Question and Answers Forum

AllQuestion and Answers: Page 1341

Question Number 79325 Answers: 0 Comments: 2

Convergence of : 1) I=∫_1 ^( ∞) ((e^(−t/5) ∣sin(lnt)∣)/((t−1)^(3/2) ))dt 2) I=∫_1 ^∞ ((√(lnx))/((x−1)(√x)))dx

$$\:\boldsymbol{{Convergence}}\:\:\boldsymbol{{of}}\:: \\ $$$$\left.\:\:\mathrm{1}\right)\:\:\:\boldsymbol{{I}}=\int_{\mathrm{1}} ^{\:\infty} \frac{\boldsymbol{{e}}^{−\boldsymbol{{t}}/\mathrm{5}} \mid\boldsymbol{{sin}}\left(\boldsymbol{{lnt}}\right)\mid}{\left(\boldsymbol{{t}}−\mathrm{1}\right)^{\mathrm{3}/\mathrm{2}} }\boldsymbol{{dt}} \\ $$$$\left.\:\:\mathrm{2}\right)\:\:\:\boldsymbol{{I}}=\int_{\mathrm{1}} ^{\infty} \frac{\sqrt{\boldsymbol{{lnx}}}}{\left(\boldsymbol{{x}}−\mathrm{1}\right)\sqrt{\boldsymbol{{x}}}}\boldsymbol{{dx}} \\ $$

Question Number 79311 Answers: 0 Comments: 2

Question Number 79309 Answers: 1 Comments: 3

Question Number 79308 Answers: 1 Comments: 3

Question Number 79306 Answers: 1 Comments: 7

(√(3−x))−(√(x+1))>(1/2)

$$ \\ $$$$\sqrt{\mathrm{3}−\mathrm{x}}−\sqrt{\mathrm{x}+\mathrm{1}}>\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Question Number 79290 Answers: 1 Comments: 0

What is the area of one petal of r=2cos(3θ)

$${What}\:{is}\:{the}\:{area}\:{of}\:{one}\:{petal}\:{of} \\ $$$${r}=\mathrm{2cos}\left(\mathrm{3}\theta\right) \\ $$

Question Number 79289 Answers: 0 Comments: 1

m^2 +n^2 =2(a^2 +b^2 ) What is 2(a+b) in terms of m and n

$${m}^{\mathrm{2}} +{n}^{\mathrm{2}} =\mathrm{2}\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} \right) \\ $$$${What}\:{is}\:\mathrm{2}\left({a}+{b}\right)\:{in}\:{terms}\:{of}\:{m}\:{and}\:{n} \\ $$

Question Number 79320 Answers: 0 Comments: 3

what the minimum value of y = sec (x)+cosec (x)?

$$\mathrm{what}\:\mathrm{the}\:\mathrm{minimum} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{y}\:=\:\mathrm{sec}\:\left(\mathrm{x}\right)+\mathrm{cosec}\:\left(\mathrm{x}\right)? \\ $$

Question Number 79279 Answers: 1 Comments: 4

solve ∣x∣^3 −7x^2 +7∣x∣+15<0

$$\mathrm{solve}\: \\ $$$$\mid\mathrm{x}\mid^{\mathrm{3}} −\mathrm{7x}^{\mathrm{2}} +\mathrm{7}\mid\mathrm{x}\mid+\mathrm{15}<\mathrm{0} \\ $$

Question Number 79266 Answers: 0 Comments: 3

let ABC be a escalene triangle of area 7. Let A_1 be a point on the side BC, and let B_1 and C_1 be points on the sides AC and AB, such that AA_1 , BB_1 and CC_1 are parallel. Find the area of triangle A_1 B_1 C_1 .

$${let}\:{ABC}\:{be}\:{a}\:{escalene}\:{triangle}\:{of} \\ $$$${area}\:\mathrm{7}.\:{Let}\:{A}_{\mathrm{1}} \:{be}\:{a}\:{point}\:{on}\:{the}\:{side} \\ $$$${BC},\:{and}\:{let}\:{B}_{\mathrm{1}} \:{and}\:{C}_{\mathrm{1}} \:{be}\:{points}\:{on} \\ $$$${the}\:{sides}\:{AC}\:{and}\:{AB},\:{such}\:{that} \\ $$$${AA}_{\mathrm{1}} ,\:{BB}_{\mathrm{1}} \:{and}\:{CC}_{\mathrm{1}} \:{are}\:{parallel}.\:{Find} \\ $$$${the}\:{area}\:{of}\:{triangle}\:{A}_{\mathrm{1}} {B}_{\mathrm{1}} {C}_{\mathrm{1}} . \\ $$

Question Number 79264 Answers: 0 Comments: 0

Question Number 79263 Answers: 0 Comments: 4

4^(2x−1) +(1/4)^2 log^2 (2x)>^2 log(x) {^2 log((1/x))−2^(2x) }

$$\mathrm{4}^{\mathrm{2x}−\mathrm{1}} +\frac{\mathrm{1}}{\mathrm{4}}\:^{\mathrm{2}} \mathrm{log}^{\mathrm{2}} \left(\mathrm{2x}\right)>\:^{\mathrm{2}} \mathrm{log}\left(\mathrm{x}\right) \\ $$$$\left\{^{\mathrm{2}} \mathrm{log}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)−\mathrm{2}^{\mathrm{2x}} \right\} \\ $$

Question Number 79256 Answers: 1 Comments: 0

3s^2 −2ps−3cp−1=0 and 3s−2p−sp^2 −3cp^2 =0 find s and p both real in terms of c ∈R.

$$\mathrm{3}{s}^{\mathrm{2}} −\mathrm{2}{ps}−\mathrm{3}{cp}−\mathrm{1}=\mathrm{0}\:\:\:{and} \\ $$$$\mathrm{3}{s}−\mathrm{2}{p}−{sp}^{\mathrm{2}} −\mathrm{3}{cp}^{\mathrm{2}} =\mathrm{0} \\ $$$${find}\:{s}\:{and}\:{p}\:{both}\:{real}\:{in}\:{terms} \\ $$$${of}\:{c}\:\in\mathbb{R}. \\ $$

Question Number 79249 Answers: 1 Comments: 3

Question Number 79254 Answers: 4 Comments: 2

Question Number 79236 Answers: 1 Comments: 3

lim_(x→+∞) x{e−(1+(1/x))^x }=?

$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\:\mathrm{x}\left\{\mathrm{e}−\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{x}} \right\}=? \\ $$

Question Number 79233 Answers: 1 Comments: 3

(1/(x(x+1)))+(1/((x+1)(x+2)))+ (1/((x+2)(x+3)))≤(3/4)

$$\frac{\mathrm{1}}{\mathrm{x}\left(\mathrm{x}+\mathrm{1}\right)}+\frac{\mathrm{1}}{\left(\mathrm{x}+\mathrm{1}\right)\left(\mathrm{x}+\mathrm{2}\right)}+ \\ $$$$\frac{\mathrm{1}}{\left(\mathrm{x}+\mathrm{2}\right)\left(\mathrm{x}+\mathrm{3}\right)}\leqslant\frac{\mathrm{3}}{\mathrm{4}} \\ $$

Question Number 79222 Answers: 0 Comments: 3

∫_0 ^1 (x^n /(Σ_(k=0) ^(n−1) x^k ))dx=?

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{{n}} }{\underset{{k}=\mathrm{0}} {\overset{{n}−\mathrm{1}} {\sum}}{x}^{{k}} }{dx}=? \\ $$

Question Number 79190 Answers: 4 Comments: 13

if x^2 +y^2 =50, find the minimum and maximum of (x+y)^2 −8(x+y)+20

$${if}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{50}, \\ $$$${find}\:{the}\:{minimum}\:{and}\:{maximum}\:{of} \\ $$$$\left({x}+{y}\right)^{\mathrm{2}} −\mathrm{8}\left({x}+{y}\right)+\mathrm{20} \\ $$

Question Number 79187 Answers: 0 Comments: 0

∫_0 ^π ((cos (nx)−cos (nα))/(cos (x)−cos (α))) dx

$$\underset{\mathrm{0}} {\overset{\pi} {\int}}\:\frac{\mathrm{cos}\:\left({nx}\right)−\mathrm{cos}\:\left({n}\alpha\right)}{\mathrm{cos}\:\left({x}\right)−\mathrm{cos}\:\left(\alpha\right)}\:{dx} \\ $$

Question Number 79186 Answers: 1 Comments: 0

∫_(−1) ^1 ((cos (x))/(1+e^(1/x) )) dx ?

$$\underset{−\mathrm{1}} {\overset{\mathrm{1}} {\int}}\:\frac{\mathrm{cos}\:\left({x}\right)}{\mathrm{1}+{e}^{\frac{\mathrm{1}}{{x}}} }\:{dx}\:? \\ $$

Question Number 79181 Answers: 1 Comments: 1

lim_(x→ 0^+ ) (x^2 + 1)^(ln x) = ...

$$\underset{{x}\rightarrow\:\mathrm{0}^{+} } {\mathrm{lim}}\:\:\left({x}^{\mathrm{2}} \:+\:\mathrm{1}\right)^{\mathrm{ln}\:{x}} \:\:=\:\:... \\ $$

Question Number 79177 Answers: 1 Comments: 0

Question Number 79667 Answers: 1 Comments: 2

find the equation of the tangent and normal to the curve xy=9 at x=4

$${find}\:{the}\:{equation}\:{of}\:{the}\:{tangent}\:{and} \\ $$$${normal}\:{to}\:{the}\:{curve}\:{xy}=\mathrm{9}\:{at}\:{x}=\mathrm{4} \\ $$

Question Number 79147 Answers: 1 Comments: 0

(√(x+(1/x^2 )))+(√(x−(1/x^2 ) ))≤(2/x)

$$\sqrt{\mathrm{x}+\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }}+\sqrt{\mathrm{x}−\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\:}\leqslant\frac{\mathrm{2}}{\mathrm{x}} \\ $$

Question Number 79131 Answers: 1 Comments: 2

Determine the set of points M such as ∣∣MA^→ +MB^→ +2MC^→ ∣∣=6(√3) AB=BC=AC=6 ABC is triangle.

$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{points}\:\mathrm{M}\: \\ $$$$\mathrm{such}\:\mathrm{as}\:\mid\mid\mathrm{M}\overset{\rightarrow} {\mathrm{A}}+\mathrm{M}\overset{\rightarrow} {\mathrm{B}}+\mathrm{2M}\overset{\rightarrow} {\mathrm{C}}\mid\mid=\mathrm{6}\sqrt{\mathrm{3}} \\ $$$$\mathrm{AB}=\mathrm{BC}=\mathrm{AC}=\mathrm{6} \\ $$$$\mathrm{ABC}\:\mathrm{is}\:\mathrm{triangle}. \\ $$

Pg 1336 Pg 1337 Pg 1338 Pg 1339 Pg 1340 Pg 1341 Pg 1342 Pg 1343 Pg 1344 Pg 1345

Contact: info@tinkutara.com