Question and Answers Forum

AllQuestion and Answers: Page 505

Question Number 168874 Answers: 0 Comments: 0

Question Number 168873 Answers: 0 Comments: 0

Question Number 168872 Answers: 0 Comments: 2

E=∫^π _0 [((a^2 σ sin θ)/(2ε(√(a^2 −x^2 −2ax cosθ))))]dθ If a>x show that E = ((a^2 σ)/(εx))

$${E}=\underset{\mathrm{0}} {\int}^{\pi} \left[\frac{{a}^{\mathrm{2}} \sigma\:\mathrm{sin}\:\theta}{\mathrm{2}\epsilon\sqrt{{a}^{\mathrm{2}} −{x}^{\mathrm{2}} −\mathrm{2}{ax}\:\mathrm{cos}\theta}}\right]{d}\theta \\ $$$$\mathrm{If}\:{a}>{x}\:\mathrm{show}\:\mathrm{that}\:{E}\:=\:\frac{{a}^{\mathrm{2}} \sigma}{\epsilon{x}} \\ $$

Question Number 168860 Answers: 0 Comments: 0

Question Number 168859 Answers: 1 Comments: 0

Prove that: 1. A + B^(−) = A^(−) ∙ B^(−) , AB^(−) = A^(−) + B^(−) 2. (A + C)(B + C) = AB + C

$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{1}.\:\overline {\mathrm{A}\:+\:\mathrm{B}}\:=\:\overline {\mathrm{A}}\:\centerdot\:\overline {\mathrm{B}}\:\:\:,\:\:\:\overline {\mathrm{AB}}\:=\:\overline {\mathrm{A}}\:+\:\overline {\mathrm{B}} \\ $$$$\mathrm{2}.\:\left(\mathrm{A}\:+\:\mathrm{C}\right)\left(\mathrm{B}\:+\:\mathrm{C}\right)\:=\:\mathrm{AB}\:+\:\mathrm{C} \\ $$

Question Number 168858 Answers: 1 Comments: 0

Simplify: 1. (A + B)(A + B^(−) ) 2. (A^(−) + B)(A^(−) + B^(−) )

$$\mathrm{Simplify}: \\ $$$$\mathrm{1}.\:\left(\mathrm{A}\:+\:\mathrm{B}\right)\left(\mathrm{A}\:+\:\overline {\mathrm{B}}\right) \\ $$$$\mathrm{2}.\:\left(\overline {\mathrm{A}}\:+\:\mathrm{B}\right)\left(\overline {\mathrm{A}}\:+\:\overline {\mathrm{B}}\right) \\ $$

Question Number 168857 Answers: 3 Comments: 0

Question Number 168856 Answers: 1 Comments: 0

Re(2+e^(iαt) )?

$$\mathrm{Re}\left(\mathrm{2}+\mathrm{e}^{\mathrm{i}\alpha\mathrm{t}} \right)? \\ $$

Question Number 168855 Answers: 0 Comments: 0

Question Number 168852 Answers: 0 Comments: 3

Question Number 168868 Answers: 0 Comments: 0

Question Number 168842 Answers: 0 Comments: 0

Question Number 168841 Answers: 0 Comments: 0

Question Number 168832 Answers: 1 Comments: 1

Question Number 168830 Answers: 0 Comments: 1

Question Number 168828 Answers: 0 Comments: 1

∫_0 ^(π/2) cos^(−1) ((1/(1+2cos x)))dx

$$ \\ $$$$\:\:\:\:\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \mathrm{cos}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2cos}\:{x}}\right){dx} \\ $$

Question Number 168821 Answers: 1 Comments: 0

lim_(x→a) ((a^x −a^n )/(nln(x)−nln(a)))=?

$$\underset{{x}\rightarrow{a}} {\mathrm{lim}}\frac{{a}^{{x}} −{a}^{{n}} }{{nln}\left({x}\right)−{nln}\left({a}\right)}=? \\ $$

Question Number 168819 Answers: 3 Comments: 0

De^ montrer que: Demonstrate that: lim_(x→0) (((e^x −1−ln (x+1))/(cos (x)−1))) = −2

$$\mathrm{D}\acute {\mathrm{e}montrer}\:\mathrm{que}: \\ $$$$\mathrm{Demonstrate}\:\mathrm{that}: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{{e}^{{x}} −\mathrm{1}−\mathrm{ln}\:\left({x}+\mathrm{1}\right)}{\mathrm{cos}\:\left({x}\right)−\mathrm{1}}\right)\:=\:−\mathrm{2} \\ $$

Question Number 168813 Answers: 1 Comments: 0

Question Number 168812 Answers: 0 Comments: 0

∫_0 ^π (sin x)^(cos x) dx

$$\int_{\mathrm{0}} ^{\pi} \left(\mathrm{sin}\:{x}\right)^{\mathrm{cos}\:{x}} {dx} \\ $$

Question Number 168801 Answers: 0 Comments: 6

Question Number 168800 Answers: 0 Comments: 1

If the function f is continuous in [a,b] express lim_(n→∞) (1/n)Σ_(k=1) ^n f((k/n)) as a definite integral.

$$\mathrm{If}\:\mathrm{the}\:\mathrm{function}\:{f}\:\mathrm{is}\:\mathrm{continuous}\:\mathrm{in}\:\left[{a},{b}\right] \\ $$$$\mathrm{express}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{{n}}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{f}\left(\frac{{k}}{{n}}\right)\:\mathrm{as}\:\mathrm{a}\:\mathrm{definite} \\ $$$$\mathrm{integral}. \\ $$

Question Number 168799 Answers: 0 Comments: 0

If the function f is continuous in [a,b] prove that lim_(x→∞ ) ((b−a)/n)Σ_(k=1) ^n f(a+((k(b−a))/n))=∫_a ^b f(x)dx

$$\mathrm{If}\:\mathrm{the}\:\mathrm{function}\:{f}\:\mathrm{is}\:\mathrm{continuous}\:\mathrm{in} \\ $$$$\left[{a},{b}\right]\: \\ $$$$\mathrm{prove}\:\mathrm{that}\: \\ $$$$\:\underset{{x}\rightarrow\infty\:} {\mathrm{lim}}\frac{{b}−{a}}{{n}}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{f}\left({a}+\frac{{k}\left({b}−{a}\right)}{{n}}\right)=\int_{{a}} ^{{b}} {f}\left({x}\right){dx} \\ $$

Question Number 168788 Answers: 0 Comments: 1

Question Number 168787 Answers: 0 Comments: 1

Question Number 168781 Answers: 0 Comments: 1

Pg 500 Pg 501 Pg 502 Pg 503 Pg 504 Pg 505 Pg 506 Pg 507 Pg 508 Pg 509

Contact: info@tinkutara.com