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Question Number 88896 Answers: 1 Comments: 2

find lim_(x→0) ((ln(sin(3x)+cos(3x)))/(ln(sin(x)+cos(x))))

$${find}\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\frac{{ln}\left({sin}\left(\mathrm{3}{x}\right)+{cos}\left(\mathrm{3}{x}\right)\right)}{{ln}\left({sin}\left({x}\right)+{cos}\left({x}\right)\right)} \\ $$

Question Number 88892 Answers: 0 Comments: 2

Question Number 88894 Answers: 0 Comments: 1

Question Number 88889 Answers: 0 Comments: 1

Question Number 88886 Answers: 1 Comments: 5

Question Number 88882 Answers: 1 Comments: 1

The coefficient of x^3 in ((√x^5 ) +(3/(√x^3 )))^6 is

$$\mathrm{The}\:\mathrm{coefficient}\:\mathrm{of}\:\:{x}^{\mathrm{3}} \:\mathrm{in}\:\left(\sqrt{{x}^{\mathrm{5}} }\:+\frac{\mathrm{3}}{\sqrt{{x}^{\mathrm{3}} }}\right)^{\mathrm{6}} \:\:\mathrm{is} \\ $$

Question Number 88881 Answers: 1 Comments: 0

Question Number 88876 Answers: 0 Comments: 2

Given a 10−digit number X = 1345789026 How many 10−digit number that can be made using every digit from X, with condition: If a number n is located in k^(th) position of X, then the new created number must not contain number n in k^(th) position Example: • Number 1 is located in 1^(st) position of X, hence 1234567890 is not valid, but 2134567890 is valid • Number 5 and 0 are located in 4^(th) and 8^(th) position of X, hence 9435162087 is not valid, but 9431506287 is valid. • 1345026789 is not valid • and so on...

$$\mathrm{Given}\:\mathrm{a}\:\mathrm{10}−\mathrm{digit}\:\mathrm{number}\:{X}\:=\:\mathrm{1345789026} \\ $$$$\mathrm{How}\:\mathrm{many}\:\mathrm{10}−\mathrm{digit}\:\mathrm{number}\:\mathrm{that}\:\mathrm{can}\:\mathrm{be}\:\mathrm{made} \\ $$$$\mathrm{using}\:\mathrm{every}\:\mathrm{digit}\:\mathrm{from}\:{X},\:\mathrm{with}\:\mathrm{condition}: \\ $$$$\mathrm{If}\:\mathrm{a}\:\mathrm{number}\:{n}\:\:\mathrm{is}\:\mathrm{located}\:\mathrm{in}\:{k}^{{th}} \:\mathrm{position}\:\mathrm{of}\:{X},\:\mathrm{then} \\ $$$$\mathrm{the}\:\mathrm{new}\:\mathrm{created}\:\mathrm{number}\:\mathrm{must}\:\mathrm{not}\:\mathrm{contain} \\ $$$$\mathrm{number}\:{n}\:\mathrm{in}\:{k}^{{th}} \:\mathrm{position} \\ $$$$ \\ $$$$\mathrm{Example}: \\ $$$$\bullet\:\mathrm{Number}\:\mathrm{1}\:\mathrm{is}\:\mathrm{located}\:\mathrm{in}\:\mathrm{1}^{{st}} \:\mathrm{position}\:\mathrm{of}\:{X},\:\mathrm{hence} \\ $$$$\mathrm{1234567890}\:\mathrm{is}\:\mathrm{not}\:\mathrm{valid},\:\mathrm{but}\:\mathrm{2134567890} \\ $$$$\mathrm{is}\:\mathrm{valid} \\ $$$$\bullet\:\mathrm{Number}\:\mathrm{5}\:\mathrm{and}\:\mathrm{0}\:\mathrm{are}\:\mathrm{located}\:\mathrm{in}\:\mathrm{4}^{{th}} \:\mathrm{and}\:\mathrm{8}^{{th}} \:\mathrm{position} \\ $$$$\mathrm{of}\:{X},\:\mathrm{hence}\:\mathrm{9435162087}\:\mathrm{is}\:\mathrm{not}\:\mathrm{valid},\:\mathrm{but} \\ $$$$\mathrm{9431506287}\:\mathrm{is}\:\mathrm{valid}. \\ $$$$\bullet\:\mathrm{1345026789}\:\mathrm{is}\:\mathrm{not}\:\mathrm{valid} \\ $$$$\bullet\:\mathrm{and}\:\mathrm{so}\:\mathrm{on}... \\ $$

Question Number 88873 Answers: 0 Comments: 1

3+(√(x^2 −5)) > ∣x−1∣

$$\mathrm{3}+\sqrt{{x}^{\mathrm{2}} −\mathrm{5}}\:>\:\mid{x}−\mathrm{1}\mid\: \\ $$

Question Number 88872 Answers: 0 Comments: 1

The system of equations kx+y+z=1, x+ky+z=k and x+y+kz=k^2 have no solution if k equals

$$\mathrm{The}\:\mathrm{system}\:\mathrm{of}\:\mathrm{equations}\:\:\:{kx}+{y}+{z}=\mathrm{1}, \\ $$$${x}+{ky}+{z}={k}\:\:\:\mathrm{and}\:\:\:{x}+{y}+{kz}={k}^{\mathrm{2}} \:\mathrm{have} \\ $$$$\mathrm{no}\:\mathrm{solution}\:\mathrm{if}\:\:\:{k}\:\:\mathrm{equals} \\ $$

Question Number 88871 Answers: 0 Comments: 0