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Question Number 109016 Answers: 2 Comments: 0

Question Number 109005 Answers: 2 Comments: 0

i^i =?

$${i}^{{i}} =? \\ $$

Question Number 109004 Answers: 4 Comments: 0

^ Solve ∣3x+5∣ = ∣4x−3∣ where x ∈ R

$$\overset{} {\:}\:\:{Solve}\:\:\:\:\mid\mathrm{3}{x}+\mathrm{5}\mid\:=\:\mid\mathrm{4}{x}−\mathrm{3}\mid \\ $$$$\:\:\:{where}\:{x}\:\in\:\mathbb{R} \\ $$$$ \\ $$

Question Number 109001 Answers: 0 Comments: 0

Question Number 109000 Answers: 0 Comments: 0

Question Number 108999 Answers: 0 Comments: 0

Question Number 108998 Answers: 0 Comments: 0

Question Number 108997 Answers: 1 Comments: 0

Question Number 108987 Answers: 1 Comments: 0

Question Number 108984 Answers: 7 Comments: 1

B_≈ eM_≈ ath_≈ (1)Σ_(n = 1) ^(100) [ (2/(4n^2 −1)) ] ? (2) (2/(4.9)) + (2/(9.14)) + (2/(14.19)) + ... + (2/(49.54)) ? (3) Given a quadratic equation x^2 (Σ_(i = 1) ^2 2)+ x(Σ_(i = 1) ^5 i)−(2/3)(Σ_(i = 1) ^3 i) = 0 has the roots are x_1 and x_2 with x_1 < x_2 . Find the value of x_1 +8x_2 .

$$\:\:\:\underset{\approx} {\mathcal{B}}{e}\underset{\approx} {\mathcal{M}}{at}\underset{\approx} {{h}} \\ $$$$\left(\mathrm{1}\right)\underset{{n}\:=\:\mathrm{1}} {\overset{\mathrm{100}} {\sum}}\left[\:\frac{\mathrm{2}}{\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}}\:\right]\:? \\ $$$$\left(\mathrm{2}\right)\:\frac{\mathrm{2}}{\mathrm{4}.\mathrm{9}}\:+\:\frac{\mathrm{2}}{\mathrm{9}.\mathrm{14}}\:+\:\frac{\mathrm{2}}{\mathrm{14}.\mathrm{19}}\:+\:...\:+\:\frac{\mathrm{2}}{\mathrm{49}.\mathrm{54}}\:? \\ $$$$\left(\mathrm{3}\right)\:{Given}\:{a}\:{quadratic}\:{equation} \\ $$$${x}^{\mathrm{2}} \left(\underset{{i}\:=\:\mathrm{1}} {\overset{\mathrm{2}} {\sum}}\mathrm{2}\right)+\:{x}\left(\underset{{i}\:=\:\mathrm{1}} {\overset{\mathrm{5}} {\sum}}{i}\right)−\frac{\mathrm{2}}{\mathrm{3}}\left(\underset{{i}\:=\:\mathrm{1}} {\overset{\mathrm{3}} {\sum}}{i}\right)\:=\:\mathrm{0} \\ $$$${has}\:{the}\:{roots}\:{are}\:{x}_{\mathrm{1}} \:{and}\:{x}_{\mathrm{2}} \:{with}\: \\ $$$${x}_{\mathrm{1}} \:<\:{x}_{\mathrm{2}} .\:{Find}\:{the}\:{value}\:{of}\:{x}_{\mathrm{1}} +\mathrm{8}{x}_{\mathrm{2}} . \\ $$

Question Number 108967 Answers: 3 Comments: 0

b^★ o^★ b^★ h^∼ a^∼ n^∼ s^∼ 1+(4/(11))+(9/(121))+((16)/(1331))+((25)/(14641))+...

$$\:\:\overset{\bigstar} {{b}}\overset{\bigstar} {{o}}\overset{\bigstar} {{b}}\overset{\sim} {{h}}\overset{\sim} {{a}}\overset{\sim} {{n}}\overset{\sim} {{s}} \\ $$$$\mathrm{1}+\frac{\mathrm{4}}{\mathrm{11}}+\frac{\mathrm{9}}{\mathrm{121}}+\frac{\mathrm{16}}{\mathrm{1331}}+\frac{\mathrm{25}}{\mathrm{14641}}+... \\ $$

Question Number 108961 Answers: 3 Comments: 2

Solve ((∣x−2∣+1)/(∣x−2∣−1))<3

$$\mathrm{Solve}\:\frac{\mid{x}−\mathrm{2}\mid+\mathrm{1}}{\mid{x}−\mathrm{2}\mid−\mathrm{1}}<\mathrm{3} \\ $$

Question Number 108956 Answers: 2 Comments: 0

b^★ o^★ b^★ h^□ a^□ n^□ s^♠ lim_(x→0) ((tan 8x−sin 4x.cos 4x)/(x.sin 4x.tan 8x)) ?

$$\:\:\:\:\:\:\:\:\:\overset{\bigstar} {{b}}\overset{\bigstar} {{o}}\overset{\bigstar} {{b}}\overset{\Box} {{h}}\overset{\Box} {{a}}\overset{\Box} {{n}}\overset{\spadesuit} {{s}} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:\mathrm{8}{x}−\mathrm{sin}\:\mathrm{4}{x}.\mathrm{cos}\:\mathrm{4}{x}}{{x}.\mathrm{sin}\:\mathrm{4}{x}.\mathrm{tan}\:\mathrm{8}{x}}\:? \\ $$

Question Number 108990 Answers: 2 Comments: 0