Question and Answers Forum

All Questions Topic List

AllQuestion and Answers: Page 239

Question Number 196957 Answers: 1 Comments: 0

Question Number 196955 Answers: 0 Comments: 1

Question Number 196954 Answers: 1 Comments: 0

Question Number 196950 Answers: 1 Comments: 0

Prove that ∫^( (π/2)) _( 0) ((ln(1+αsint))/(sint))dt= (π^2 /8)−(1/2)(arccosα)^2

$$\mathrm{Prove}\:\mathrm{that}\:\underset{\:\mathrm{0}} {\int}^{\:\frac{\pi}{\mathrm{2}}} \frac{\mathrm{ln}\left(\mathrm{1}+\alpha\mathrm{sin}{t}\right)}{\mathrm{sin}{t}}{dt}=\:\frac{\pi^{\mathrm{2}} }{\mathrm{8}}−\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{arccos}\alpha\right)^{\mathrm{2}} \\ $$

Question Number 196946 Answers: 2 Comments: 0

Question Number 196940 Answers: 1 Comments: 0

Question Number 196938 Answers: 1 Comments: 0

Question Number 196953 Answers: 1 Comments: 0

Question Number 196934 Answers: 1 Comments: 0

Question Number 196929 Answers: 1 Comments: 0

Question Number 196928 Answers: 0 Comments: 1

I_n =∫_0 ^(π/2) sin^n x dx

$${I}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {sin}^{{n}} {x}\:{dx} \\ $$

Question Number 196918 Answers: 1 Comments: 0

Question Number 196917 Answers: 3 Comments: 0

Question Number 196916 Answers: 0 Comments: 0

Question Number 196915 Answers: 0 Comments: 1

Question Number 196914 Answers: 2 Comments: 0

Question Number 196913 Answers: 1 Comments: 0

soit {_(r_(n+1) =r_n /(2+r_n ^2 )) ^(r_0 =1) demontrer sans recurrence que r_n >0 demontrer par recurrence que r_(n+1) ≤(1/2)r_n demontrer sans recurrence que r_n ≤((1/2))^n •erly rolvinst•

$${soit}\:\left\{_{{r}_{{n}+\mathrm{1}} ={r}_{{n}} /\left(\mathrm{2}+{r}_{{n}} ^{\mathrm{2}} \right)} ^{{r}_{\mathrm{0}} =\mathrm{1}} \right. \\ $$$${demontrer}\:{sans}\:{recurrence}\:{que}\:{r}_{{n}} >\mathrm{0} \\ $$$${demontrer}\:{par}\:{recurrence}\:{que}\:{r}_{{n}+\mathrm{1}} \leq\frac{\mathrm{1}}{\mathrm{2}}{r}_{{n}} \\ $$$${demontrer}\:{sans}\:{recurrence}\:{que}\:{r}_{{n}} \leq\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{{n}} \\ $$$$\bullet{erly}\:{rolvinst}\bullet \\ $$

Question Number 196910 Answers: 0 Comments: 0

Question Number 196902 Answers: 1 Comments: 0

Question Number 196893 Answers: 1 Comments: 0

Question Number 196886 Answers: 2 Comments: 0

Question Number 196885 Answers: 2 Comments: 0

Question Number 196883 Answers: 1 Comments: 0

Question Number 196881 Answers: 1 Comments: 1

Question Number 196880 Answers: 1 Comments: 0

1. A container of milk is (4/5) full. When 10L of milk is poured into it the container becomes (9/(10)) full. What is the capacity of the container?

$$\mathrm{1}.\:{A}\:{container}\:{of}\:{milk}\:{is}\:\frac{\mathrm{4}}{\mathrm{5}}\:{full}.\:{When}\:\mathrm{10}{L}\:{of}\:{milk}\:{is}\:{poured}\:{into}\:{it}\:{the}\:{container}\:{becomes}\:\:\frac{\mathrm{9}}{\mathrm{10}}\:{full}.\:{What}\:{is}\:{the}\:{capacity}\:{of}\:{the}\:{container}? \\ $$

Question Number 196872 Answers: 1 Comments: 0

Let ξ be a positive Root of x^2 −2023x−1 Define a sequence ϕ_i such That ϕ_0 =1 ϕ_(n+1) =⌊ϕ_n ξ⌋, find The Remainder When ϕ_(2023 ) is divided by (√ϕ_2 )

$${Let}\:\xi\:{be}\:{a}\:{positive}\:{Root}\:{of}\:{x}^{\mathrm{2}} −\mathrm{2023}{x}−\mathrm{1} \\ $$$${Define}\:{a}\:{sequence}\:\varphi_{{i}} \:{such}\:{That}\:\varphi_{\mathrm{0}} =\mathrm{1} \\ $$$$\varphi_{{n}+\mathrm{1}} =\lfloor\varphi_{{n}} \xi\rfloor,\:{find}\:{The}\:{Remainder}\:{When}\:\varphi_{\mathrm{2023}\:} {is}\:{divided}\:{by}\:\sqrt{\varphi_{\mathrm{2}} } \\ $$

Pg 234 Pg 235 Pg 236 Pg 237 Pg 238 Pg 239 Pg 240 Pg 241 Pg 242 Pg 243

Terms of Service

Contact: info@tinkutara.com