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Question Number 193280 Answers: 1 Comments: 0

Question Number 193278 Answers: 1 Comments: 0

Please Help...!! ∫^( ∞) _( 0) x.e^(−x) .sinx.dx

$${Please}\:{Help}...!! \\ $$$$\:\:\:\:\underset{\:\:\:\:\mathrm{0}} {\int}^{\:\:\infty} {x}.{e}^{−{x}} .{sinx}.{dx}\: \\ $$$$ \\ $$

Question Number 193272 Answers: 2 Comments: 0

Question Number 193268 Answers: 1 Comments: 0

Question Number 193267 Answers: 1 Comments: 0

Question Number 193266 Answers: 0 Comments: 0

Question Number 193262 Answers: 1 Comments: 0

lim_(x→+∞) (ln((x+(√(x^2 +1)))/(x+(√(x^2 −1)))).ln^2 ((x+1)/(x−1)))

$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\left({ln}\frac{{x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}{{x}+\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}.{ln}^{\mathrm{2}} \:\frac{{x}+\mathrm{1}}{{x}−\mathrm{1}}\right) \\ $$$$ \\ $$

Question Number 193256 Answers: 1 Comments: 0

Question Number 193253 Answers: 1 Comments: 0

Select the correct option with explaination: If (1/3)log_3 M + 3log_3 N = 1 + log_(0.008) 5 then a. M^9 = (9/N) b. N^9 = (9/M) c. M^3 = (3/N) d. N^3 = (3/M)

$$\boldsymbol{\mathrm{Select}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{correct}}\:\boldsymbol{\mathrm{option}}\:\boldsymbol{\mathrm{with}}\: \\ $$$$\boldsymbol{\mathrm{explaination}}: \\ $$$$\mathrm{If}\:\frac{\mathrm{1}}{\mathrm{3}}\mathrm{log}_{\mathrm{3}} {M}\:+\:\mathrm{3log}_{\mathrm{3}} {N}\:=\:\mathrm{1}\:+\:\mathrm{log}_{\mathrm{0}.\mathrm{008}} \mathrm{5}\:\mathrm{then} \\ $$$$\mathrm{a}.\:{M}^{\mathrm{9}} \:=\:\frac{\mathrm{9}}{{N}} \\ $$$$\mathrm{b}.\:{N}^{\mathrm{9}} \:=\:\frac{\mathrm{9}}{{M}} \\ $$$$\mathrm{c}.\:{M}^{\mathrm{3}} \:=\:\frac{\mathrm{3}}{{N}} \\ $$$$\mathrm{d}.\:{N}^{\mathrm{3}} \:=\:\frac{\mathrm{3}}{{M}}\: \\ $$

Question Number 193250 Answers: 0 Comments: 0

Solve: y′(x)=y^2 (t)+t^2

$${Solve}: \\ $$$${y}'\left({x}\right)={y}^{\mathrm{2}} \left({t}\right)+{t}^{\mathrm{2}} \: \\ $$

Question Number 193248 Answers: 1 Comments: 0

L= lim_( x→0) (( sin(x )−arcsin(x))/(tan(x)− arctan(x)))=?

$$ \\ $$$$\:\mathrm{L}=\:\mathrm{lim}_{\:{x}\rightarrow\mathrm{0}} \:\frac{\:\mathrm{sin}\left({x}\:\right)−\mathrm{arcsin}\left({x}\right)}{\mathrm{tan}\left({x}\right)−\:\mathrm{arctan}\left({x}\right)}=?\:\:\:\:\:\:\: \\ $$$$ \\ $$$$\:\:\:\: \\ $$

Question Number 193247 Answers: 2 Comments: 0

if f(x) = ((ax+1)/(x+b)) find f^( 100) (x) and f^(101) (x) ?

$${if}\:{f}\left({x}\right)\:=\:\frac{{ax}+\mathrm{1}}{{x}+{b}}\:{find}\:{f}^{\:\mathrm{100}} \left({x}\right)\:{and}\:{f}^{\mathrm{101}} \left({x}\right)\:? \\ $$

Question Number 193245 Answers: 0 Comments: 0

Question Number 193239 Answers: 2 Comments: 0

Question Number 193238 Answers: 1 Comments: 0

s=a+b+c+d+..... number terms :n {a;b;c;d.....}>0 then E=s/(s−a)+s/(s−b)+s/s−c)+.... a) E>=n^2 b)E>=n^2 /(n−1) c) E>=n/(n+1) d) E>=n^2 /(n+1) e) E>=n^2 −1

$${s}={a}+{b}+{c}+{d}+..... \\ $$$${number}\:{terms}\::{n} \\ $$$$\left\{{a};{b};{c};{d}.....\right\}>\mathrm{0} \\ $$$$\left.{then}\:{E}={s}/\left({s}−{a}\right)+{s}/\left({s}−{b}\right)+{s}/{s}−{c}\right)+.... \\ $$$$\left.{a}\left.\right)\:{E}>={n}^{\mathrm{2}} \:\:\:\:\:\:\:\:\:{b}\right){E}>={n}^{\mathrm{2}} /\left({n}−\mathrm{1}\right) \\ $$$$\left.{c}\left.\right)\:{E}>={n}/\left({n}+\mathrm{1}\right)\:\:\:\:\:\:{d}\right)\:{E}>={n}^{\mathrm{2}} /\left({n}+\mathrm{1}\right) \\ $$$$\left.{e}\right)\:{E}>={n}^{\mathrm{2}} −\mathrm{1} \\ $$$$ \\ $$$$ \\ $$

Question Number 193237 Answers: 1 Comments: 0

Prove that: In any acute △ABC, cot^2 A+cot^2 B+cot^2 C≥1. Equality is possible if and only if A=B=C=(π/3).

$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{In}\:\mathrm{any}\:\mathrm{acute}\:\bigtriangleup{ABC},\:\mathrm{cot}^{\mathrm{2}} {A}+\mathrm{cot}^{\mathrm{2}} {B}+\mathrm{cot}^{\mathrm{2}} {C}\geqslant\mathrm{1}. \\ $$$$\mathrm{Equality}\:\mathrm{is}\:\mathrm{possible}\:\mathrm{if}\:\mathrm{and}\:\mathrm{only}\:\mathrm{if}\:{A}={B}={C}=\frac{\pi}{\mathrm{3}}. \\ $$

Question Number 193235 Answers: 1 Comments: 0

Question Number 193236 Answers: 2 Comments: 0

Question Number 193231 Answers: 1 Comments: 0

Question Number 193230 Answers: 1 Comments: 0

Choose the correct option: If a, b and c are consecutive positive integers and log(1 + ac) = 2k then the value of k is: a) log a b) log b c) 2 d) 1 Give the explaination also.

$$\boldsymbol{\mathrm{Choose}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{correct}}\:\boldsymbol{\mathrm{option}}: \\ $$$$\mathrm{If}\:{a},\:{b}\:\mathrm{and}\:{c}\:\mathrm{are}\:\mathrm{consecutive}\:\mathrm{positive} \\ $$$$\mathrm{integers}\:\mathrm{and}\:\mathrm{log}\left(\mathrm{1}\:+\:{ac}\right)\:=\:\mathrm{2}{k}\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:{k}\:\mathrm{is}: \\ $$$$\left.\mathrm{a}\right)\:\mathrm{log}\:{a} \\ $$$$\left.\mathrm{b}\right)\:\mathrm{log}\:{b} \\ $$$$\left.\mathrm{c}\right)\:\mathrm{2} \\ $$$$\left.\mathrm{d}\right)\:\mathrm{1} \\ $$$$\boldsymbol{\mathrm{Give}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{explaination}}\:\boldsymbol{\mathrm{also}}. \\ $$

Question Number 193226 Answers: 1 Comments: 0

(a) 5 out of 12 articles are known to be defective. If three articles are picked, one after the other, without replacement, find the probability that all the three articles are non-defective. (b) Two coins are tossed and a dice is thrown. What is the probability of obtaining a head, a tail and a 4?

$$ \\ $$(a) 5 out of 12 articles are known to be defective. If three articles are picked, one after the other, without replacement, find the probability that all the three articles are non-defective. (b) Two coins are tossed and a dice is thrown. What is the probability of obtaining a head, a tail and a 4?

Question Number 193232 Answers: 0 Comments: 0

Question Number 193222 Answers: 0 Comments: 0

Question Number 193221 Answers: 1 Comments: 0

find the cube root of 9ab^2 + (b^2 +24a^2 )(√(b^2 −3a^2 ))

$$ \\ $$$$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{cube}}\:\boldsymbol{{root}}\:\boldsymbol{{of}} \\ $$$$\mathrm{9}\boldsymbol{{ab}}^{\mathrm{2}} \:+\:\left(\boldsymbol{{b}}^{\mathrm{2}} +\mathrm{24}\boldsymbol{{a}}^{\mathrm{2}} \right)\sqrt{\boldsymbol{{b}}^{\mathrm{2}} −\mathrm{3}\boldsymbol{{a}}^{\mathrm{2}} } \\ $$

Question Number 193214 Answers: 0 Comments: 0

Evaluate Ω=∫_(−∞) ^( ∞) ((e^(x/2) ln((√((3−x)/(3+x)))))/(tanh^(−1) ((x/3))(1+e^x )))dx

$${Evaluate} \\ $$$$\Omega=\int_{−\infty} ^{\:\infty} \frac{{e}^{\frac{{x}}{\mathrm{2}}} {ln}\left(\sqrt{\frac{\mathrm{3}−{x}}{\mathrm{3}+{x}}}\right)}{{tanh}^{−\mathrm{1}} \left(\frac{{x}}{\mathrm{3}}\right)\left(\mathrm{1}+{e}^{{x}} \right)}{dx} \\ $$

Question Number 193213 Answers: 3 Comments: 0

((a^m /a^(−n) ))^(m−n)

$$\left(\frac{{a}^{{m}} }{{a}^{−{n}} }\right)^{{m}−{n}} \\ $$

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