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Question Number 82175 Answers: 1 Comments: 4

lim_(x→−∞) ((8x^3 −4x^2 +1))^(1/(3 )) −((8x^3 +∣px∣^2 −1))^(1/(3 )) = (1/4) find p

$$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\sqrt[{\mathrm{3}\:}]{\mathrm{8}{x}^{\mathrm{3}} −\mathrm{4}{x}^{\mathrm{2}} +\mathrm{1}}−\sqrt[{\mathrm{3}\:}]{\mathrm{8}{x}^{\mathrm{3}} +\mid{px}\mid^{\mathrm{2}} −\mathrm{1}}\:=\:\frac{\mathrm{1}}{\mathrm{4}} \\ $$$${find}\:{p}\: \\ $$

Question Number 82174 Answers: 1 Comments: 1

∫_0 ^π x ln(sin x) dx = ?

$$\underset{\mathrm{0}} {\overset{\pi} {\int}}\:{x}\:{ln}\left(\mathrm{sin}\:{x}\right)\:{dx}\:=\:?\: \\ $$

Question Number 82160 Answers: 2 Comments: 0

prove that lim_(x→∞) n^2 (√((1−cos((1/n))(√((1−cos(1/n))(√((1−cos(1/n))...)))))) =(1/2)

$${prove}\:{that} \\ $$$$\underset{{x}\rightarrow\infty} {{lim}}\:{n}^{\mathrm{2}} \:\sqrt{\left(\mathrm{1}−{cos}\left(\frac{\mathrm{1}}{{n}}\right)\sqrt{\left(\mathrm{1}−{cos}\frac{\mathrm{1}}{{n}}\right)\sqrt{\left(\mathrm{1}−{cos}\frac{\mathrm{1}}{{n}}\right)...}}\right.}\:=\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Question Number 82149 Answers: 1 Comments: 1

Evaluate the greatest coefficient of (7 − 5x)^(− 3)

$$\mathrm{Evaluate}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{coefficient}\:\mathrm{of}\:\:\:\:\left(\mathrm{7}\:−\:\mathrm{5x}\right)^{−\:\mathrm{3}} \\ $$

Question Number 82139 Answers: 1 Comments: 0

∫ ((√(x^4 +x^(−4) +2))/x^3 ) dx

$$\int\:\:\frac{\sqrt{{x}^{\mathrm{4}} +{x}^{−\mathrm{4}} +\mathrm{2}}}{{x}^{\mathrm{3}} }\:{dx}\: \\ $$

Question Number 82138 Answers: 0 Comments: 1

Question Number 82134 Answers: 0 Comments: 6

Question Number 82131 Answers: 2 Comments: 4

Question Number 82125 Answers: 0 Comments: 5

Question Number 82127 Answers: 0 Comments: 0

Question Number 82115 Answers: 1 Comments: 0

Q. Find the number of solution of thd equation tanx + secx = 2 cosx lying in the interval [0, 2π] ??

$${Q}.\:{Find}\:{the}\:{number}\:{of}\:{solution}\:{of}\:{thd} \\ $$$${equation}\:{tanx}\:+\:{secx}\:=\:\mathrm{2}\:{cosx}\:{lying}\:{in} \\ $$$${the}\:{interval}\:\left[\mathrm{0},\:\mathrm{2}\pi\right]\:?? \\ $$

Question Number 82111 Answers: 0 Comments: 6

a word is formed with 3 vowels and 3 consonants without repetition . the probability the formation of words begining the letter z is?

$${a}\:{word}\:{is}\:{formed}\:{with}\:\mathrm{3}\:{vowels} \\ $$$${and}\:\mathrm{3}\:{consonants}\:{without}\: \\ $$$${repetition}\:.\:{the}\:{probability}\:{the} \\ $$$${formation}\:{of}\:{words}\:{begining}\:{the} \\ $$$${letter}\:{z}\:{is}? \\ $$

Question Number 82110 Answers: 0 Comments: 0

Question Number 82101 Answers: 0 Comments: 2

Make 2 3×3 matrices i and j such that i^2 =j j^2 =i ij=−1

$${Make}\:\mathrm{2}\:\mathrm{3}×\mathrm{3}\:{matrices}\:{i}\:{and}\:{j} \\ $$$${such}\:{that} \\ $$$${i}^{\mathrm{2}} ={j} \\ $$$${j}^{\mathrm{2}} ={i} \\ $$$${ij}=−\mathrm{1} \\ $$

Question Number 82088 Answers: 0 Comments: 0

Question Number 82109 Answers: 0 Comments: 2

what is solution (dy/dx) = sin (x+y)

$${what}\:{is}\:{solution} \\ $$$$\frac{{dy}}{{dx}}\:=\:\mathrm{sin}\:\left({x}+{y}\right) \\ $$

Question Number 82084 Answers: 0 Comments: 2

Question Number 82082 Answers: 0 Comments: 4

Evaluate: (((√(30 + (√8) + (√5)))/((√8) + (√5))))^(1/4)

$$\mathrm{Evaluate}:\:\:\:\:\:\:\left(\frac{\sqrt{\mathrm{30}\:+\:\sqrt{\mathrm{8}}\:+\:\sqrt{\mathrm{5}}}}{\sqrt{\mathrm{8}}\:+\:\sqrt{\mathrm{5}}}\right)^{\mathrm{1}/\mathrm{4}} \\ $$

Question Number 82073 Answers: 1 Comments: 3

Show that: j_(3/2) (x) = ((√2)/(πx)) (((sin x)/x) − cos x)

$$\mathrm{Show}\:\mathrm{that}:\:\:\:\:\mathrm{j}_{\mathrm{3}/\mathrm{2}} \left(\mathrm{x}\right)\:\:=\:\:\frac{\sqrt{\mathrm{2}}}{\pi\mathrm{x}}\:\left(\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{x}}\:−\:\mathrm{cos}\:\mathrm{x}\right) \\ $$

Question Number 82071 Answers: 2 Comments: 0

x≠ y ≠z ≠ 0 xy + xz + yz = 0 prove that ((x+y)/z)+((x+z)/y)+((y+z)/x) = −3

$${x}\neq\:{y}\:\neq{z}\:\neq\:\mathrm{0} \\ $$$${xy}\:+\:{xz}\:+\:{yz}\:=\:\mathrm{0} \\ $$$${prove}\:{that}\:\frac{{x}+{y}}{{z}}+\frac{{x}+{z}}{{y}}+\frac{{y}+{z}}{{x}}\:=\:−\mathrm{3} \\ $$$$ \\ $$

Question Number 82067 Answers: 1 Comments: 5

{ ((∣x∣ −((y+3 ))^(1/(3 )) = 1)),(((−x(√(−x)))^2 = y +10)) :} find solution

$$\begin{cases}{\mid{x}\mid\:−\sqrt[{\mathrm{3}\:}]{{y}+\mathrm{3}\:}\:=\:\mathrm{1}}\\{\left(−{x}\sqrt{−{x}}\right)^{\mathrm{2}} \:=\:{y}\:+\mathrm{10}}\end{cases} \\ $$$${find}\:{solution} \\ $$

Question Number 82066 Answers: 0 Comments: 1

log_(3+2x−x^2 ) (((sin x+(√3)cos x)/(sin 3x))) = (1/(log_2 (3+2x−x^2 )))

$$\mathrm{log}_{\mathrm{3}+\mathrm{2}{x}−{x}^{\mathrm{2}} } \:\left(\frac{\mathrm{sin}\:{x}+\sqrt{\mathrm{3}}\mathrm{cos}\:{x}}{\mathrm{sin}\:\mathrm{3}{x}}\right)\:=\:\frac{\mathrm{1}}{\mathrm{log}_{\mathrm{2}} \left(\mathrm{3}+\mathrm{2}{x}−{x}^{\mathrm{2}} \right)}\: \\ $$

Question Number 82078 Answers: 1 Comments: 1

f(10^x ) = (√x) what is f^(−1) (x)=?

$${f}\left(\mathrm{10}^{{x}} \right)\:=\:\sqrt{{x}}\: \\ $$$${what}\:{is}\:{f}^{−\mathrm{1}} \left({x}\right)=? \\ $$

Question Number 82059 Answers: 2 Comments: 0

what is derivative of h = (√(ln(x))) by first principle method

$${what}\:{is}\:{derivative}\:{of}\:\:{h}\:=\:\sqrt{{ln}\left({x}\right)} \\ $$$${by}\:{first}\:{principle}\:{method}\: \\ $$

Question Number 82057 Answers: 2 Comments: 1

Question Number 82056 Answers: 0 Comments: 0

g(M)=2MB^→ .MC^→ +MC^→ .MA^→ +MA^→ .MB^→ g(G)=4MA^2 +3MA^→ (AB^→ +AC^→ ) 1) show that ∀ M ∈ plan g(M)=g(G)+4MG^2 2) Determine the set of point M of plan such as g(M)=g(A) 2) Construct this set of point M in the case where g(G)=5.

$${g}\left({M}\right)=\mathrm{2}{M}\overset{\rightarrow} {{B}}.{M}\overset{\rightarrow} {{C}}+{M}\overset{\rightarrow} {{C}}.{M}\overset{\rightarrow} {{A}}+{M}\overset{\rightarrow} {{A}}.{M}\overset{\rightarrow} {{B}} \\ $$$${g}\left({G}\right)=\mathrm{4}{MA}^{\mathrm{2}} +\mathrm{3}{M}\overset{\rightarrow} {{A}}\left({A}\overset{\rightarrow} {{B}}+{A}\overset{\rightarrow} {{C}}\right) \\ $$$$ \\ $$$$\left.\mathrm{1}\right)\:{show}\:{that}\:\forall\:{M}\:\in\:{plan} \\ $$$${g}\left({M}\right)={g}\left({G}\right)+\mathrm{4}{MG}^{\mathrm{2}} \\ $$$$\left.\mathrm{2}\right)\:{Determine}\:{the}\:{set}\:{of}\:{point}\:{M}\:{of}\:{plan} \\ $$$${such}\:{as}\:{g}\left({M}\right)={g}\left({A}\right) \\ $$$$\left.\mathrm{2}\right)\:{Construct}\:{this}\:{set}\:{of}\:{point}\:{M} \\ $$$${in}\:{the}\:{case}\:{where}\:{g}\left({G}\right)=\mathrm{5}. \\ $$

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