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Question Number 66225 Answers: 1 Comments: 2

Given that f(x)= { ((−x + 1, x≤ 3_ )),((kx −8, x >3)) :} is continuous then f(5) = A 2 B 0 C −2 D −1

$${Given}\:{that}\:\:\:\:\:{f}\left({x}\right)=\begin{cases}{−{x}\:+\:\mathrm{1},\:\:{x}\leqslant\:\mathrm{3}_{} }\\{{kx}\:−\mathrm{8},\:\:\:\:{x}\:>\mathrm{3}}\end{cases} \\ $$$${is}\:{continuous}\:{then}\:\:{f}\left(\mathrm{5}\right)\:=\: \\ $$$${A}\:\:\:\mathrm{2} \\ $$$${B}\:\:\:\mathrm{0} \\ $$$${C}\:\:−\mathrm{2} \\ $$$${D}\:\:−\mathrm{1} \\ $$$$ \\ $$

Question Number 66216 Answers: 1 Comments: 2

∣a ∣ = 3 ,∣b∣= 5 , a.b =−14 ∣a − b∣ = ?

$$\mid{a}\:\mid\:=\:\mathrm{3}\:,\mid{b}\mid=\:\mathrm{5}\:,\:{a}.{b}\:=−\mathrm{14} \\ $$$$\:\:\mid{a}\:−\:{b}\mid\:=\:? \\ $$

Question Number 66816 Answers: 0 Comments: 3

let x>0 and f(x)=∫_1 ^2 (t+1)(√(t^2 −2xt−1))dt 1) find a explicit form of f(x) 2) determine also g(x)=∫_1 ^2 ((t^2 +t)/(√(t^2 −2xt−1)))dt 3)find the value of integrals ∫_1 ^2 (t+1)(√(t^2 −t−1))dt and ∫_1 ^2 ((t^(2 ) +t)/(√(t^2 −t−1)))dt .

$${let}\:{x}>\mathrm{0}\:{and}\:{f}\left({x}\right)=\int_{\mathrm{1}} ^{\mathrm{2}} \left({t}+\mathrm{1}\right)\sqrt{{t}^{\mathrm{2}} −\mathrm{2}{xt}−\mathrm{1}}{dt} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{also}\:{g}\left({x}\right)=\int_{\mathrm{1}} ^{\mathrm{2}} \frac{{t}^{\mathrm{2}} \:+{t}}{\sqrt{{t}^{\mathrm{2}} −\mathrm{2}{xt}−\mathrm{1}}}{dt} \\ $$$$\left.\mathrm{3}\right){find}\:{the}\:{value}\:{of}\:{integrals}\:\:\int_{\mathrm{1}} ^{\mathrm{2}} \left({t}+\mathrm{1}\right)\sqrt{{t}^{\mathrm{2}} −{t}−\mathrm{1}}{dt} \\ $$$${and}\:\int_{\mathrm{1}} ^{\mathrm{2}} \:\:\frac{{t}^{\mathrm{2}\:} +{t}}{\sqrt{{t}^{\mathrm{2}} −{t}−\mathrm{1}}}{dt}\:. \\ $$$$ \\ $$

Question Number 66815 Answers: 2 Comments: 1

solve the congruence equation 6x ≡ 4 (mod 5) i need help please with some explanations

$${solve}\:{the}\:{congruence}\:{equation}\: \\ $$$$\:\:\mathrm{6}{x}\:\equiv\:\mathrm{4}\:\left({mod}\:\mathrm{5}\right)\:\:{i}\:{need}\:{help}\:{please}\:{with}\:{some}\:{explanations} \\ $$

Question Number 66213 Answers: 0 Comments: 3

calculate A_n =∫_0 ^∞ cos(x^n )dx and B_n =∫_0 ^∞ sin(x^n )dx with n integr and n≥2

$${calculate}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:{cos}\left({x}^{{n}} \right){dx}\:{and}\:{B}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:{sin}\left({x}^{{n}} \right){dx} \\ $$$${with}\:{n}\:{integr}\:{and}\:{n}\geqslant\mathrm{2} \\ $$

Question Number 66211 Answers: 1 Comments: 4

Question Number 66199 Answers: 0 Comments: 3

calculate cos(79)=?

$${calculate} \\ $$$${cos}\left(\mathrm{79}\right)=? \\ $$

Question Number 66197 Answers: 3 Comments: 3

If x+(1/x)=1,prove that: x^n +x^(n−2) +x^(n−4) =0

$$\mathrm{If}\:\:\mathrm{x}+\frac{\mathrm{1}}{\mathrm{x}}=\mathrm{1},\mathrm{prove}\:\mathrm{that}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{x}^{\mathrm{n}} +\mathrm{x}^{\mathrm{n}−\mathrm{2}} +\mathrm{x}^{\mathrm{n}−\mathrm{4}} =\mathrm{0} \\ $$

Question Number 66194 Answers: 0 Comments: 0

∫(x^a /(bx^n +c)) dx

$$\int\frac{{x}^{{a}} }{{bx}^{{n}} +{c}}\:{dx} \\ $$

Question Number 66250 Answers: 1 Comments: 0

Question Number 66185 Answers: 1 Comments: 1

(e^(1/e) )^((e^(1/e) )^(.∙^(.(e^(1/e) )) ) ) =?

$$\left({e}^{\frac{\mathrm{1}}{{e}}} \right)^{\left({e}^{\frac{\mathrm{1}}{{e}}} \right)^{.\centerdot^{.\left({e}^{\frac{\mathrm{1}}{{e}}} \right)} } } =? \\ $$

Question Number 66183 Answers: 0 Comments: 1

why Σ_(j=1) ^∞ ((sin(j^2 x))/j^2 ) can′t differantial anywhere?? plz ploof....help

$$\mathrm{why}\:\underset{{j}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{sin}\left({j}^{\mathrm{2}} {x}\right)}{{j}^{\mathrm{2}} }\:\mathrm{can}'\mathrm{t}\:\mathrm{differantial} \\ $$$$\mathrm{anywhere}??\:\:\mathrm{plz}\:\mathrm{ploof}....\mathrm{help} \\ $$

Question Number 66173 Answers: 1 Comments: 0

x^x^(x∙^.^(.x) ) =2 x=?

$${x}^{{x}^{{x}\centerdot^{.^{.{x}} } } } =\mathrm{2} \\ $$$${x}=? \\ $$

Question Number 66172 Answers: 0 Comments: 4

let A_n =Π_(k=1) ^n (1+(k^2 /n^2 )) calculate lim_(n→+∞) ((ln(A_n ))/n)

$$ \\ $$$${let}\:{A}_{{n}} =\prod_{{k}=\mathrm{1}} ^{{n}} \left(\mathrm{1}+\frac{{k}^{\mathrm{2}} }{{n}^{\mathrm{2}} }\right)\:\:\:{calculate}\:{lim}_{{n}\rightarrow+\infty} \:\frac{{ln}\left({A}_{{n}} \right)}{{n}} \\ $$

Question Number 66171 Answers: 1 Comments: 1

find lim_(n→+∞) (1/n^2 ){sin((1/n^2 ))+2sin((4/n^2 ))+....(n−1)sin((((n−1)^2 )/n^2 ))}

$${find}\:{lim}_{{n}\rightarrow+\infty} \:\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\left\{{sin}\left(\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\right)+\mathrm{2}{sin}\left(\frac{\mathrm{4}}{{n}^{\mathrm{2}} }\right)+....\left({n}−\mathrm{1}\right){sin}\left(\frac{\left({n}−\mathrm{1}\right)^{\mathrm{2}} }{{n}^{\mathrm{2}} }\right)\right\} \\ $$

Question Number 66170 Answers: 0 Comments: 1

calculate ∫_0 ^∞ sin(x^3 )dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:{sin}\left({x}^{\mathrm{3}} \right){dx} \\ $$

Question Number 66169 Answers: 0 Comments: 1

find the values of ∫_0 ^∞ cos(x^2 )dx and ∫_0 ^∞ sin(x^2 )dx(fresnel integrals) by using Γ(z) =∫_0 ^∞ t^(z−1) e^(−t) dt

$${find}\:{the}\:{values}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:{cos}\left({x}^{\mathrm{2}} \right){dx}\:{and}\:\int_{\mathrm{0}} ^{\infty} \:{sin}\left({x}^{\mathrm{2}} \right){dx}\left({fresnel}\:{integrals}\right) \\ $$$${by}\:{using}\:\Gamma\left({z}\right)\:=\int_{\mathrm{0}} ^{\infty} \:{t}^{{z}−\mathrm{1}} \:{e}^{−{t}} \:{dt}\:\: \\ $$

Question Number 66168 Answers: 0 Comments: 0

prove without calculus that ∫_0 ^∞ cos(x^2 )dx=∫_0 ^∞ sin(x^2 )dx

$${prove}\:{without}\:{calculus}\:{that}\:\:\int_{\mathrm{0}} ^{\infty} \:{cos}\left({x}^{\mathrm{2}} \right){dx}=\int_{\mathrm{0}} ^{\infty} {sin}\left({x}^{\mathrm{2}} \right){dx} \\ $$

Question Number 66163 Answers: 1 Comments: 0

Question Number 66162 Answers: 3 Comments: 3

Question Number 66161 Answers: 1 Comments: 0

Question Number 66160 Answers: 0 Comments: 0

Question Number 66150 Answers: 0 Comments: 1

find ∫_0 ^∞ e^(−x^3 ) sin(x^3 )dx

$${find}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{x}^{\mathrm{3}} } {sin}\left({x}^{\mathrm{3}} \right){dx}\: \\ $$

Question Number 66149 Answers: 2 Comments: 0

f(x) =2x^3 −x−4 show that f(x) =0 has roots between 1 and 2

$${f}\left({x}\right)\:=\mathrm{2}{x}^{\mathrm{3}} −{x}−\mathrm{4}\: \\ $$$${show}\:{that}\:{f}\left({x}\right)\:=\mathrm{0}\:{has}\:{roots}\:{between} \\ $$$$\mathrm{1}\:{and}\:\mathrm{2} \\ $$

Question Number 66140 Answers: 0 Comments: 0

1.Show that: ∫_0 ^(π/2) f(sin 2x)sin x dx=(√2) ∫_0 ^(π/4) f(cos 2x)cos x dx. 2.If f(z)=(d/dz){5^(∣f(z)∣) } then what is the value of f′(e)?

$$\mathrm{1}.\boldsymbol{{Show}}\:\boldsymbol{{that}}:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {f}\left(\mathrm{sin}\:\mathrm{2}{x}\right)\mathrm{sin}\:{x}\:{dx}=\sqrt{\mathrm{2}}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {f}\left(\mathrm{cos}\:\mathrm{2}{x}\right)\mathrm{cos}\:{x}\:{dx}. \\ $$$$\mathrm{2}.\boldsymbol{{If}}\:\boldsymbol{{f}}\left(\boldsymbol{{z}}\right)=\frac{\boldsymbol{{d}}}{\boldsymbol{{dz}}}\left\{\mathrm{5}^{\mid\boldsymbol{{f}}\left(\boldsymbol{{z}}\right)\mid} \right\}\:\:\boldsymbol{{then}}\:\boldsymbol{{what}}\:\boldsymbol{{is}}\:\boldsymbol{{the}}\:\boldsymbol{{value}}\:\boldsymbol{{of}}\:\boldsymbol{{f}}'\left(\boldsymbol{{e}}\right)? \\ $$

Question Number 66126 Answers: 1 Comments: 0

Is there any formula to find sum of 1 + n^2 + n^4 + n^6 + n^8 + ... + n^(2k) + ... where n,k ∈ Z^+

$$\mathrm{Is}\:\mathrm{there}\:\mathrm{any}\:\mathrm{formula}\:\mathrm{to}\:\mathrm{find}\:\mathrm{sum}\:\mathrm{of} \\ $$$$\mathrm{1}\:+\:{n}^{\mathrm{2}} \:+\:{n}^{\mathrm{4}} \:+\:{n}^{\mathrm{6}} \:+\:{n}^{\mathrm{8}} \:+\:...\:+\:{n}^{\mathrm{2}{k}} \:+\:... \\ $$$$\mathrm{where}\:{n},{k}\:\in\:\mathbb{Z}^{+} \: \\ $$

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