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Question Number 207949 Answers: 2 Comments: 0

Find the value of : 𝛀 = ∫_0 ^( (𝛑/2)) (( dx)/(sin^6 x + cos^6 x)) = ? −−−−−−−−−

$$ \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:{Find}\:{the}\:{value}\:{of}\:: \\ $$$$ \\ $$$$\:\:\:\:\boldsymbol{\Omega}\:=\:\int_{\mathrm{0}} ^{\:\frac{\boldsymbol{\pi}}{\mathrm{2}}} \:\frac{\:\boldsymbol{{dx}}}{\boldsymbol{{sin}}^{\mathrm{6}} \boldsymbol{{x}}\:+\:\boldsymbol{{cos}}^{\mathrm{6}} \boldsymbol{{x}}}\:=\:?\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:−−−−−−−−− \\ $$

Question Number 207947 Answers: 0 Comments: 0

find the domain of f(x)= ((⌊ln(x)⌋(fractional part((√(x−tanx)))))/(⌈sin((1/x))⌉))

$${find}\:{the}\:{domain}\:{of}\: \\ $$$${f}\left({x}\right)=\:\frac{\lfloor{ln}\left({x}\right)\rfloor\left({fractional}\:{part}\left(\sqrt{{x}−{tanx}}\right)\right)}{\lceil{sin}\left(\frac{\mathrm{1}}{{x}}\right)\rceil} \\ $$

Question Number 207946 Answers: 1 Comments: 0

Question Number 207943 Answers: 0 Comments: 11

Find: lim_(x→2^− ) (((x + 2)∙(x + 1))/(∣x + 2∣)) = ?

$$\mathrm{Find}: \\ $$$$\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{2}^{−} } {\mathrm{lim}}\:\frac{\left(\mathrm{x}\:+\:\mathrm{2}\right)\centerdot\left(\mathrm{x}\:+\:\mathrm{1}\right)}{\mid\mathrm{x}\:+\:\mathrm{2}\mid}\:\:=\:\:? \\ $$

Question Number 207938 Answers: 1 Comments: 0

what is the area bounded by the curve y=x(x−2)(x−5) and the x axis?

$${what}\:{is}\:{the}\:{area}\:{bounded}\:{by}\:{the}\:{curve} \\ $$$${y}={x}\left({x}−\mathrm{2}\right)\left({x}−\mathrm{5}\right)\:{and}\:{the}\:{x}\:{axis}? \\ $$$$ \\ $$

Question Number 207937 Answers: 0 Comments: 0

An ordered data consists of 6 even numbers and 4 odd numbers. The average of the odd numbers is 2022. The 3rd, 5th, 6th and 8 th numbers are odd. The data range is 24 , and the interquartile range is 14. The largest possible average of the ten numbers is ___

$$\:\:\mathrm{An}\:\mathrm{ordered}\:\mathrm{data}\:\mathrm{consists}\:\mathrm{of}\: \\ $$$$\:\mathrm{6}\:\mathrm{even}\:\mathrm{numbers}\:\mathrm{and}\:\mathrm{4}\:\mathrm{odd}\:\mathrm{numbers}. \\ $$$$\:\mathrm{The}\:\mathrm{average}\:\mathrm{of}\:\mathrm{the}\:\mathrm{odd}\:\mathrm{numbers}\: \\ $$$$\:\mathrm{is}\:\mathrm{2022}.\:\mathrm{The}\:\mathrm{3rd},\:\mathrm{5th},\:\mathrm{6th}\:\mathrm{and} \\ $$$$\:\mathrm{8}\:\mathrm{th}\:\mathrm{numbers}\:\mathrm{are}\:\mathrm{odd}.\: \\ $$$$\:\mathrm{The}\:\mathrm{data}\:\mathrm{range}\:\mathrm{is}\:\mathrm{24}\:,\:\mathrm{and}\:\mathrm{the}\: \\ $$$$\:\mathrm{interquartile}\:\mathrm{range}\:\mathrm{is}\:\mathrm{14}.\: \\ $$$$\:\mathrm{The}\:\mathrm{largest}\:\mathrm{possible}\:\mathrm{average} \\ $$$$\:\mathrm{of}\:\mathrm{the}\:\mathrm{ten}\:\mathrm{numbers}\:\mathrm{is}\:\_\_\_\: \\ $$

Question Number 207935 Answers: 1 Comments: 0

Question Number 207931 Answers: 2 Comments: 0

Question Number 207930 Answers: 0 Comments: 1

a_n number series a_(k+3) ^2 + a_k = a_(k+2) + a_(k+7) find: k = ?

$$\mathrm{a}_{\boldsymbol{\mathrm{n}}} \:\:\:\mathrm{number}\:\mathrm{series} \\ $$$$\mathrm{a}_{\boldsymbol{\mathrm{k}}+\mathrm{3}} ^{\mathrm{2}} \:\:+\:\:\mathrm{a}_{\boldsymbol{\mathrm{k}}} \:\:=\:\:\mathrm{a}_{\boldsymbol{\mathrm{k}}+\mathrm{2}} \:\:+\:\:\mathrm{a}_{\boldsymbol{\mathrm{k}}+\mathrm{7}} \\ $$$$\mathrm{find}:\:\:\:\boldsymbol{\mathrm{k}}\:=\:? \\ $$

Question Number 207925 Answers: 1 Comments: 0

Question Number 207924 Answers: 0 Comments: 0

∫f(x)g(x)dx=Σ_(n=0) ^∞ (−1)^n lim_(h→0) (1/h^n ) Σ_(i=o) ^n [ (−1)^i (((n!)/(i!(n−i)!)))f(x+(n−i)h)] (1/(n!))∫_a ^x (x−t)^n g(t)dt prove that right its a relation that i have derrived

$$\int{f}\left({x}\right){g}\left({x}\right){dx}=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:\left(−\mathrm{1}\right)^{{n}} \:\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{{h}^{{n}} }\:\underset{{i}={o}} {\overset{{n}} {\sum}}\left[\:\left(−\mathrm{1}\right)^{{i}} \left(\frac{{n}!}{{i}!\left({n}−{i}\right)!}\right){f}\left({x}+\left({n}−{i}\right){h}\right)\right]\:\frac{\mathrm{1}}{{n}!}\underset{{a}} {\overset{{x}} {\int}}\left({x}−{t}\right)^{{n}} {g}\left({t}\right){dt}\: \\ $$$${prove}\:{that}\:{right} \\ $$$${its}\:{a}\:{relation}\:{that}\:{i}\:{have}\:{derrived} \\ $$

Question Number 207910 Answers: 1 Comments: 0