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Question Number 115194 Answers: 0 Comments: 0

Find a three−digits number whose digits form a geometry progression ;if you known that after substract that number by 495 ,get a number written by the same digits as the number you are looking for but in the reverse order;if the digits of the number obtained after substraction(from left right)reduced by 1,1 and 2 respectively ,you obtain an arithmetic progression

$$\mathrm{Find}\:\mathrm{a}\:\mathrm{three}−\mathrm{digits}\:\mathrm{number}\:\mathrm{whose} \\ $$$$\mathrm{digits}\:\mathrm{form}\:\mathrm{a}\:\mathrm{geometry}\:\mathrm{progression} \\ $$$$;\mathrm{if}\:\mathrm{you}\:\mathrm{known}\:\mathrm{that}\:\mathrm{after}\:\mathrm{substract}\:\mathrm{that} \\ $$$$\mathrm{number}\:\mathrm{by}\:\mathrm{495}\:,\mathrm{get}\:\mathrm{a}\:\mathrm{number} \\ $$$$\mathrm{written}\:\mathrm{by}\:\mathrm{the}\:\mathrm{same}\:\mathrm{digits}\:\mathrm{as}\:\mathrm{the} \\ $$$$\mathrm{number}\:\mathrm{you}\:\mathrm{are}\:\mathrm{looking}\:\mathrm{for}\:\mathrm{but}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{reverse}\:\mathrm{order};\mathrm{if}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{number}\:\mathrm{obtained}\:\mathrm{after} \\ $$$$\mathrm{substraction}\left(\mathrm{from}\:\mathrm{left}\:\mathrm{right}\right)\mathrm{reduced} \\ $$$$\mathrm{by}\:\mathrm{1},\mathrm{1}\:\mathrm{and}\:\mathrm{2}\:\mathrm{respectively}\:,\mathrm{you}\:\mathrm{obtain} \\ $$$$\mathrm{an}\:\mathrm{arithmetic}\:\mathrm{progression} \\ $$

Question Number 115193 Answers: 1 Comments: 1

...advanced mathematics... :: digamma limit :: if k>0 then prove that lim_(x→0) (1/x)(ψ(((k+x)/(2x))) − ψ((k/(2x)))) =(1/k) ✓ m.n.july.1970...

$$\:\:\:\:\:\:\:\:\:\:\:...{advanced}\:\:{mathematics}...\:\: \\ $$$$\:\:\:\:\:\:\:::\:\:\:{digamma}\:\:{limit}\:\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:{if}\:\:\:{k}>\mathrm{0}\:\:{then} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{prove}\:\:{that}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{lim}_{{x}\rightarrow\mathrm{0}} \:\frac{\mathrm{1}}{{x}}\left(\psi\left(\frac{{k}+{x}}{\mathrm{2}{x}}\right)\:−\:\psi\left(\frac{{k}}{\mathrm{2}{x}}\right)\right)\:=\frac{\mathrm{1}}{{k}}\:\:\:\:\checkmark \\ $$$$ \\ $$$$\:\:\:\:\:{m}.{n}.{july}.\mathrm{1970}... \\ $$$$\: \\ $$

Question Number 115174 Answers: 2 Comments: 0

lim_(x→1) ((tan (cos^(−1) ((1/x))))/( (√(x−1)))) = ?

$$\:\:\:\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:\left(\mathrm{cos}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{{x}}\right)\right)}{\:\sqrt{{x}−\mathrm{1}}}\:=\:? \\ $$

Question Number 115170 Answers: 3 Comments: 0

(1)Given ((P _(n−1)^(2n+1) )/(P _n^(2n−1) )) = (3/5) , find n = ? (2) in how many ways can 6 persons stand in a queue? (3) how many different 4 letter words can be formed by using letters of EDUCATION using each letter at most once ?

$$\left(\mathrm{1}\right){Given}\:\frac{{P}\:_{{n}−\mathrm{1}} ^{\mathrm{2}{n}+\mathrm{1}} }{{P}\:_{{n}} ^{\mathrm{2}{n}−\mathrm{1}} }\:=\:\frac{\mathrm{3}}{\mathrm{5}}\:,\:{find}\:{n}\:=\:? \\ $$$$\left(\mathrm{2}\right)\:{in}\:{how}\:{many}\:{ways}\:{can}\:\mathrm{6}\:{persons} \\ $$$${stand}\:{in}\:{a}\:{queue}? \\ $$$$\left(\mathrm{3}\right)\:{how}\:{many}\:{different}\:\mathrm{4}\:{letter}\:{words} \\ $$$${can}\:{be}\:{formed}\:{by}\:{using}\:{letters}\:{of}\: \\ $$$${EDUCATION}\:{using}\:{each}\:{letter}\:{at}\: \\ $$$${most}\:{once}\:? \\ $$$$ \\ $$

Question Number 115169 Answers: 3 Comments: 0

∫ sin^2 (ln x) dx

$$\int\:\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{ln}\:{x}\right)\:{dx}\: \\ $$

Question Number 115167 Answers: 1 Comments: 0

lim_(x→0) ((sec (sin^(−1) (1−x)))/(3(√x))) = ?

$$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sec}\:\:\left(\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{1}−{x}\right)\right)}{\mathrm{3}\sqrt{{x}}}\:=\:? \\ $$

Question Number 115166 Answers: 2 Comments: 0