Question and Answers Forum

AllQuestion and Answers: Page 642

Question Number 147234 Answers: 0 Comments: 0

Question Number 147233 Answers: 0 Comments: 1

Question Number 147231 Answers: 1 Comments: 0

if 3^(a+2) = 5^(3b−1) = 7^(3−2c) find a∙b∙c = ?

$${if}\:\:\:\mathrm{3}^{\boldsymbol{{a}}+\mathrm{2}} \:=\:\mathrm{5}^{\mathrm{3}\boldsymbol{{b}}−\mathrm{1}} \:=\:\mathrm{7}^{\mathrm{3}−\mathrm{2}\boldsymbol{{c}}} \\ $$$${find}\:\:\:\boldsymbol{{a}}\centerdot\boldsymbol{{b}}\centerdot\boldsymbol{{c}}\:=\:? \\ $$

Question Number 147232 Answers: 0 Comments: 2

Question Number 147229 Answers: 2 Comments: 0

Question Number 147226 Answers: 0 Comments: 0

Question Number 147223 Answers: 1 Comments: 1

Question Number 147222 Answers: 3 Comments: 0

S = Σ_(k=1) ^p k^2 e^k Find S

$${S}\:=\:\underset{{k}=\mathrm{1}} {\overset{{p}} {\sum}}{k}^{\mathrm{2}} {e}^{{k}} \\ $$$${Find}\:{S} \\ $$

Question Number 147218 Answers: 0 Comments: 0

calculate ∫_(∣z−1∣=2) (e^z /((z+i(√2))^2 (z+i)^2 (2z−1)))dz

$$\mathrm{calculate}\:\int_{\mid\mathrm{z}−\mathrm{1}\mid=\mathrm{2}} \:\:\:\:\frac{\mathrm{e}^{\mathrm{z}} }{\left(\mathrm{z}+\mathrm{i}\sqrt{\mathrm{2}}\right)^{\mathrm{2}} \left(\mathrm{z}+\mathrm{i}\right)^{\mathrm{2}} \left(\mathrm{2z}−\mathrm{1}\right)}\mathrm{dz} \\ $$

Question Number 147213 Answers: 2 Comments: 0

(1)∫ ((cosz)/((z+1)^2 ))dz , ∣z∣=1 (2) ∫ ((cosz)/((z−1)^2 ))dz ,∣z∣=1

$$\left(\mathrm{1}\right)\int\:\frac{{cosz}}{\left({z}+\mathrm{1}\right)^{\mathrm{2}} }{dz}\:\:\:\:\:,\:\:\mid{z}\mid=\mathrm{1} \\ $$$$ \\ $$$$\left(\mathrm{2}\right)\:\int\:\frac{{cosz}}{\left({z}−\mathrm{1}\right)^{\mathrm{2}} }{dz}\:\:\:\:\:,\mid{z}\mid=\mathrm{1} \\ $$

Question Number 147209 Answers: 2 Comments: 1

Question Number 147206 Answers: 0 Comments: 0

calculste ∫_0 ^1 (√(1+x^4 ))dx

$$\mathrm{calculste}\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{4}} }\mathrm{dx} \\ $$

Question Number 147205 Answers: 1 Comments: 0

calculate ∫_1 ^∞ ((arctan((3/x)))/(2x^2 +1))dx

$$\mathrm{calculate}\:\int_{\mathrm{1}} ^{\infty} \:\frac{\mathrm{arctan}\left(\frac{\mathrm{3}}{\mathrm{x}}\right)}{\mathrm{2x}^{\mathrm{2}} \:+\mathrm{1}}\mathrm{dx} \\ $$

Question Number 147204 Answers: 0 Comments: 0

find ∫_0 ^1 lnxln(1−x)ln(1−x^2 )dx

$$\mathrm{find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{lnxln}\left(\mathrm{1}−\mathrm{x}\right)\mathrm{ln}\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)\mathrm{dx} \\ $$

Question Number 147203 Answers: 1 Comments: 0

find U_n =∫_0 ^∞ (e^(−nx^2 ) /(x^2 +n^2 ))dx (n≥1) nature of ΣU_n and Σ nU_n

$$\mathrm{find}\:\mathrm{U}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{e}^{−\mathrm{nx}^{\mathrm{2}} } }{\mathrm{x}^{\mathrm{2}} \:+\mathrm{n}^{\mathrm{2}} }\mathrm{dx}\:\:\:\:\:\left(\mathrm{n}\geqslant\mathrm{1}\right) \\ $$$$\mathrm{nature}\:\mathrm{of}\:\Sigma\mathrm{U}_{\mathrm{n}} \:\mathrm{and}\:\Sigma\:\mathrm{nU}_{\mathrm{n}} \\ $$

Question Number 147202 Answers: 0 Comments: 0

find ∫_0 ^1 ((√x)/( (√(x^2 +3))+(√(2x^2 +1))))dx

$$\mathrm{find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\sqrt{\mathrm{x}}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{3}}+\sqrt{\mathrm{2x}^{\mathrm{2}} +\mathrm{1}}}\mathrm{dx} \\ $$

Question Number 147201 Answers: 0 Comments: 0

f(x)=cos(sinx) developp f at fourier serie

$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{cos}\left(\mathrm{sinx}\right)\:\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$

Question Number 147195 Answers: 2 Comments: 0

Ω := ∫_0 ^( 1) Li_( 2) ( (√x) )dx = ?

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\Omega\::=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \mathrm{Li}_{\:\mathrm{2}} \left(\:\sqrt{{x}}\:\right){dx}\:=\:? \\ $$$$ \\ $$

Question Number 147188 Answers: 0 Comments: 0

find the remainder when 10^(10^n ) divides 7

$${find}\:{the}\:{remainder}\:{when}\: \\ $$$$\mathrm{10}^{\mathrm{10}^{{n}} } \:{divides}\:\mathrm{7} \\ $$$$ \\ $$

Question Number 147187 Answers: 1 Comments: 2

if (xyz^(−) )^2 = (x+y+z)^5 then find: x^3 +y^3 +z^3 −∣(x+y+z)+(x^2 +y^2 +z^2 )∣

$${if}\:\:\left(\overline {{xyz}}\right)^{\mathrm{2}} \:=\:\left({x}+{y}+{z}\right)^{\mathrm{5}} \:\:{then}\:{find}: \\ $$$${x}^{\mathrm{3}} +{y}^{\mathrm{3}} +{z}^{\mathrm{3}} −\mid\left({x}+{y}+{z}\right)+\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \right)\mid \\ $$

Question Number 147183 Answers: 1 Comments: 0

prove that e^((√2) + (√3)) > ((13 + 2(√6))/2)

$${prove}\:{that} \\ $$$$\boldsymbol{{e}}^{\sqrt{\mathrm{2}}\:+\:\sqrt{\mathrm{3}}} \:>\:\frac{\mathrm{13}\:+\:\mathrm{2}\sqrt{\mathrm{6}}}{\mathrm{2}} \\ $$

Question Number 147176 Answers: 1 Comments: 0

Question Number 147175 Answers: 0 Comments: 0

Question Number 147169 Answers: 1 Comments: 4

lim_(x→0) (((3^x + 5^x + 6^x )/3))^(1/x) = ?

$$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\left(\frac{\mathrm{3}^{\boldsymbol{{x}}} \:+\:\mathrm{5}^{\boldsymbol{{x}}} \:+\:\mathrm{6}^{\boldsymbol{{x}}} }{\mathrm{3}}\right)^{\frac{\mathrm{1}}{\boldsymbol{{x}}}} =\:? \\ $$

Question Number 147166 Answers: 2 Comments: 0

∫_R e^(ixt) e^(−t^2 ) dt..

$$\int_{\mathbb{R}} \mathrm{e}^{\mathrm{ixt}} \mathrm{e}^{−\mathrm{t}^{\mathrm{2}} } \mathrm{dt}.. \\ $$

Question Number 147163 Answers: 0 Comments: 0

Pg 637 Pg 638 Pg 639 Pg 640 Pg 641 Pg 642 Pg 643 Pg 644 Pg 645 Pg 646

Contact: info@tinkutara.com