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Question Number 103346 Answers: 0 Comments: 1

Question Number 103345 Answers: 4 Comments: 5

Question Number 103343 Answers: 1 Comments: 0

∫_0 ^1 x^(−x) dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{−{x}} {dx} \\ $$

Question Number 103338 Answers: 0 Comments: 7

Question Number 103322 Answers: 2 Comments: 1

A differentiable function f(x) satisfies f(x^3 −x^2 +x)=2^(x+1) for every real number x. When g(x) is the inverse function of f(x), find g′(4)?

$$\mathrm{A}\:\mathrm{differentiable}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{satisfies} \\ $$$$\mathrm{f}\left(\mathrm{x}^{\mathrm{3}} −\mathrm{x}^{\mathrm{2}} +\mathrm{x}\right)=\mathrm{2}^{\mathrm{x}+\mathrm{1}} \:\:\mathrm{for}\:\mathrm{every}\:\mathrm{real}\:\mathrm{number}\:{x}. \\ $$$$\mathrm{When}\:\mathrm{g}\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{the}\:\mathrm{inverse}\:\mathrm{function}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x}\right), \\ $$$$\mathrm{find}\:\mathrm{g}'\left(\mathrm{4}\right)? \\ $$

Question Number 103321 Answers: 2 Comments: 0

5+(√(5−(√(5+(√(5−(√(5+(√(5−(√(5+...))))))))))))

$$\mathrm{5}+\sqrt{\mathrm{5}−\sqrt{\mathrm{5}+\sqrt{\mathrm{5}−\sqrt{\mathrm{5}+\sqrt{\mathrm{5}−\sqrt{\mathrm{5}+...}}}}}} \\ $$

Question Number 103318 Answers: 1 Comments: 3

Question Number 103314 Answers: 1 Comments: 0

Linearise cos^(2(p−1)) (t)

$$\mathrm{Linearise}\:\mathrm{cos}^{\mathrm{2}\left(\mathrm{p}−\mathrm{1}\right)} \left(\mathrm{t}\right) \\ $$

Question Number 103313 Answers: 0 Comments: 0

lim_(n→+∞) (ln (n!))^(2/n)

$${li}\underset{{n}\rightarrow+\infty} {{m}}\left(\mathrm{ln}\:\left({n}!\right)\right)^{\frac{\mathrm{2}}{{n}}} \\ $$

Question Number 103312 Answers: 4 Comments: 0

∫_0 ^∞ (1/((1+x^2 )^6 )) dx ?

$$\underset{\mathrm{0}} {\overset{\infty} {\int}}\:\frac{\mathrm{1}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{6}} }\:{dx}\:? \\ $$

Question Number 103310 Answers: 1 Comments: 1

Question Number 103306 Answers: 0 Comments: 0

Question Number 103305 Answers: 0 Comments: 0

Question Number 103300 Answers: 1 Comments: 0

many positive five−digit integers with the first number 1 and there are three equal numbers ? (a) 810 (b) 720 (c)120 (d) 60 (e) 20

$$\mathrm{many}\:\mathrm{positive}\:\mathrm{five}−\mathrm{digit} \\ $$$$\mathrm{integers}\:\mathrm{with}\:\mathrm{the}\:\mathrm{first}\:\mathrm{number}\:\mathrm{1} \\ $$$$\mathrm{and}\:\mathrm{there}\:\mathrm{are}\:\mathrm{three}\:\mathrm{equal} \\ $$$$\mathrm{numbers}\:? \\ $$$$\left(\mathrm{a}\right)\:\mathrm{810}\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{720}\:\:\:\:\left(\mathrm{c}\right)\mathrm{120} \\ $$$$\left(\mathrm{d}\right)\:\mathrm{60}\:\:\:\:\:\left(\mathrm{e}\right)\:\mathrm{20} \\ $$

Question Number 103299 Answers: 2 Comments: 0

cos20°cos40°cos80°=...?

$${cos}\mathrm{20}°{cos}\mathrm{40}°{cos}\mathrm{80}°=...? \\ $$

Question Number 103298 Answers: 0 Comments: 0

Question Number 103294 Answers: 1 Comments: 0

from letters in ′MATEMATIKA′ words formed by using all the letters . How many words that can be formed with the five consonant are always side by side

$$\mathrm{from}\:\mathrm{letters}\:\mathrm{in} \\ $$$$'\mathrm{MATEMATIKA}'\:\mathrm{words} \\ $$$$\mathrm{formed}\:\mathrm{by}\:\mathrm{using}\:\mathrm{all}\:\mathrm{the}\:\mathrm{letters}\:. \\ $$$$\mathrm{How}\:\mathrm{many}\:\mathrm{words}\:\mathrm{that}\:\mathrm{can}\:\mathrm{be} \\ $$$$\mathrm{formed}\:\mathrm{with}\:\mathrm{the}\:\mathrm{five}\:\mathrm{consonant} \\ $$$$\mathrm{are}\:\mathrm{always}\:\mathrm{side}\:\mathrm{by}\:\mathrm{side}\: \\ $$

Question Number 103286 Answers: 3 Comments: 1

((1/9))^(1/3) −((2/9))^(1/3) + ((4/9))^(1/3) = ?

$$\sqrt[{\mathrm{3}}]{\frac{\mathrm{1}}{\mathrm{9}}}−\sqrt[{\mathrm{3}}]{\frac{\mathrm{2}}{\mathrm{9}}}+\:\sqrt[{\mathrm{3}}]{\frac{\mathrm{4}}{\mathrm{9}}}\:=\:? \\ $$

Question Number 103283 Answers: 1 Comments: 0

y′′ + y = sin 2x

$${y}''\:+\:{y}\:=\:\mathrm{sin}\:\mathrm{2}{x}\: \\ $$

Question Number 103278 Answers: 0 Comments: 2

Σ_(k=0) ^∞ (1/(k!(k^4 +k^2 +1)))=?

$$\:\:\:\:\:\underset{\boldsymbol{{k}}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\boldsymbol{{k}}!\left(\boldsymbol{{k}}^{\mathrm{4}} +\boldsymbol{{k}}^{\mathrm{2}} +\mathrm{1}\right)}=? \\ $$

Question Number 103266 Answers: 0 Comments: 1

How can we solve second-order differential equations with non-constant coefficients ? Any idea, please ?

$$\mathrm{How}\:\mathrm{can}\:\mathrm{we}\:\mathrm{solve}\:\mathrm{second}-\mathrm{order}\:\mathrm{differential}\:\mathrm{equations}\:\mathrm{with} \\ $$$$\mathrm{non}-\mathrm{constant}\:\mathrm{coefficients}\:?\:\mathrm{Any}\:\mathrm{idea},\:\mathrm{please}\:? \\ $$$$ \\ $$

Question Number 103260 Answers: 1 Comments: 0

Question Number 103255 Answers: 1 Comments: 1

lim_(x→0) (((sin^6 (√2)x)/(tan^7 (x/2))))^(cos^(12) x) =???

$${li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\left(\frac{{sin}^{\mathrm{6}} \sqrt{\mathrm{2}}{x}}{{tan}^{\mathrm{7}} \frac{{x}}{\mathrm{2}}}\right)^{{cos}^{\mathrm{12}} {x}} =??? \\ $$

Question Number 103254 Answers: 0 Comments: 2

2^(3x) −f(x+4)=k∙f(x) ; k=????

$$\:\mathrm{2}^{\mathrm{3}{x}} −{f}\left({x}+\mathrm{4}\right)={k}\centerdot{f}\left({x}\right)\:\:\:\:\:;\:\:\:{k}=???? \\ $$

Question Number 103253 Answers: 3 Comments: 0

(i)^(1/i) =?????

$$\:\sqrt[{{i}}]{{i}}=????? \\ $$

Question Number 103241 Answers: 0 Comments: 0

∫x^(−x) dx

$$\int{x}^{−{x}} {dx} \\ $$

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