Question and Answers Forum

AllQuestion and Answers: Page 665

Question Number 146854 Answers: 1 Comments: 2

Solve for real numbers the following system of equations { ((a(a+1) = b−1)),((a^2 (b+3)+2a = −1)) :}

$${Solve}\:{for}\:{real}\:{numbers}\:{the}\:{following} \\ $$$${system}\:{of}\:{equations} \\ $$$$\begin{cases}{{a}\left({a}+\mathrm{1}\right)\:=\:{b}−\mathrm{1}}\\{{a}^{\mathrm{2}} \left({b}+\mathrm{3}\right)+\mathrm{2}{a}\:=\:−\mathrm{1}}\end{cases} \\ $$

Question Number 146853 Answers: 0 Comments: 0

Question Number 146850 Answers: 0 Comments: 0

$$ \\ $$$$ \\ $$

Question Number 146849 Answers: 1 Comments: 1

Question Number 146840 Answers: 2 Comments: 0

Question Number 146839 Answers: 0 Comments: 0

Question Number 146838 Answers: 1 Comments: 0

Given 4^x +4^(−x) −2^(2−x) +2^(2+x) −7=0 ,x>0 find 2^x +2^(−x) . if x∈[ −(π/6),0 ] then minimum value of function f(x)=cot (x+(π/3))−tan (((2π)/3)−x) when x = ?

$$\mathrm{Given}\:\mathrm{4}^{\mathrm{x}} +\mathrm{4}^{−\mathrm{x}} −\mathrm{2}^{\mathrm{2}−\mathrm{x}} +\mathrm{2}^{\mathrm{2}+\mathrm{x}} −\mathrm{7}=\mathrm{0}\:,\mathrm{x}>\mathrm{0} \\ $$$$\:\mathrm{find}\:\mathrm{2}^{\mathrm{x}} +\mathrm{2}^{−\mathrm{x}} . \\ $$$$\: \\ $$$$\:\mathrm{if}\:\mathrm{x}\in\left[\:−\frac{\pi}{\mathrm{6}},\mathrm{0}\:\right]\:\mathrm{then}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{cot}\:\left(\mathrm{x}+\frac{\pi}{\mathrm{3}}\right)−\mathrm{tan}\:\left(\frac{\mathrm{2}\pi}{\mathrm{3}}−\mathrm{x}\right)\: \\ $$$$\mathrm{when}\:\mathrm{x}\:=\:?\: \\ $$

Question Number 146837 Answers: 0 Comments: 0

$${p} \\ $$

Question Number 146836 Answers: 0 Comments: 0

Σ_(n=1) ^∞ (1/(ϕ^( n) F_n )) =?

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\varphi^{\:{n}} \:\mathrm{F}_{{n}} }\:=? \\ $$

Question Number 146835 Answers: 2 Comments: 0

calculate ∫_0 ^∞ (dx/((x^2 +3)^2 (x^2 +4)^2 ))

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{3}\right)^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{4}\right)^{\mathrm{2}} } \\ $$

Question Number 146824 Answers: 1 Comments: 0

Question Number 146868 Answers: 1 Comments: 0

if tan^2 x+sec x=a+1 has at least one solution then find the complete set of values of ′a′?

$${if}\:\mathrm{tan}\:^{\mathrm{2}} {x}+\mathrm{sec}\:{x}={a}+\mathrm{1}\:{has}\:{at}\:{least}\: \\ $$$${one}\:{solution}\:{then}\:{find}\:{the}\:{complete}\:{set} \\ $$$${of}\:{values}\:{of}\:\:'{a}'? \\ $$

Question Number 146817 Answers: 1 Comments: 0

Question Number 146856 Answers: 0 Comments: 0

3. Calcula mediante una suma de Riemann una aproximaci´on al ´area limitada por la funci´on f(x) = −2x 2 − 4x + 30 y el eje x en el intervalo [−5, 3] con n rect´angulos. Δx=((3−(−5))/n) ⇒(8/n) ∴ x_0 =−5 ∴ a=x_0 =−5 x_1 =−5+1Δx x_2 =−5+2Δx x_3 =−5+3Δx ⋮ x_n =−5+nΔx

$$ \\ $$3. Calcula mediante una suma de Riemann una aproximaci´on al ´area limitada por la funci´on f(x) = −2x 2 − 4x + 30 y el eje x en el intervalo [−5, 3] con n rect´angulos. $$ \\ $$$$\Delta{x}=\frac{\mathrm{3}−\left(−\mathrm{5}\right)}{{n}}\:\Rightarrow\frac{\mathrm{8}}{{n}} \\ $$$$\therefore\:{x}_{\mathrm{0}} =−\mathrm{5} \\ $$$$ \\ $$$$\therefore\:{a}={x}_{\mathrm{0}} =−\mathrm{5} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{x}_{\mathrm{1}} =−\mathrm{5}+\mathrm{1}\Delta{x} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{x}_{\mathrm{2}} =−\mathrm{5}+\mathrm{2}\Delta{x} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{x}_{\mathrm{3}} =−\mathrm{5}+\mathrm{3}\Delta{x} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\vdots \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{x}_{{n}} =−\mathrm{5}+{n}\Delta{x} \\ $$$$ \\ $$

Question Number 146799 Answers: 1 Comments: 0