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Question Number 144424 Answers: 2 Comments: 0

make c the subject in S=(1/(2(a+b+c)))

$${make}\:{c}\:{the}\:{subject}\:{in}\:{S}=\frac{\mathrm{1}}{\mathrm{2}\left({a}+{b}+{c}\right)} \\ $$

Question Number 144422 Answers: 1 Comments: 0

make n the subject of the formular if A=p(1+(r/(100)))^n

$${make}\:{n}\:{the}\:{subject}\:{of}\:{the}\:{formular} \\ $$$${if}\:{A}={p}\left(\mathrm{1}+\frac{{r}}{\mathrm{100}}\right)^{{n}} \\ $$

Question Number 144421 Answers: 0 Comments: 0

Let a,b,c > 0 and a+b+c = 3. Prove that ((a^(2021) +b^(2021) +c^(2021) )/3) ≥ 1+((4042)/3)(1−((ab+bc+ca)/3))

$$\mathrm{Let}\:{a},{b},{c}\:>\:\mathrm{0}\:\mathrm{and}\:{a}+{b}+{c}\:=\:\mathrm{3}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{{a}^{\mathrm{2021}} +{b}^{\mathrm{2021}} +{c}^{\mathrm{2021}} }{\mathrm{3}}\:\geqslant\:\mathrm{1}+\frac{\mathrm{4042}}{\mathrm{3}}\left(\mathrm{1}−\frac{{ab}+{bc}+{ca}}{\mathrm{3}}\right)\:\:\:\:\:\:\:\:\:\:\: \\ $$

Question Number 144420 Answers: 2 Comments: 1

Question Number 144419 Answers: 1 Comments: 0

...Advanced ....Calculus... Without using the Feynman′s trick , Find the value of :: I :=∫_0 ^( 1) ((Log (1+ x^( 2) ))/(1 +x)) dx=? m.n...

$$\:\:\:\:\:...{Advanced}\:....{Calculus}... \\ $$$${Without}\:{using}\:{the}\:{Feynman}'{s}\:{trick}\:, \\ $$$$\:\:\:\:\:{Find}\:{the}\:{value}\:{of}\:\:\::: \\ $$$$\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{I}\::=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{Log}\:\left(\mathrm{1}+\:\mathrm{x}^{\:\mathrm{2}} \right)}{\mathrm{1}\:+\mathrm{x}}\:\mathrm{dx}=? \\ $$$$\:\:\:\:\mathrm{m}.\mathrm{n}... \\ $$

Question Number 144414 Answers: 1 Comments: 0

find Lourant series of f(z)=(1/(1−z+z^2 )) ,0<∣z−1∣<1

$${find}\:{Lourant}\:{series}\:{of}\: \\ $$$$ \\ $$$${f}\left({z}\right)=\frac{\mathrm{1}}{\mathrm{1}−{z}+{z}^{\mathrm{2}} }\:\:\:\:,\mathrm{0}<\mid{z}−\mathrm{1}\mid<\mathrm{1} \\ $$

Question Number 144413 Answers: 2 Comments: 0

lim_(x→1) [ (1/(4−4(√x)))−(1/(5−5(x)^(1/5) )) ] =?

$$\:\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\left[\:\frac{\mathrm{1}}{\mathrm{4}−\mathrm{4}\sqrt{\mathrm{x}}}−\frac{\mathrm{1}}{\mathrm{5}−\mathrm{5}\sqrt[{\mathrm{5}}]{\mathrm{x}}}\:\right]\:=? \\ $$

Question Number 144403 Answers: 1 Comments: 0

A=lim_(x→0) ((∫_(2x) ^(4x) ((sint)/t)dt)/(e^x −1)) =?

$$\mathrm{A}=\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\int_{\mathrm{2x}} ^{\mathrm{4x}} \frac{\mathrm{sint}}{\mathrm{t}}\mathrm{dt}}{\mathrm{e}^{\mathrm{x}} −\mathrm{1}}\:=? \\ $$

Question Number 144402 Answers: 1 Comments: 2

Question Number 144406 Answers: 0 Comments: 0

Question Number 144409 Answers: 2 Comments: 0

∫ (dx/((x+3)(√(1−x^2 )))) ?

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

Question Number 144408 Answers: 3 Comments: 0

lg(2)=x lg(7)=y lg_5 (9,8)=?

$$\boldsymbol{{lg}}\left(\mathrm{2}\right)=\boldsymbol{{x}} \\ $$$$\boldsymbol{{lg}}\left(\mathrm{7}\right)=\boldsymbol{{y}} \\ $$$$\boldsymbol{{lg}}_{\mathrm{5}} \left(\mathrm{9},\mathrm{8}\right)=? \\ $$

Question Number 144396 Answers: 1 Comments: 1

L=lim_(n→+∝) ((1/(n^2 +1^2 )) + (2/(n^2 +2^2 )) +..+ (n/(n^2 +n^2 )))=?

$$\mathrm{L}=\underset{\mathrm{n}\rightarrow+\propto} {\mathrm{lim}}\left(\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} +\mathrm{1}^{\mathrm{2}} }\:+\:\frac{\mathrm{2}}{\mathrm{n}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} }\:+..+\:\frac{\mathrm{n}}{\mathrm{n}^{\mathrm{2}} +\mathrm{n}^{\mathrm{2}} }\right)=? \\ $$

Question Number 144395 Answers: 0 Comments: 0

L=lim_(n→+∝) ((n+n^2 +n^3 +n^4 +...+n^n )/(1^n +2^n +3^n +4^n +...+n^n )) =?

$$\mathrm{L}=\underset{\mathrm{n}\rightarrow+\propto} {\mathrm{lim}}\frac{\mathrm{n}+\mathrm{n}^{\mathrm{2}} +\mathrm{n}^{\mathrm{3}} +\mathrm{n}^{\mathrm{4}} +...+\mathrm{n}^{\mathrm{n}} }{\mathrm{1}^{\mathrm{n}} +\mathrm{2}^{\mathrm{n}} +\mathrm{3}^{\mathrm{n}} +\mathrm{4}^{\mathrm{n}} +...+\mathrm{n}^{\mathrm{n}} }\:=? \\ $$

Question Number 144394 Answers: 0 Comments: 1

L=lim_(n→+∝) ((1/(n+1)) + (1/(n+2)) +...+ (1/(n+n)))=?

$$\mathrm{L}=\underset{\mathrm{n}\rightarrow+\propto} {\mathrm{lim}}\left(\frac{\mathrm{1}}{\mathrm{n}+\mathrm{1}}\:+\:\frac{\mathrm{1}}{\mathrm{n}+\mathrm{2}}\:+...+\:\frac{\mathrm{1}}{\mathrm{n}+\mathrm{n}}\right)=? \\ $$

Question Number 144389 Answers: 1 Comments: 0

∫ (x−1)h(x)dx = x^3 −sin 2x+(√(x^2 +1)) + c ⇒h ′(1)= ?

$$\:\int\:\left(\mathrm{x}−\mathrm{1}\right)\mathrm{h}\left(\mathrm{x}\right)\mathrm{dx}\:=\:\mathrm{x}^{\mathrm{3}} −\mathrm{sin}\:\mathrm{2x}+\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\:+\:\mathrm{c}\: \\ $$$$\Rightarrow\mathrm{h}\:'\left(\mathrm{1}\right)=\:? \\ $$

Question Number 144387 Answers: 1 Comments: 0

A=((log_2 9)^2 )^(1/(log_2 (log_2 9))) ×((√7))^(1/(log_4 7)) =?

$$\mathrm{A}=\left(\left(\mathrm{log}_{\mathrm{2}} \mathrm{9}\right)^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{log}_{\mathrm{2}} \left(\mathrm{log}_{\mathrm{2}} \mathrm{9}\right)}} ×\left(\sqrt{\mathrm{7}}\right)^{\frac{\mathrm{1}}{\mathrm{log}_{\mathrm{4}} \mathrm{7}}} =? \\ $$

Question Number 144380 Answers: 1 Comments: 0

L=lim_(n→+∝) ((1/(1^2 +2(1))) + (1/(2^2 +2n)) +...+ (1/(n^2 +2n)))=?

$$\mathrm{L}=\underset{\mathrm{n}\rightarrow+\propto} {\mathrm{lim}}\left(\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{2}} +\mathrm{2}\left(\mathrm{1}\right)}\:+\:\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} +\mathrm{2n}}\:+...+\:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} +\mathrm{2n}}\right)=? \\ $$

Question Number 144379 Answers: 2 Comments: 0

cos^2 x+tan^2 x=(3/2) xεR

$$\:\:\:\:\:\:\:\:\:\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}+\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}=\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{x}\epsilon\mathrm{R}\: \\ $$

Question Number 144374 Answers: 0 Comments: 0

Question Number 144372 Answers: 0 Comments: 0

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Question Number 144373 Answers: 0 Comments: 0

Question Number 144367 Answers: 0 Comments: 1

Question Number 144359 Answers: 1 Comments: 0

∫ ((x^4 e^x dx)/((x^4 +4x^3 +12x^2 +24x+24+72e^x )^2 )) = ?

$$\int\:\frac{{x}^{\mathrm{4}} {e}^{{x}} \:{dx}}{\left({x}^{\mathrm{4}} +\mathrm{4}{x}^{\mathrm{3}} +\mathrm{12}{x}^{\mathrm{2}} +\mathrm{24}{x}+\mathrm{24}+\mathrm{72}{e}^{{x}} \right)^{\mathrm{2}} }\:=\:? \\ $$

Question Number 144353 Answers: 1 Comments: 1

Question Number 144351 Answers: 1 Comments: 0

Evaluate :: 𝛗:=∫_0 ^( ∞) (( sin (x)^(1/( 3 )) )log ((1/x) ))/x)dx=?

$$ \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:{Evaluate}\:\:\::: \\ $$$$\:\: \\ $$$$\boldsymbol{\phi}:=\int_{\mathrm{0}} ^{\:\infty} \frac{\left.\:{sin}\:\sqrt[{\:\mathrm{3}\:}]{{x}}\:\right){log}\:\left(\frac{\mathrm{1}}{{x}}\:\right)}{{x}}{dx}=? \\ $$$$\:\:\: \\ $$$$ \\ $$

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