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Question Number 212327    Answers: 3   Comments: 0

if (a+(1/a))=15 find the value of (a^2 +(1/a^2 ))

$${if}\:\left({a}+\frac{\mathrm{1}}{{a}}\right)=\mathrm{15}\:{find}\:{the}\:{value}\:{of}\:\left({a}^{\mathrm{2}} \:+\frac{\mathrm{1}}{{a}^{\mathrm{2}} }\right) \\ $$

Question Number 212326    Answers: 0   Comments: 0

Σ_(n=1) ^∞ (((−3)^n n!)/(1.4...(3n+1))) (1) check its a absolute conergent series (2) show that its a convergent series

$$\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{3}\right)^{{n}} \:{n}!}{\mathrm{1}.\mathrm{4}...\left(\mathrm{3}{n}+\mathrm{1}\right)} \\ $$$$\:\left(\mathrm{1}\right)\:{check}\:\:{its}\:{a}\:{absolute}\:{conergent}\:{series} \\ $$$$\:\:\left(\mathrm{2}\right)\:{show}\:{that}\:{its}\:{a}\:{convergent}\:{series} \\ $$

Question Number 212325    Answers: 1   Comments: 0

show that 1+(√(2 ))+2+..........+32(√(2 )) is 63(√2) +63

$${show}\:{that}\:\mathrm{1}+\sqrt{\mathrm{2}\:}+\mathrm{2}+..........+\mathrm{32}\sqrt{\mathrm{2}\:}\:{is}\:\mathrm{63}\sqrt{\mathrm{2}}\:+\mathrm{63} \\ $$

Question Number 212320    Answers: 1   Comments: 1

a+b+c+d=2, a^2 +b^2 +c^2 +d^2 =2 a^3 +b^3 +c^3 +d^3 =−4, a^4 +b^4 +c^4 +d^4 =−6 find real value of a^(2023) +b^(2023) +c^(2023) +d^(2023) .

$$\:{a}+{b}+{c}+{d}=\mathrm{2},\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} +{d}^{\mathrm{2}} =\mathrm{2} \\ $$$$\:{a}^{\mathrm{3}} +{b}^{\mathrm{3}} +{c}^{\mathrm{3}} +{d}^{\mathrm{3}} =−\mathrm{4},\:{a}^{\mathrm{4}} +{b}^{\mathrm{4}} +{c}^{\mathrm{4}} +{d}^{\mathrm{4}} =−\mathrm{6} \\ $$$$\:{find}\:{real}\:{value}\:{of}\:{a}^{\mathrm{2023}} +{b}^{\mathrm{2023}} +{c}^{\mathrm{2023}} +{d}^{\mathrm{2023}} . \\ $$

Question Number 212319    Answers: 2   Comments: 2

find G=(1/4)∫_0 ^(π/2) ln ((1+sin x)/(1−sin x)) dx

$$\mathrm{find} \\ $$$${G}=\frac{\mathrm{1}}{\mathrm{4}}\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\mathrm{ln}\:\frac{\mathrm{1}+\mathrm{sin}\:{x}}{\mathrm{1}−\mathrm{sin}\:{x}}\:{dx} \\ $$

Question Number 212314    Answers: 2   Comments: 0

Question Number 212311    Answers: 0   Comments: 0

lim_(n→∞) Σ_(k=1) ^n Σ_(j=1) ^n^2 sin(k/n)∙sin(k/n^2 )∙(1/( (√(n^2 +j))))ln(1+(1/n))

$$ \\ $$$$\:\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\:\underset{{j}=\mathrm{1}} {\overset{{n}^{\mathrm{2}} } {\sum}}\:\mathrm{sin}\frac{{k}}{{n}}\centerdot\mathrm{sin}\frac{{k}}{{n}^{\mathrm{2}} }\centerdot\frac{\mathrm{1}}{\:\sqrt{{n}^{\mathrm{2}} +{j}}}\mathrm{l}{n}\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right) \\ $$

Question Number 212457    Answers: 1   Comments: 0

Question Number 212456    Answers: 2   Comments: 0

∫ ((√(9x^2 −49))/x^3 ) dx = ?

$$\int\:\:\frac{\sqrt{\mathrm{9}{x}^{\mathrm{2}} −\mathrm{49}}}{{x}^{\mathrm{3}} }\:\:{dx}\:=\:? \\ $$

Question Number 212307    Answers: 1   Comments: 0

I=∫_0 ^∞ (((x−arctan x)^2 )/x^4 )dx.

$$ \\ $$$$\:\:{I}=\int_{\mathrm{0}} ^{\infty} \frac{\left({x}−\mathrm{arctan}\:{x}\right)^{\mathrm{2}} }{{x}^{\mathrm{4}} }{dx}. \\ $$

Question Number 212304    Answers: 0   Comments: 1

Hmmm...... does this Series Convergence?? Let′s define a_h as j_(ν,h) zero point of J_ν (z) ex. j_(1,1) is first zeros of J_1 (z) j_(2,2) is secondary zeros of J_2 (z)..... and that′s Sum S=Σ (1/(h!))a_(h ) , h=1,2,3.... div conv?? pls answer me...

$$\mathrm{Hmmm}...... \\ $$$$\mathrm{does}\:\mathrm{this}\:\mathrm{Series}\:\mathrm{Convergence}?? \\ $$$$\mathrm{Let}'\mathrm{s}\:\mathrm{define}\:{a}_{{h}} \:\mathrm{as}\:{j}_{\nu,{h}} \:\mathrm{zero}\:\mathrm{point}\:\mathrm{of}\:{J}_{\nu} \left({z}\right) \\ $$$$\mathrm{ex}.\:\:{j}_{\mathrm{1},\mathrm{1}} \:\mathrm{is}\:\mathrm{first}\:\mathrm{zeros}\:\mathrm{of}\:{J}_{\mathrm{1}} \left({z}\right) \\ $$$$\:\:\:\:\:{j}_{\mathrm{2},\mathrm{2}} \:\mathrm{is}\:\mathrm{secondary}\:\mathrm{zeros}\:\mathrm{of}\:\:{J}_{\mathrm{2}} \left({z}\right)..... \\ $$$$\mathrm{and}\:\mathrm{that}'\mathrm{s}\:\mathrm{Sum}\:{S}=\Sigma\:\frac{\mathrm{1}}{{h}!}{a}_{{h}\:} \:,\:{h}=\mathrm{1},\mathrm{2},\mathrm{3}.... \\ $$$$\mathrm{div}\:\mathrm{conv}??\:\mathrm{pls}\:\mathrm{answer}\:\mathrm{me}... \\ $$

Question Number 212301    Answers: 2   Comments: 0

3x+(2/( (√x)))=1, x−(√x) =?

$$\:\:\:\:\mathrm{3}{x}+\frac{\mathrm{2}}{\:\sqrt{{x}}}=\mathrm{1},\:{x}−\sqrt{{x}}\:=? \\ $$$$\:\: \\ $$

Question Number 212291    Answers: 1   Comments: 2

Question Number 212242    Answers: 0   Comments: 7

Help

$$\mathrm{Help} \\ $$

Question Number 212239    Answers: 2   Comments: 0

Question Number 212233    Answers: 1   Comments: 1

sin^(−1) (((12)/(13)))+cos^(−1) ((3/5))+tan^(−1) (((63)/(16)))=?

$$\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{12}}{\mathrm{13}}\right)+\mathrm{cos}^{−\mathrm{1}} \left(\frac{\mathrm{3}}{\mathrm{5}}\right)+\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{63}}{\mathrm{16}}\right)=? \\ $$

Question Number 212232    Answers: 1   Comments: 1

a^3 cos(A−B)+b^3 cos(B−C)+c^3 cos(A−C)=?

$${a}^{\mathrm{3}} {cos}\left({A}−{B}\right)+{b}^{\mathrm{3}} {cos}\left({B}−{C}\right)+{c}^{\mathrm{3}} {cos}\left({A}−{C}\right)=? \\ $$

Question Number 212231    Answers: 1   Comments: 11

(√(2+(√(2+(√(2+(√(2cos8x))))))))=?

$$\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}{cos}\mathrm{8}{x}}}}}=? \\ $$

Question Number 212229    Answers: 0   Comments: 0

Question Number 212228    Answers: 0   Comments: 0

Question Number 212224    Answers: 1   Comments: 0

a,b,c∈R a+b+c=1, a^2 +b^2 +c^2 =1 a^(10) +b^(10) +c^(10) =1, a^4 +b^4 +c^4 =?

$$\:{a},{b},{c}\in{R} \\ $$$$\:{a}+{b}+{c}=\mathrm{1},\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} =\mathrm{1} \\ $$$$\:{a}^{\mathrm{10}} +{b}^{\mathrm{10}} +{c}^{\mathrm{10}} =\mathrm{1},\:{a}^{\mathrm{4}} +{b}^{\mathrm{4}} +{c}^{\mathrm{4}} =? \\ $$

Question Number 212219    Answers: 3   Comments: 0

Find: (√(21∙22∙23∙24 + 1)) = ?

$$\mathrm{Find}: \\ $$$$\sqrt{\mathrm{21}\centerdot\mathrm{22}\centerdot\mathrm{23}\centerdot\mathrm{24}\:+\:\mathrm{1}}\:=\:? \\ $$

Question Number 212214    Answers: 1   Comments: 1

Find tanθ.

$$\mathrm{Find}\:\mathrm{tan}\theta. \\ $$

Question Number 212213    Answers: 1   Comments: 0

Can some please explain is there any use of imaginary numbers in real life? I have heard that this number has been used in many different fields. Why use a number which is not real.

$$\mathrm{Can}\:\mathrm{some}\:\mathrm{please}\:\mathrm{explain}\:\mathrm{is}\:\mathrm{there}\:\mathrm{any}\:\mathrm{use}\:\mathrm{of}\:\mathrm{imaginary}\:\mathrm{numbers}\:\mathrm{in}\:\mathrm{real}\:\mathrm{life}? \\ $$$$\mathrm{I}\:\mathrm{have}\:\mathrm{heard}\:\mathrm{that}\:\mathrm{this}\:\mathrm{number}\:\mathrm{has}\:\mathrm{been}\:\mathrm{used}\:\mathrm{in}\:\mathrm{many}\:\mathrm{different}\:\mathrm{fields}.\: \\ $$$$\mathrm{Why}\:\mathrm{use}\:\mathrm{a}\:\mathrm{number}\:\mathrm{which}\:\mathrm{is}\:\mathrm{not}\:\mathrm{real}. \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 212209    Answers: 1   Comments: 0

⋗

$$\:\:\:\cancel{\underbrace{\gtrdot}}\: \\ $$

Question Number 212204    Answers: 0   Comments: 2

f(x) is continous and lim_(x→∞) f(x)=−∞ prove max(f(x)) exist

$${f}\left({x}\right)\:{is}\:{continous}\:{and} \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}{f}\left({x}\right)=−\infty \\ $$$${prove}\:{max}\left({f}\left({x}\right)\right)\:{exist} \\ $$

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