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Question Number 203329 Answers: 1 Comments: 0

find the ranges of value of x for which series convergent or divergent 𝚺_(n=1) ^∞ (((n+1))/n^3 )x^n

$$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{ranges}}\:\boldsymbol{{of}}\:\boldsymbol{{value}}\:\boldsymbol{{of}}\:\boldsymbol{{x}}\:\boldsymbol{{for}}\:\boldsymbol{{which}}\: \\ $$$$\boldsymbol{{series}}\:\boldsymbol{{convergent}}\:\boldsymbol{{or}}\:\boldsymbol{{divergent}} \\ $$$$\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\boldsymbol{\sum}}}\frac{\left(\boldsymbol{{n}}+\mathrm{1}\right)}{\boldsymbol{{n}}^{\mathrm{3}} }\boldsymbol{{x}}^{\boldsymbol{{n}}} \\ $$

Question Number 203327 Answers: 2 Comments: 0

Question Number 203325 Answers: 1 Comments: 0

sin^2 x+cos^2 (2x)+sin^2 (3x)=(3/2)

$$\mathrm{sin}^{\mathrm{2}} {x}+\mathrm{cos}^{\mathrm{2}} \left(\mathrm{2}{x}\right)+\mathrm{sin}^{\mathrm{2}} \left(\mathrm{3}{x}\right)=\frac{\mathrm{3}}{\mathrm{2}} \\ $$

Question Number 203321 Answers: 1 Comments: 0

Help-me! Observe points A, B and C below and find the widthof a lake according to the following data: (AB)m; C^ = 39°52′12′′ (BC − 257.5)m; A^ = 97°7′56′′ (CA − 30)m; B^ = 42°59′52′′ CA is the width of the lake •^C •_A •_B

$$\mathrm{Help}-\mathrm{me}! \\ $$$$\: \\ $$$$\mathrm{Observe}\:\mathrm{points}\:\mathrm{A},\:\mathrm{B}\:\mathrm{and}\:\mathrm{C}\:\mathrm{below}\:\mathrm{and}\:\mathrm{find}\:\mathrm{the}\:\mathrm{widthof}\:\mathrm{a}\:\mathrm{lake}\:\mathrm{according}\:\mathrm{to}\:\mathrm{the}\:\mathrm{following}\:\mathrm{data}: \\ $$$$\: \\ $$$$\left(\mathrm{AB}\right)\mathrm{m};\:\hat {\mathrm{C}}\:=\:\mathrm{39}°\mathrm{52}'\mathrm{12}'' \\ $$$$\left(\mathrm{BC}\:−\:\mathrm{257}.\mathrm{5}\right)\mathrm{m};\:\hat {\mathrm{A}}\:=\:\mathrm{97}°\mathrm{7}'\mathrm{56}'' \\ $$$$\left(\mathrm{CA}\:−\:\mathrm{30}\right)\mathrm{m};\:\hat {\mathrm{B}}\:=\:\mathrm{42}°\mathrm{59}'\mathrm{52}'' \\ $$$$\mathrm{CA}\:\mathrm{is}\:\mathrm{the}\:\mathrm{width}\:\mathrm{of}\:\mathrm{the}\:\mathrm{lake}\: \\ $$$$\: \\ $$$$\bullet^{\mathrm{C}} \\ $$$$\: \\ $$$$\: \\ $$$$\: \\ $$$$\: \\ $$$$\: \\ $$$$\: \\ $$$$\bullet_{\mathrm{A}} \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\bullet_{\mathrm{B}} \\ $$

Question Number 203319 Answers: 0 Comments: 6

Question Number 203313 Answers: 1 Comments: 0

a_(n+1) =a_n ^2 +2a_n −2, a_1 =3. Prove thatΣ (1/(a_n +2)) ≤ (3/(10)).

$${a}_{{n}+\mathrm{1}} ={a}_{{n}} ^{\mathrm{2}} +\mathrm{2}{a}_{{n}} −\mathrm{2},\:{a}_{\mathrm{1}} =\mathrm{3}. \\ $$$$\mathrm{Prove}\:\mathrm{that}\Sigma\:\frac{\mathrm{1}}{{a}_{{n}} +\mathrm{2}}\:\leqslant\:\frac{\mathrm{3}}{\mathrm{10}}. \\ $$

Question Number 203309 Answers: 3 Comments: 0

If z_1 = 3 + 3(√3) i and z_2 = -1 − (√3) i Find: (z_1 ^( 3) /z_2 ^( 6) ) = ?

$$\mathrm{If}\:\:\:\mathrm{z}_{\mathrm{1}} =\:\mathrm{3}\:+\:\mathrm{3}\sqrt{\mathrm{3}}\:\boldsymbol{\mathrm{i}}\:\:\:\mathrm{and}\:\:\:\mathrm{z}_{\mathrm{2}} =\:-\mathrm{1}\:−\:\sqrt{\mathrm{3}}\:\boldsymbol{\mathrm{i}} \\ $$$$\mathrm{Find}:\:\:\:\frac{\mathrm{z}_{\mathrm{1}} ^{\:\mathrm{3}} }{\mathrm{z}_{\mathrm{2}} ^{\:\mathrm{6}} }\:=\:? \\ $$

Question Number 203308 Answers: 1 Comments: 0

my iq is not good enough to be a mathematician. i dont know what to do with my life now. what is there for me.

$$\:\:\mathrm{my}\:\mathrm{iq}\:\mathrm{is}\:\mathrm{not}\:\mathrm{good}\:\mathrm{enough}\:\mathrm{to}\:\mathrm{be}\:\mathrm{a}\:\mathrm{mathematician}.\:\: \\ $$$$\:\:\mathrm{i}\:\mathrm{dont}\:\mathrm{know}\:\mathrm{what}\:\mathrm{to}\:\mathrm{do}\:\mathrm{with}\:\mathrm{my}\:\mathrm{life}\:\mathrm{now}.\:\: \\ $$$$\:\:\mathrm{what}\:\mathrm{is}\:\mathrm{there}\:\mathrm{for}\:\mathrm{me}.\:\: \\ $$

Question Number 203305 Answers: 1 Comments: 0

Question Number 203304 Answers: 0 Comments: 0

Question Number 203301 Answers: 1 Comments: 0

is ∫(√x)e^(−x) dx =Σ_(n=1) ^∞ ((Π_(k=1) ^n (2/(2k+1)))x^n (√x)e^(−x) )+C?

$$\mathrm{is} \\ $$$$\int\sqrt{{x}}{e}^{−{x}} {dx} \\ $$$$=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\left(\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}\frac{\mathrm{2}}{\mathrm{2}{k}+\mathrm{1}}\right){x}^{{n}} \sqrt{{x}}{e}^{−{x}} \right)+{C}? \\ $$

Question Number 203291 Answers: 1 Comments: 0

f(x)={1+((√x^2 )/x) if x#0 2 if x=0 study the continuty of f in 0

$${f}\left({x}\right)=\left\{\mathrm{1}+\frac{\sqrt{{x}^{\mathrm{2}} }}{{x}}\:\:\:{if}\:{x}#\mathrm{0}\right. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}\:\:{if}\:\:{x}=\mathrm{0} \\ $$$${study}\:{the}\:{continuty}\:{of}\:{f}\:{in}\:\mathrm{0} \\ $$

Question Number 203288 Answers: 3 Comments: 0

Find: lim_(x→0) ((1 − cos4x)/x^2 ) = ?

$$\mathrm{Find}:\:\:\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}\:−\:\mathrm{cos4x}}{\mathrm{x}^{\mathrm{2}} }\:=\:? \\ $$

Question Number 203282 Answers: 2 Comments: 2

Question Number 203277 Answers: 0 Comments: 0

Question Number 203275 Answers: 0 Comments: 2

Show this has exactly 7 solutions for x∈C: x^(ln x) =1

$$\mathrm{Show}\:\mathrm{this}\:\mathrm{has}\:\mathrm{exactly}\:\mathrm{7}\:\mathrm{solutions}\:\mathrm{for}\:{x}\in\mathbb{C}: \\ $$$${x}^{\mathrm{ln}\:{x}} =\mathrm{1} \\ $$

Question Number 203270 Answers: 1 Comments: 0

find the last 4 digits of 2024^(2023)

$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{last}}\:\mathrm{4}\:\boldsymbol{\mathrm{digits}}\:\boldsymbol{\mathrm{of}}\:\mathrm{2024}^{\mathrm{2023}} \\ $$

Question Number 203264 Answers: 2 Comments: 0

If x = ((1 + (√5))/2) find: x^(12) = ?

$$\mathrm{If}\:\:\:\:\:\mathrm{x}\:=\:\frac{\mathrm{1}\:+\:\sqrt{\mathrm{5}}}{\mathrm{2}}\:\:\:\:\:\mathrm{find}:\:\mathrm{x}^{\mathrm{12}} \:=\:? \\ $$

Question Number 203260 Answers: 0 Comments: 0

f(x)=2ln∣x−1∣+ln(2x+1) •1)−the intersextion Curve with axe XX^′ ? •2)−find the equation of Circle tengent to the Curve (f) and axe (O,Y):Y>0 and the relative maximum of f(x) •3)−the Area delimited by x=3 max relative and Circle ? •4)Graphe f(x)

$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{2ln}\mid\mathrm{x}−\mathrm{1}\mid+\mathrm{ln}\left(\mathrm{2x}+\mathrm{1}\right) \\ $$$$\left.\bullet\mathrm{1}\right)−\mathrm{the}\:\mathrm{intersextion}\:\:\mathrm{Curve}\:\mathrm{with} \\ $$$$\mathrm{axe}\:\mathrm{XX}^{'} ? \\ $$$$\left.\bullet\mathrm{2}\right)−\mathrm{find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{Circle}\:\mathrm{tengent}\:\mathrm{to} \\ $$$$\mathrm{the}\:\mathrm{Curve}\:\left(\mathrm{f}\right)\:\mathrm{and}\:\mathrm{axe}\:\left(\mathrm{O},\mathrm{Y}\right):\mathrm{Y}>\mathrm{0} \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{relative}\:\mathrm{maximum}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x}\right) \\ $$$$\left.\bullet\mathrm{3}\right)−\mathrm{the}\:\mathrm{Area}\:\mathrm{delimited}\:\mathrm{by}\:\mathrm{x}=\mathrm{3} \\ $$$$\:\:\:\:\:\mathrm{max}\:\mathrm{relative}\:\mathrm{and}\:\mathrm{Circle}\:? \\ $$$$\left.\bullet\mathrm{4}\right)\mathrm{Graphe}\:\:\mathrm{f}\left(\mathrm{x}\right) \\ $$

Question Number 203269 Answers: 2 Comments: 0

Question Number 203247 Answers: 2 Comments: 0

lim_(x→0) x tan(π/2)(1+x)=?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{x}\:{tan}\frac{\pi}{\mathrm{2}}\left(\mathrm{1}+{x}\right)=? \\ $$

Question Number 203245 Answers: 2 Comments: 0

If x = ((2019))^(1/3) + 1 Find: (x + 1)^3 −6∙(x + 1)^2 + 12x − 3

$$\mathrm{If}\:\:\:\mathrm{x}\:=\:\sqrt[{\mathrm{3}}]{\mathrm{2019}}\:+\:\mathrm{1} \\ $$$$\mathrm{Find}: \\ $$$$\left(\mathrm{x}\:+\:\mathrm{1}\right)^{\mathrm{3}} −\mathrm{6}\centerdot\left(\mathrm{x}\:+\:\mathrm{1}\right)^{\mathrm{2}} \:+\:\mathrm{12x}\:−\:\mathrm{3} \\ $$

Question Number 203244 Answers: 0 Comments: 0

Question Number 203242 Answers: 1 Comments: 0

sin6°∙sin12°∙sin24°∙sin28°

$${sin}\mathrm{6}°\centerdot{sin}\mathrm{12}°\centerdot{sin}\mathrm{24}°\centerdot{sin}\mathrm{28}° \\ $$

Question Number 203236 Answers: 0 Comments: 0

how is solution Q203144

$$\mathrm{how}\:\mathrm{is}\:\mathrm{solution}\:\mathrm{Q203144} \\ $$

Question Number 203222 Answers: 1 Comments: 1

XYZ Ltd wants to borrow money to finance a project. They can pay N2500 monthly in repayments. If the interest rate is 5% and the load will be paid back fully in 30 years, how much can the company afford to borrow?

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