Question and Answers Forum

All Questions Topic List

AllQuestion and Answers: Page 1

Question Number 227353 Answers: 0 Comments: 0

Question Number 227346 Answers: 0 Comments: 0

Question Number 227329 Answers: 0 Comments: 0

1) Does half open interval A=[0,1) is Compact Space ? 2) Prove for a Compact Space X_k Product Space X=Π_k {X_k ^ ; k∈I} also Compact Space 3) Show that for a Compact Space X and Continuous function f if f satisfy f;X→Y ,Image Y also Compact Space

$$\left.\mathrm{1}\right)\:\mathrm{Does}\:\mathrm{half}\:\mathrm{open}\:\mathrm{interval}\:{A}=\left[\mathrm{0},\mathrm{1}\right)\:\mathrm{is}\:\mathrm{Compact}\:\mathrm{Space}\:? \\ $$$$\left.\mathrm{2}\right)\:\mathrm{Prove}\:\mathrm{for}\:\mathrm{a}\:\:\mathrm{Compact}\:\mathrm{Space}\:{X}_{{k}} \:\: \\ $$$$\mathrm{Product}\:\mathrm{Space}\:{X}=\underset{{k}} {\prod}\:\left\{{X}_{{k}} ^{\:} \:;\:{k}\in{I}\right\}\:\:\mathrm{also}\:\mathrm{Compact}\:\mathrm{Space} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{Show}\:\mathrm{that}\:\mathrm{for}\:\mathrm{a}\:\mathrm{Compact}\:\mathrm{Space}\:{X}\:\mathrm{and}\:\mathrm{Continuous}\:\mathrm{function}\:{f} \\ $$$$\mathrm{if}\:\:{f}\:\:\mathrm{satisfy}\:\:{f};{X}\rightarrow{Y}\:,\mathrm{Image}\:{Y}\:\mathrm{also}\:\mathrm{Compact}\:\mathrm{Space} \\ $$

Question Number 227328 Answers: 5 Comments: 0

Question Number 227325 Answers: 0 Comments: 0

Prove that in any acute △ABC if I is the in-center and H is the ortho-center then: (1/(IA)) + (1/(IB)) + (1/(IC)) ≤ (1/(HA)) + (1/(HB)) + (1/(HC))

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{in}\:\mathrm{any}\:\mathrm{acute}\:\bigtriangleup\mathrm{ABC}\: \\ $$$$\mathrm{if}\:\mathrm{I}\:\mathrm{is}\:\mathrm{the}\:\mathrm{in}-\mathrm{center}\:\mathrm{and}\:\mathrm{H}\:\mathrm{is}\:\mathrm{the}\:\mathrm{ortho}-\mathrm{center} \\ $$$$\mathrm{then}: \\ $$$$\frac{\mathrm{1}}{\mathrm{IA}}\:+\:\frac{\mathrm{1}}{\mathrm{IB}}\:+\:\frac{\mathrm{1}}{\mathrm{IC}}\:\:\leqslant\:\:\frac{\mathrm{1}}{\mathrm{HA}}\:+\:\frac{\mathrm{1}}{\mathrm{HB}}\:+\:\frac{\mathrm{1}}{\mathrm{HC}} \\ $$

Question Number 227326 Answers: 1 Comments: 0

∣ x+1 ∣ + ∣ x ∣ + ∣ x−3∣ > 8

$$\:\:\:\mid\:{x}+\mathrm{1}\:\mid\:+\:\mid\:{x}\:\mid\:+\:\mid\:{x}−\mathrm{3}\mid\:>\:\mathrm{8}\:\: \\ $$

Question Number 227323 Answers: 0 Comments: 0

Is there an n>11 such that every digit of 2^n in decimal representation is even?

$$\mathrm{Is}\:\mathrm{there}\:\mathrm{an}\:{n}>\mathrm{11}\:\mathrm{such}\:\mathrm{that}\:\mathrm{every}\:\mathrm{digit}\:\mathrm{of}\:\mathrm{2}^{{n}} \\ $$$$\mathrm{in}\:\mathrm{decimal}\:\mathrm{representation}\:\mathrm{is}\:\mathrm{even}? \\ $$

Question Number 227341 Answers: 0 Comments: 8

find the surface area of a spherical cap

$${find}\:{the}\:{surface}\:{area}\:{of}\:{a}\:{spherical} \\ $$$${cap} \\ $$

Question Number 227340 Answers: 0 Comments: 0

Question Number 227319 Answers: 2 Comments: 0

f(z^3 +(1/z^3 ))=z f(z)=?

$${f}\left({z}^{\mathrm{3}} +\frac{\mathrm{1}}{{z}^{\mathrm{3}} }\right)={z} \\ $$$${f}\left({z}\right)=? \\ $$

Question Number 227312 Answers: 2 Comments: 0

tg(15) + ctg(5) = ?

$$\mathrm{tg}\left(\mathrm{15}\right)\:+\:\mathrm{ctg}\left(\mathrm{5}\right)\:=\:? \\ $$

Question Number 227306 Answers: 1 Comments: 1

Question Number 227295 Answers: 1 Comments: 0

Question Number 227294 Answers: 6 Comments: 1

Question Number 227286 Answers: 2 Comments: 0

tg(4) + ctg(4) = ?

$$\mathrm{tg}\left(\mathrm{4}\right)\:+\:\mathrm{ctg}\left(\mathrm{4}\right)\:=\:? \\ $$

Question Number 227283 Answers: 1 Comments: 0

Proof that (√2) is irrational

$${Proof}\:{that}\:\sqrt{\mathrm{2}}\:{is}\:{irrational} \\ $$

Question Number 227276 Answers: 4 Comments: 1

Question Number 227274 Answers: 1 Comments: 0

Does condition sup_(x∈R) ∣∣f^((1)) (x)∣∣<∞ , Gaurantee f(x) is Bounded in R?

$$\mathrm{Does}\:\mathrm{condition} \\ $$$$\underset{{x}\in\mathbb{R}} {\mathrm{sup}}\:\mid\mid{f}^{\left(\mathrm{1}\right)} \left({x}\right)\mid\mid<\infty\:,\:\:\mathrm{Gaurantee}\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{Bounded}\:\mathrm{in}\:\mathbb{R}? \\ $$

Question Number 227273 Answers: 1 Comments: 0

Question Number 227272 Answers: 1 Comments: 0

Question Number 227271 Answers: 3 Comments: 0

Question Number 227255 Answers: 8 Comments: 0

Question Number 227250 Answers: 1 Comments: 0

Question Number 227249 Answers: 1 Comments: 0

Question Number 227248 Answers: 5 Comments: 0

Question Number 227247 Answers: 2 Comments: 0

Pg 1 Pg 2 Pg 3 Pg 4 Pg 5 Pg 6 Pg 7 Pg 8 Pg 9 Pg 10

Terms of Service

Contact: info@tinkutara.com