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Question Number 102078 Answers: 5 Comments: 0

Question Number 102076 Answers: 0 Comments: 4

A car is currently valued at $70350.00. If it loses 12% of its value at the beginning of each year, a) find its value after three and half years. b) find the depreciation after three years

$$\mathrm{A}\:\mathrm{car}\:\mathrm{is}\:\mathrm{currently}\:\mathrm{valued}\:\mathrm{at}\:\$\mathrm{70350}.\mathrm{00}. \\ $$$$\mathrm{If}\:\mathrm{it}\:\mathrm{loses}\:\mathrm{12\%}\:\mathrm{of}\:\mathrm{its}\:\mathrm{value}\:\mathrm{at}\:\mathrm{the}\:\mathrm{beginning} \\ $$$$\mathrm{of}\:\mathrm{each}\:\mathrm{year}, \\ $$$$\left.\mathrm{a}\right)\:\mathrm{find}\:\mathrm{its}\:\mathrm{value}\:\mathrm{after}\:\mathrm{three}\:\mathrm{and}\:\mathrm{half}\:\mathrm{years}. \\ $$$$\left.\mathrm{b}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{depreciation}\:\mathrm{after}\:\mathrm{three}\:\mathrm{years} \\ $$

Question Number 102066 Answers: 3 Comments: 0

(1)∫ ((cos (ax) dx)/(√(sin ax−b))) (2) (D^3 +2D^2 +D)y = e^(2x) +x^2 −x (3)the area between the curves y = (2/x) and y = −x+3

$$\left(\mathrm{1}\right)\int\:\frac{\mathrm{cos}\:\left(\mathrm{ax}\right)\:\mathrm{dx}}{\sqrt{\mathrm{sin}\:\mathrm{ax}−\mathrm{b}}} \\ $$$$\left(\mathrm{2}\right)\:\left(\mathrm{D}^{\mathrm{3}} +\mathrm{2D}^{\mathrm{2}} +\mathrm{D}\right)\mathrm{y}\:=\:\mathrm{e}^{\mathrm{2x}} +\mathrm{x}^{\mathrm{2}} −\mathrm{x} \\ $$$$\left(\mathrm{3}\right)\mathrm{the}\:\mathrm{area}\:\mathrm{between}\:\mathrm{the}\:\mathrm{curves} \\ $$$$\mathrm{y}\:=\:\frac{\mathrm{2}}{\mathrm{x}}\:\mathrm{and}\:\mathrm{y}\:=\:−\mathrm{x}+\mathrm{3}\: \\ $$

Question Number 102065 Answers: 1 Comments: 0

∫ ((x^2 dx)/((1−x)(√x))) ?

$$\int\:\frac{\mathrm{x}^{\mathrm{2}} \:\mathrm{dx}}{\left(\mathrm{1}−\mathrm{x}\right)\sqrt{\mathrm{x}}}\:? \\ $$

Question Number 102064 Answers: 1 Comments: 0

∫ ((sin 3x)/(cos 5x. cos 2x)) dx ?

$$\int\:\frac{\mathrm{sin}\:\mathrm{3x}}{\mathrm{cos}\:\mathrm{5x}.\:\mathrm{cos}\:\mathrm{2x}}\:\mathrm{dx}\:? \\ $$

Question Number 102060 Answers: 2 Comments: 1

Question Number 102043 Answers: 0 Comments: 1

∫e^(√(ax+b)) dx

$$\int{e}^{\sqrt{{ax}+{b}}} {dx} \\ $$

Question Number 102036 Answers: 3 Comments: 0

lim_(x→0) ((((x^2 −1))^(1/5) +((x+1))^(1/3) )/(((x−1))^(1/3) +(√(x+1))))=?

$${li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\frac{\sqrt[{\mathrm{5}}]{{x}^{\mathrm{2}} −\mathrm{1}}\:+\sqrt[{\mathrm{3}}]{{x}+\mathrm{1}}}{\sqrt[{\mathrm{3}}]{{x}−\mathrm{1}}\:+\sqrt{{x}+\mathrm{1}}}=? \\ $$

Question Number 102034 Answers: 2 Comments: 0

lim_(x→2) ((((2x+4))^(1/3) −2)/(x^2 −x−2))=?

$${li}\underset{{x}\rightarrow\mathrm{2}} {{m}}\frac{\sqrt[{\mathrm{3}}]{\mathrm{2}{x}+\mathrm{4}}\:−\mathrm{2}}{{x}^{\mathrm{2}} −{x}−\mathrm{2}}=? \\ $$

Question Number 105269 Answers: 0 Comments: 0

a;b;c are real numbers 1<b<c^2 <a^(10) log_a b+2log_b c+5log_c a=12 prove that 2log_a c+5log_c b+10log_b a≥21

$${a};{b};{c}\:{are}\:{real}\:{numbers} \\ $$$$\mathrm{1}<{b}<{c}^{\mathrm{2}} <{a}^{\mathrm{10}} \\ $$$${log}_{{a}} {b}+\mathrm{2}{log}_{{b}} {c}+\mathrm{5}{log}_{{c}} {a}=\mathrm{12} \\ $$$${prove}\:{that} \\ $$$$\mathrm{2}{log}_{{a}} {c}+\mathrm{5}{log}_{{c}} {b}+\mathrm{10}{log}_{{b}} {a}\geqslant\mathrm{21} \\ $$

Question Number 105300 Answers: 0 Comments: 0

what is the absolute speed of A that moves via y = (1/(1+x)) (upper part) when it crosses y −axis meanwhile B moves at constant speed of 1 the x−axis ?

$${what}\:{is}\:{the}\:{absolute}\:{speed}\:{of}\:{A}\:{that} \\ $$$${moves}\:{via}\:{y}\:=\:\frac{\mathrm{1}}{\mathrm{1}+{x}}\:\left({upper}\:{part}\right)\:{when} \\ $$$${it}\:{crosses}\:{y}\:−{axis}\:{meanwhile}\:{B} \\ $$$${moves}\:{at}\:{constant}\:{speed}\:{of}\:\mathrm{1}\:{the} \\ $$$${x}−{axis}\:? \\ $$

Question Number 102020 Answers: 2 Comments: 0

lim_(x→0) (tan((π/4)−x))^(1/x)

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left({tan}\left(\frac{\pi}{\mathrm{4}}−{x}\right)\right)^{\frac{\mathrm{1}}{{x}}} \\ $$

Question Number 102015 Answers: 0 Comments: 0

how many rotational symetry triangle isosceles ? 1 or 0??

$${how}\:{many}\:{rotational}\:{symetry}\:\:{triangle} \\ $$$${isosceles}\:? \\ $$$$\mathrm{1}\:{or}\:\mathrm{0}?? \\ $$

Question Number 102002 Answers: 0 Comments: 6

Question Number 102001 Answers: 2 Comments: 0

evaluate ∫cos^3 xsin^3 xdx.

$${evaluate}\:\int\mathrm{cos}\:^{\mathrm{3}} {x}\mathrm{sin}\:^{\mathrm{3}} {xdx}. \\ $$

Question Number 101998 Answers: 0 Comments: 0

1)solve inside C x^n −e^(−inα) =0 (α real) 2) let P(x) =x^n −e^(−inα) factorize P(x)inside C[x] 2) decompose inside C(x) thefraction F =(1/(P(x))) and deyermine ∫ F(x)dx

$$\left.\mathrm{1}\right)\mathrm{solve}\:\mathrm{inside}\:\mathrm{C}\:\:\mathrm{x}^{\mathrm{n}} −\mathrm{e}^{−\mathrm{in}\alpha} \:=\mathrm{0}\:\:\:\:\:\left(\alpha\:\mathrm{real}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{let}\:\mathrm{P}\left(\mathrm{x}\right)\:=\mathrm{x}^{\mathrm{n}} −\mathrm{e}^{−\mathrm{in}\alpha} \:\:\mathrm{factorize}\:\mathrm{P}\left(\mathrm{x}\right)\mathrm{inside}\:\mathrm{C}\left[\mathrm{x}\right] \\ $$$$\left.\mathrm{2}\right)\:\mathrm{decompose}\:\mathrm{inside}\:\mathrm{C}\left(\mathrm{x}\right)\:\mathrm{thefraction}\:\mathrm{F}\:=\frac{\mathrm{1}}{\mathrm{P}\left(\mathrm{x}\right)} \\ $$$$\mathrm{and}\:\mathrm{deyermine}\:\int\:\mathrm{F}\left(\mathrm{x}\right)\mathrm{dx} \\ $$

Question Number 101994 Answers: 1 Comments: 1

Question Number 101985 Answers: 1 Comments: 0

∫ ((3x^5 − x^4 + 9x^3 − 12x^2 − 2x + 1)/((x^3 − 1)^2 )) dx

$$\int\:\frac{\mathrm{3x}^{\mathrm{5}} \:−\:\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{9x}^{\mathrm{3}} \:−\:\mathrm{12x}^{\mathrm{2}} \:−\:\mathrm{2x}\:\:+\:\:\mathrm{1}}{\left(\mathrm{x}^{\mathrm{3}} \:−\:\mathrm{1}\right)^{\mathrm{2}} }\:\mathrm{dx} \\ $$

Question Number 102058 Answers: 1 Comments: 0

∫_0 ^1 ((sin(logx))/(logx))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{sin}\left({logx}\right)}{{logx}}{dx} \\ $$

Question Number 102183 Answers: 4 Comments: 0

∫ ((cos θ)/(sin θ−cos θ)) dθ ?

$$\int\:\frac{\mathrm{cos}\:\theta}{\mathrm{sin}\:\theta−\mathrm{cos}\:\theta}\:{d}\theta\:? \\ $$

Question Number 101981 Answers: 3 Comments: 0

lim_(x→0) (((tanx)/x))^(1/x^2 )

$${li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\left(\frac{{tanx}}{{x}}\right)^{\frac{\mathrm{1}}{{x}^{\mathrm{2}} }} \\ $$

Question Number 101977 Answers: 0 Comments: 0

Given 2 functions, f and g, n-times derivable within the open interval, R and verify the property f(x_0 )=f^((k)) (x_0 )=0 , g(x_0 )=g^((k)) (x_0 )=0 , ∀k∈{1,2,...,n−1} Show that lim_(x→x_0 ) ((f(x))/(g(x)))=((f^((n)) (x_0 ))/(g^((n)) (x_0 )))

$$\mathrm{Given}\:\mathrm{2}\:\mathrm{functions},\:\mathrm{f}\:\mathrm{and}\:\mathrm{g},\:\mathrm{n}-\mathrm{times}\:\mathrm{derivable}\:\mathrm{within} \\ $$$$\mathrm{the}\:\mathrm{open}\:\mathrm{interval},\:\mathbb{R}\:\mathrm{and}\:\mathrm{verify}\:\mathrm{the}\:\mathrm{property} \\ $$$$\mathrm{f}\left(\mathrm{x}_{\mathrm{0}} \right)=\mathrm{f}^{\left(\mathrm{k}\right)} \left(\mathrm{x}_{\mathrm{0}} \right)=\mathrm{0}\:,\:\mathrm{g}\left(\mathrm{x}_{\mathrm{0}} \right)=\mathrm{g}^{\left(\mathrm{k}\right)} \left(\mathrm{x}_{\mathrm{0}} \right)=\mathrm{0}\:,\:\forall\mathrm{k}\in\left\{\mathrm{1},\mathrm{2},...,\mathrm{n}−\mathrm{1}\right\} \\ $$$$\mathrm{Show}\:\mathrm{that}\:\underset{\mathrm{x}\rightarrow\mathrm{x}_{\mathrm{0}} } {\mathrm{lim}}\frac{\mathrm{f}\left(\mathrm{x}\right)}{\mathrm{g}\left(\mathrm{x}\right)}=\frac{\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{x}_{\mathrm{0}} \right)}{\mathrm{g}^{\left(\mathrm{n}\right)} \left(\mathrm{x}_{\mathrm{0}} \right)} \\ $$

Question Number 101974 Answers: 2 Comments: 1

Question Number 101971 Answers: 0 Comments: 2

Question Number 101970 Answers: 1 Comments: 0

∫_0 ^∞ ((Cos(ax))/(x^2 +b^2 )) dx

$$\int_{\mathrm{0}} ^{\infty} \:\frac{{Cos}\left({ax}\right)}{{x}^{\mathrm{2}} +{b}^{\mathrm{2}} }\:{dx} \\ $$

Question Number 101961 Answers: 0 Comments: 4

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