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AllQuestion and Answers: Page 1271

Question Number 80084 Answers: 0 Comments: 3

−1=(−1)^1 =(−1)^(2/2) =((−1)^2 )^(1/2) =(1)^(1/2) = =(√1)=1 what do you think about this?

$$\:\:−\mathrm{1}=\left(−\mathrm{1}\right)^{\mathrm{1}} =\left(−\mathrm{1}\right)^{\frac{\mathrm{2}}{\mathrm{2}}} =\left(\left(−\mathrm{1}\right)^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} =\left(\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} = \\ $$$$=\sqrt{\mathrm{1}}=\mathrm{1}\:\: \\ $$$$\mathrm{what}\:\mathrm{do}\:\mathrm{you}\:\mathrm{think}\:\mathrm{about}\:\mathrm{this}? \\ $$

Question Number 80068 Answers: 2 Comments: 3

Question Number 80065 Answers: 0 Comments: 0

Question Number 80064 Answers: 1 Comments: 6

lim_(x→−∞) [(√(1−xe^x ))]

$$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\left[\sqrt{\mathrm{1}−{xe}^{{x}} \:}\right] \\ $$

Question Number 80057 Answers: 1 Comments: 2

Question Number 80053 Answers: 0 Comments: 4

Find integer x, y such that 2^x −y^2 =615

$${Find}\:{integer}\:{x},\:{y}\:{such}\:{that} \\ $$$$\mathrm{2}^{{x}} −{y}^{\mathrm{2}} =\mathrm{615} \\ $$

Question Number 80052 Answers: 0 Comments: 0

∫ e^(sin 2x) .cos x dx =

$$\int\:\mathrm{e}^{\mathrm{sin}\:\mathrm{2x}} .\mathrm{cos}\:\mathrm{x}\:\mathrm{dx}\:= \\ $$$$ \\ $$

Question Number 80108 Answers: 1 Comments: 3

a,b,c ∈R ((b+c+d)/a)=((a+c+d)/b)=((a+b+c)/d)=((a+b+d)/c)=r what is r?

$${a},{b},{c}\:\in\mathbb{R} \\ $$$$\frac{{b}+{c}+{d}}{{a}}=\frac{{a}+{c}+{d}}{{b}}=\frac{{a}+{b}+{c}}{{d}}=\frac{{a}+{b}+{d}}{{c}}={r} \\ $$$${what}\:{is}\:{r}? \\ $$

Question Number 80039 Answers: 1 Comments: 6

prove that (1+x)(1+(1/x))≥4

$${prove}\:{that} \\ $$$$\left(\mathrm{1}+{x}\right)\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)\geqslant\mathrm{4} \\ $$

Question Number 80037 Answers: 0 Comments: 0

A matrix A= [(a_(ij) ) ] is an upper triangular matrix if

$$\mathrm{A}\:\mathrm{matrix}\:{A}=\begin{bmatrix}{{a}_{{ij}} }\end{bmatrix}\:\mathrm{is}\:\mathrm{an}\:\mathrm{upper}\:\mathrm{triangular} \\ $$$$\mathrm{matrix}\:\mathrm{if} \\ $$

Question Number 80036 Answers: 1 Comments: 3

Σ_(n=1) ^∞ (1/((n+1)(n+2)(n+3)))=

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)\left({n}+\mathrm{3}\right)}=\: \\ $$

Question Number 80027 Answers: 0 Comments: 4

find minimum value of (√(x^2 +4))+(√(x^2 −24x+153)) for x≥0 in R

$${find}\:{minimum} \\ $$$${value}\:{of}\:\sqrt{{x}^{\mathrm{2}} +\mathrm{4}}+\sqrt{{x}^{\mathrm{2}} −\mathrm{24}{x}+\mathrm{153}} \\ $$$${for}\:{x}\geqslant\mathrm{0}\:{in}\:\mathbb{R} \\ $$

Question Number 80015 Answers: 2 Comments: 2

Question Number 79992 Answers: 0 Comments: 2

lim_(x→0) [(1/x)] = ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left[\frac{\mathrm{1}}{\mathrm{x}}\right]\:=\:? \\ $$

Question Number 80000 Answers: 1 Comments: 2

prove that lim_(x→0) ((arcsin(x/(√(1−x^2 ))))/(ln(1−x))) = −1

$$\boldsymbol{{prove}}\:\boldsymbol{{that}} \\ $$$$\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}} {\boldsymbol{{lim}}}\:\frac{\boldsymbol{{arcsin}}\frac{\boldsymbol{{x}}}{\sqrt{\mathrm{1}−\boldsymbol{{x}}^{\mathrm{2}} }}}{\boldsymbol{{ln}}\left(\mathrm{1}−\boldsymbol{{x}}\right)}\:=\:−\mathrm{1} \\ $$

Question Number 79998 Answers: 0 Comments: 3

given 3x + 4y+1 = 3(√x) + 2(√y) find the value of (√(x.y))

$$\mathrm{given}\:\mathrm{3x}\:+\:\mathrm{4y}+\mathrm{1}\:=\:\mathrm{3}\sqrt{\mathrm{x}}\:+\:\mathrm{2}\sqrt{\mathrm{y}}\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\sqrt{\mathrm{x}.\mathrm{y}}\: \\ $$

Question Number 79978 Answers: 3 Comments: 0

Given for x,y,z>0: 2^x =3^y =5^z Arrange 2x, 3y, 5z in increasing order.

$${Given}\:{for}\:{x},{y},{z}>\mathrm{0}: \\ $$$$\mathrm{2}^{{x}} =\mathrm{3}^{{y}} =\mathrm{5}^{{z}} \\ $$$${Arrange}\:\mathrm{2}{x},\:\mathrm{3}{y},\:\mathrm{5}{z}\:{in}\:{increasing}\:{order}. \\ $$

Question Number 79974 Answers: 1 Comments: 0

Question Number 80004 Answers: 1 Comments: 2

x and y any integer satisfy equation (x−2004)(x−2006)=2^y the greatest possible value of x+y

$${x}\:{and}\:{y}\:{any}\:{integer}\:{satisfy} \\ $$$${equation}\:\left({x}−\mathrm{2004}\right)\left({x}−\mathrm{2006}\right)=\mathrm{2}^{{y}} \\ $$$${the}\:{greatest}\:{possible}\:{value} \\ $$$${of}\:{x}+{y} \\ $$

Question Number 79969 Answers: 1 Comments: 0

find the general solution for 2sin 3x = sin 2x

$${find}\:{the}\:{general}\:{solution}\:{for}\: \\ $$$$\:\:\mathrm{2sin}\:\mathrm{3}{x}\:=\:\mathrm{sin}\:\mathrm{2}{x} \\ $$

Question Number 79968 Answers: 0 Comments: 3

Find the 50^(th) entry of 3.127356432...

$${Find}\:{the}\:\mathrm{50}^{{th}} \:{entry}\:{of}\:\:\mathrm{3}.\mathrm{127356432}... \\ $$

Question Number 79966 Answers: 1 Comments: 1

Question Number 79950 Answers: 0 Comments: 3

If ∫_a ^b (x^n /(x^n +(16−x)^n )) dx = 6, then

$$\mathrm{If}\:\underset{{a}} {\overset{{b}} {\int}}\:\:\frac{{x}^{{n}} }{{x}^{{n}} +\left(\mathrm{16}−{x}\right)^{{n}} }\:{dx}\:=\:\mathrm{6},\:\mathrm{then}\: \\ $$

Question Number 79932 Answers: 1 Comments: 1

Question Number 79929 Answers: 0 Comments: 0

∫e^(√(sin x)) dx=?

$$\int{e}^{\sqrt{\mathrm{sin}\:{x}}} {dx}=? \\ $$

Question Number 79913 Answers: 0 Comments: 1

Convergence of I=∫_0 ^( ∞) (e^t /(e^(−t) +e^(2t) ∣sint∣))dt

$$\:{Convergence}\:\:{of}\:\:{I}=\int_{\mathrm{0}} ^{\:\infty} \frac{{e}^{{t}} }{{e}^{−{t}} +{e}^{\mathrm{2}{t}} \mid{sint}\mid}{dt} \\ $$

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