$${such}\:{that}\:{x}<{a}<{y}\:{in}\:{case}\:{we}\:{say}\:{that} \\ $$$$\left.{a}\right){Q}^{{c}} \:{is}\:{an}\:{ordered}\:{field} \\ $$$$\left.{b}\right){Q}\:{dense}\:{inQ}^{{c}} \\ $$$$\left.{c}\right){not}\:{ordered}\:{field} \\ $$$$ \\ $$$$\left.\mathrm{2}\right){let}\:{Q}\neq{A}\:\in\:{Q},{A}\:{not}\:{necessary}\:{has} \\ $$$${least}\:{upper}\:{bound}\:{and}\:{greatest}\:{lower} \\ $$$${bound}\:{that}\:{mean}\:\left({Q},+,.,\leqslant\right){is}....... \\ $$$$\left.{a}\right){not}\:{complete} \\ $$$$\left.{b}\right){complete} \\ $$$$\left.{c}\right){dense}\:{in}\:{R} \\ $$$$ \\ $$$$\left.\mathrm{3}\right){the}\:{sequence}\:{a}_{{n}} =\frac{{n}}{{n}+\mathrm{1}}\:{is}\:{convergent} \\ $$$${to}...... \\ $$$$\left.{a}\right)\mathrm{0} \\ $$$$\left.{b}\right)\mathrm{1} \\ $$$$\left.\mathrm{3}\right)\infty \\ $$$$ \\ $$$$\left.\mathrm{4}\right)\:{let}\:{f}:{A}\rightarrow{B}\:{be}\:{a}\:{real}\:{valued}\:{function} \\ $$$${and}\:{Q}\neq{S}\subseteq{A}\:{such}\:{that}\:{f}\:{is}\:{not}\:{continuous} \\ $$$${on}\:{S} \\ $$$${then}\:{f}\:{is} \\ $$$$\left.{a}\right){contiuous}\:{on}\:{A} \\ $$$$\left.{b}\right)\:{continuous}\:{at}\:{any}\:{points}\:{x}_{\mathrm{0}} \:{in}\:\:{A} \\ $$$$\left.{c}\right)\:{continuous}\:{on}\:\:{A}/{S} \\ $$$$ \\ $$$$\left.\mathrm{4}\right){every}\:{set}\:{of}\:{natural}\:{numbers}\:{has} \\ $$$${a}\:{least}\:{element}\:{so}\:{the}\:{order}\:{set}\:{of} \\ $$$${natural}\:{number}\:{is}...... \\ $$$$\left.{a}\right){bounded}\:{from}\:{above} \\ $$$$\left.{b}\right){bounded}\:{from}\:{below} \\ $$$$\left.{c}\right){well}\:{ordered} \\ $$

Question Number 88606 Answers: 2 Comments: 2

Question Number 88603 Answers: 1 Comments: 0

Question Number 88594 Answers: 0 Comments: 3

solve for x∈C cos (x)=a+bi

$${solve}\:{for}\:{x}\in\mathbb{C} \\ $$$$\mathrm{cos}\:\left({x}\right)={a}+{bi} \\ $$

Question Number 88592 Answers: 1 Comments: 0

show that the variance δ^2 of a set of observations x_1 ,x_2 ,...x_n with mean x^_ can be expressed in the form δ^2 = ((Σ_(i=1) ^n x_i ^2 )/n) − x^ ^(2 )

$$\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{variance}\:\delta^{\mathrm{2}} \:\mathrm{of}\:\mathrm{a}\:\mathrm{set}\:\mathrm{of}\:\mathrm{observations}\:{x}_{\mathrm{1}} ,{x}_{\mathrm{2}} ,...{x}_{{n}} \:\mathrm{with}\:\mathrm{mean} \\ $$$$\overset{\_} {{x}}\:\mathrm{can}\:\mathrm{be}\:\mathrm{expressed}\:\mathrm{in}\:\mathrm{the}\:\mathrm{form}\:\:\delta^{\mathrm{2}} \:=\:\frac{\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}{x}_{{i}} ^{\mathrm{2}} }{{n}}\:−\:\bar {{x}}\:^{\mathrm{2}\:} \\ $$

Question Number 88586 Answers: 1 Comments: 0

∫((√(cos(2x)+3))/(cos(x)))dx

$$\int\frac{\sqrt{{cos}\left(\mathrm{2}{x}\right)+\mathrm{3}}}{{cos}\left({x}\right)}{dx} \\ $$

Question Number 88590 Answers: 0 Comments: 0

a^a^a^a^3 =5 find−a

$${a}^{{a}^{{a}^{{a}^{\mathrm{3}} } } } =\mathrm{5} \\ $$$${find}−{a} \\ $$

Question Number 88580 Answers: 0 Comments: 4

lim_(x→0) (((√(1+4x)) −((1+6x))^(1/(3 )) )/(1−cos 3x)) =

$$ \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{1}+\mathrm{4x}}\:−\sqrt[{\mathrm{3}\:\:}]{\mathrm{1}+\mathrm{6x}}}{\mathrm{1}−\mathrm{cos}\:\mathrm{3x}}\:= \\ $$

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