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Question Number 146528 Answers: 1 Comments: 0

Question Number 146524 Answers: 0 Comments: 0

find ∫_0 ^∞ ((xsinx)/((x^4 +1)^3 ))dx

$$\mathrm{find}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{xsinx}}{\left(\mathrm{x}^{\mathrm{4}} \:+\mathrm{1}\right)^{\mathrm{3}} }\mathrm{dx} \\ $$

Question Number 146523 Answers: 2 Comments: 0

Question Number 146521 Answers: 1 Comments: 0

(i - 1)^(−100) = ?

$$\left(\boldsymbol{{i}}\:-\:\mathrm{1}\right)^{−\mathrm{100}} \:=\:? \\ $$

Question Number 146519 Answers: 0 Comments: 0

Question Number 146508 Answers: 1 Comments: 0

Find the sum of the roots of the equation: 16 ∙ 2^(∣x∣) + 5 ∙ 2^x = 42

$${Find}\:{the}\:{sum}\:{of}\:{the}\:{roots}\:{of}\:{the} \\ $$$${equation}: \\ $$$$\mathrm{16}\:\centerdot\:\mathrm{2}^{\mid\boldsymbol{{x}}\mid} \:+\:\mathrm{5}\:\centerdot\:\mathrm{2}^{\boldsymbol{{x}}} \:=\:\mathrm{42} \\ $$

Question Number 146505 Answers: 2 Comments: 0

lim_(x→7) (((√(x - a)) - 4)/(x - 7)) = b find a∙b=?

$$\underset{{x}\rightarrow\mathrm{7}} {{lim}}\:\frac{\sqrt{{x}\:-\:{a}}\:-\:\mathrm{4}}{{x}\:-\:\mathrm{7}}\:=\:{b}\:\:{find}\:\:{a}\centerdot{b}=? \\ $$

Question Number 146504 Answers: 0 Comments: 0

find the sigular point (1)f(z)=ln∣z∣ (2)f(z)=((1−cosz)/(sinz^2 ))

$${find}\:{the}\:{sigular}\:{point}\: \\ $$$$ \\ $$$$\left(\mathrm{1}\right){f}\left({z}\right)={ln}\mid{z}\mid \\ $$$$ \\ $$$$\left(\mathrm{2}\right){f}\left({z}\right)=\frac{\mathrm{1}−{cosz}}{{sinz}^{\mathrm{2}} } \\ $$

Question Number 146500 Answers: 0 Comments: 0

Z = −2∙(cos80−sin80) Show it in trigonometry

$${Z}\:=\:−\mathrm{2}\centerdot\left({cos}\mathrm{80}−{sin}\mathrm{80}\right) \\ $$$${Show}\:{it}\:{in}\:{trigonometry} \\ $$

Question Number 146494 Answers: 0 Comments: 0

Solid cube ABCD.EFGH is cut by a plane X so that it forms a plane of slices IJKLMN where I is mid AB, J is mid BF K is mid FG, L is mid HG, M mid DH and N mid AD. If the edge of the cube is X, find the area of the IJKLMN field

$$ \\ $$$$\mathrm{Solid}\:\mathrm{cube}\:\mathrm{ABCD}.\mathrm{EFGH}\:\mathrm{is}\:\mathrm{cut}\:\mathrm{by}\:\mathrm{a} \\ $$$$\mathrm{pla}{ne}\:{X}\:\mathrm{so}\:\mathrm{that}\:\mathrm{it}\:\mathrm{forms}\:\mathrm{a}\:\mathrm{plane}\:\mathrm{of}\:\mathrm{slices}\: \\ $$$$\mathrm{IJK}{LM}\mathrm{N}\:\mathrm{where}\:\mathrm{I}\:\mathrm{is}\:\mathrm{mid}\:\mathrm{AB},\:\mathrm{J}\:\mathrm{is}\:\mathrm{mid}\:\mathrm{BF} \\ $$$$\:{K}\:\mathrm{is}\:\mathrm{mid}\:\mathrm{FG},\:\:\mathrm{L}\:\mathrm{is}\:\mathrm{mid}\:\mathrm{HG},\:\:\mathrm{M}\:\mathrm{mid}\:\mathrm{DH}\: \\ $$$$\mathrm{and}\:\mathrm{N}\:\mathrm{mid}\:\mathrm{AD}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{edge}\:\mathrm{of}\:\mathrm{the}\:\mathrm{cube}\: \\ $$$$\mathrm{is}\:{X},\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{IJKLMN}\:\mathrm{field} \\ $$

Question Number 146488 Answers: 2 Comments: 2

if x+y=216 and dcm(x;y)=18 find x−y=?

$${if}\:\:\:{x}+{y}=\mathrm{216}\:\:\:{and}\:\:\:\boldsymbol{{dcm}}\left({x};{y}\right)=\mathrm{18} \\ $$$${find}\:\:\:{x}−{y}=? \\ $$

Question Number 146487 Answers: 0 Comments: 0

Cube ABCD.EFGH has side length a. Point P lies on AC such that AP : PC = 3 : 1 Through P a line l parallel to BD is drawn such that l each intersect BC at X and CD at Y. If AC and BD intersect at O find the distance between XY with OG!

$$ \\ $$$$\mathrm{Cube}\:\mathrm{ABCD}.\mathrm{EFGH}\:\mathrm{has}\:\mathrm{side}\:\mathrm{length}\:\mathrm{a}. \\ $$$$\mathrm{P}{o}\mathrm{int}\:\mathrm{P}\:\mathrm{lies}\:\mathrm{on}\:\mathrm{AC}\:\mathrm{such}\:\mathrm{that}\:\mathrm{AP}\::\:\mathrm{PC}\:=\:\mathrm{3}\::\:\mathrm{1}\:\mathrm{Through}\:\mathrm{P}\:\mathrm{a}\:\mathrm{line}\:\mathrm{l}\:\mathrm{parallel}\:\mathrm{to}\:\mathrm{BD}\:\mathrm{is} \\ $$$$\mathrm{dr}{a}\mathrm{wn}\:\mathrm{such}\:\mathrm{that}\:\mathrm{l}\:\mathrm{each}\:\mathrm{intersect}\:\mathrm{BC}\:\mathrm{at}\: \\ $$$$\mathrm{X}\:\mathrm{and}\:\mathrm{CD}\:\mathrm{at}\:\mathrm{Y}.\:\mathrm{If}\:\mathrm{AC}\:\mathrm{and}\:\mathrm{BD}\: \\ $$$$\mathrm{intersect}\:\mathrm{at}\:\mathrm{O}\:\mathrm{find}\:\mathrm{the}\:\mathrm{distance}\: \\ $$$$\mathrm{between}\:\mathrm{XY}\:\mathrm{with}\:\mathrm{OG}! \\ $$

Question Number 146497 Answers: 1 Comments: 0

f(x)=(2/x)∫_0 ^x (t^2 /( (√(1+t^2 ))))dt calculate lim_(x→0) f(x)

$$\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{2}}{\mathrm{x}}\int_{\mathrm{0}} ^{\mathrm{x}} \:\:\frac{\mathrm{t}^{\mathrm{2}} }{\:\sqrt{\mathrm{1}+\mathrm{t}^{\mathrm{2}} }}\mathrm{dt}\:\:\mathrm{calculate}\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{0}} \mathrm{f}\left(\mathrm{x}\right) \\ $$

Question Number 146472 Answers: 0 Comments: 1