Question and Answers Forum

AllQuestion and Answers: Page 79

Question Number 215467 Answers: 0 Comments: 0

Question Number 215454 Answers: 1 Comments: 0

Question Number 215439 Answers: 2 Comments: 0

( 2 + (√2) )^8 = (√A) + (√B) Find: A−B = ?

$$\left(\:\mathrm{2}\:\:+\:\:\sqrt{\mathrm{2}}\:\right)^{\mathrm{8}} \:=\:\:\sqrt{\mathrm{A}}\:\:+\:\:\sqrt{\mathrm{B}} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{A}−\mathrm{B}\:=\:? \\ $$

Question Number 215434 Answers: 0 Comments: 0

∫_0 ^( t) (√(t/(b−t))) e^t dt =?

$$\int_{\mathrm{0}} ^{\:\:{t}} \sqrt{\frac{{t}}{{b}−{t}}}\:{e}^{{t}} {dt}\:=? \\ $$

Question Number 215458 Answers: 1 Comments: 0

Evaluate lim_(n→∞) n^2 ∫_0 ^1 x^(n+1) sin(πx)dx

$$\mathrm{Evaluate}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{n}^{\mathrm{2}} \:\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{{n}+\mathrm{1}} \mathrm{sin}\left(\pi{x}\right){dx} \\ $$

Question Number 215418 Answers: 1 Comments: 0

Question Number 215417 Answers: 1 Comments: 0

a and b are complex numbers such that ∣b∣ = 1. Find ∣((b − a)/(1 − a^(−) b))∣

$${a}\:\mathrm{and}\:{b}\:\mathrm{are}\:\mathrm{complex}\:\mathrm{numbers}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mid{b}\mid\:=\:\mathrm{1}.\:\mathrm{Find}\:\mid\frac{{b}\:−\:{a}}{\mathrm{1}\:−\:\overline {{a}b}}\mid \\ $$

Question Number 215414 Answers: 1 Comments: 2

∫ ((sin^3 ((x/2))sec((x/2)))/( (√(cos^3 x + cos^2 x + cosx)))) dx Solve this integral.

$$\int\:\frac{\mathrm{sin}^{\mathrm{3}} \left(\frac{{x}}{\mathrm{2}}\right)\mathrm{sec}\left(\frac{{x}}{\mathrm{2}}\right)}{\:\sqrt{\mathrm{cos}^{\mathrm{3}} {x}\:+\:\mathrm{cos}^{\mathrm{2}} {x}\:+\:\mathrm{cos}{x}}}\:{dx} \\ $$$$\mathrm{Solve}\:\mathrm{this}\:\mathrm{integral}. \\ $$

Question Number 215445 Answers: 3 Comments: 0

Question Number 215404 Answers: 1 Comments: 0

∫_a ^( x) ((√(1+4x^2 ))/( (√(a^2 −x^2 ))))dx = ?

$$\int_{{a}} ^{\:\:{x}} \:\frac{\sqrt{\mathrm{1}+\mathrm{4}{x}^{\mathrm{2}} }}{\:\sqrt{{a}^{\mathrm{2}} −{x}^{\mathrm{2}} }}{dx}\:=\:? \\ $$

Question Number 215400 Answers: 3 Comments: 1

Question Number 215393 Answers: 0 Comments: 1

∫_0 ^∞ (x^(2ν) /((x^2 +β^2 )^(μ+1) ))sin(ax)dx

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{{x}^{\mathrm{2}\nu} }{\left({x}^{\mathrm{2}} +\beta^{\mathrm{2}} \right)^{\mu+\mathrm{1}} }\mathrm{sin}\left({ax}\right){dx} \\ $$$$ \\ $$

Question Number 215386 Answers: 1 Comments: 0

Question Number 215372 Answers: 1 Comments: 0

Question Number 215390 Answers: 1 Comments: 0

∮_γ x^2 dx [γ: x^2 +y^2 =1]

$$\oint_{\gamma} {x}^{\mathrm{2}} {dx}\:\left[\gamma:\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{1}\right] \\ $$

Question Number 215356 Answers: 1 Comments: 0

Solve: x^2 =a+(y−z)^2 y^2 =b+(z−x)^2 z^2 =c+(x−y)^2

$$\:{Solve}: \\ $$$$\:\:{x}^{\mathrm{2}} ={a}+\left({y}−{z}\right)^{\mathrm{2}} \\ $$$$\:\:{y}^{\mathrm{2}} ={b}+\left({z}−{x}\right)^{\mathrm{2}} \\ $$$$\:\:{z}^{\mathrm{2}} ={c}+\left({x}−{y}\right)^{\mathrm{2}} \\ $$

Question Number 215350 Answers: 2 Comments: 0

Find: x^x = 2^(√(200)) ⇒ x = ?

$$\mathrm{Find}:\:\:\:\mathrm{x}^{\boldsymbol{\mathrm{x}}} \:=\:\mathrm{2}^{\sqrt{\mathrm{200}}} \:\:\Rightarrow\:\:\mathrm{x}\:=\:? \\ $$

Question Number 215349 Answers: 1 Comments: 0

Find the type of triangle such that the following relationship holds between its angles. tan (B)tan(C)= tan^2 (((B+C)/2) ) ■

$$ \\ $$$$\:\:\:\:{Find}\:{the}\:{type}\:{of}\:{triangle} \\ $$$$\:\:\:\:{such}\:{that}\:{the}\:{following} \\ $$$$\:\:\:\:\:{relationship}\:{holds}\:{between}\: \\ $$$${its}\:{angles}. \\ $$$$\:\:\:\:\:\: \\ $$$$\:{tan}\:\left({B}\right){tan}\left({C}\right)=\:{tan}^{\mathrm{2}} \left(\frac{{B}+{C}}{\mathrm{2}}\:\right)\:\:\:\:\blacksquare \\ $$$$ \\ $$

Question Number 215344 Answers: 2 Comments: 0

Question Number 215343 Answers: 1 Comments: 1

lim_(x→0) ((sin 3xcos5x )/x^2 )

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:\mathrm{3}{x}\mathrm{cos5}{x}\:}{{x}^{\mathrm{2}} } \\ $$

Question Number 215340 Answers: 0 Comments: 17

Question Number 215331 Answers: 1 Comments: 0

Question Number 215395 Answers: 1 Comments: 3

Question Number 215322 Answers: 1 Comments: 0

Question Number 215315 Answers: 2 Comments: 0

Evaluate lim_(n→∞) ((1/(2n+1))+(1/(2n+2))+...+(1/(4n)))

$$\mathrm{Evaluate}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\mathrm{1}}{\mathrm{2}{n}+\mathrm{1}}+\frac{\mathrm{1}}{\mathrm{2}{n}+\mathrm{2}}+...+\frac{\mathrm{1}}{\mathrm{4}{n}}\right) \\ $$

Question Number 215313 Answers: 2 Comments: 0

Pg 74 Pg 75 Pg 76 Pg 77 Pg 78 Pg 79 Pg 80 Pg 81 Pg 82 Pg 83

Contact: info@tinkutara.com