Question and Answers Forum

AllQuestion and Answers: Page 1210

Question Number 93950 Answers: 2 Comments: 0

Let ∗ be the binary operation on N given by a∗b=L.C.M. of a and b. Find (i) 5∗7 , 20∗16 (ii) is ∗ communitative? (iii) is ∗ associative? (iv)Find the identity of ∗ in N (v) which elements of N are invertible for the operation ∗?

$${Let}\:\ast\:{be}\:{the}\:{binary}\:{operation}\:{on}\:\mathrm{N} \\ $$$${given}\:{by}\:\mathrm{a}\ast\mathrm{b}=\mathrm{L}.\mathrm{C}.\mathrm{M}.\:{of}\:\boldsymbol{{a}}\:{and}\:\boldsymbol{\mathrm{b}}.\:\mathrm{F}{ind} \\ $$$$\left(\mathrm{i}\right)\:\mathrm{5}\ast\mathrm{7}\:,\:\:\mathrm{20}\ast\mathrm{16}\:\:\:\left(\mathrm{ii}\right)\:\mathrm{is}\:\ast\:{communitative}? \\ $$$$\left(\mathrm{iii}\right)\:\mathrm{is}\:\ast\:{associative}? \\ $$$$\left(\mathrm{iv}\right)\mathrm{F}{ind}\:{the}\:{identity}\:{of}\:\ast\:{in}\:\boldsymbol{\mathrm{N}} \\ $$$$\left(\mathrm{v}\right)\:\mathrm{which}\:\mathrm{elements}\:\mathrm{of}\:\boldsymbol{\mathrm{N}}\:{are}\:{invertible} \\ $$$$\:\:\:\:\:\:\:{for}\:{the}\:{operation}\:\ast? \\ $$

Question Number 93941 Answers: 0 Comments: 2

Show that the function f(x)=e^(x ) is of Reimann within x∈[1;5] hence calculate ∫_1 ^5 e^x dx

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{e}^{\mathrm{x}\:} \:\mathrm{is}\:\mathrm{of}\:\mathrm{Reimann}\:\mathrm{within} \\ $$$$\mathrm{x}\in\left[\mathrm{1};\mathrm{5}\right]\:\mathrm{hence}\:\mathrm{calculate}\:\int_{\mathrm{1}} ^{\mathrm{5}} \mathrm{e}^{\mathrm{x}} \mathrm{dx} \\ $$

Question Number 93940 Answers: 0 Comments: 2

Question Number 93937 Answers: 0 Comments: 5

∫(1/(√(tan x)))dx=?

$$\int\frac{\mathrm{1}}{\sqrt{\mathrm{tan}\:{x}}}{dx}=? \\ $$

Question Number 93933 Answers: 0 Comments: 5

Let ∗′ be the binary operation on the set {1,2,3,4,5} defined by a∗′b=H.C.Fof a and b. Is the operation ∗′ same as the operation ∗ defined above? justify your answer.

$${Let}\:\ast'\:{be}\:{the}\:{binary}\:{operation}\:{on}\:{the}\:{set}\:\left\{\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5}\right\}\:{defined}\:{by}\:\mathrm{a}\ast'\mathrm{b}=\mathrm{H}.\mathrm{C}.\mathrm{F}{of}\:{a}\:{and}\:{b}.\: \\ $$$${Is}\:{the}\:{operation}\:\ast'\:{same}\:{as}\:{the}\:{operation}\:\ast\:{defined}\:{above}?\:{justify}\:{your}\:{answer}. \\ $$

Question Number 93916 Answers: 0 Comments: 2

Question Number 93911 Answers: 0 Comments: 8

number of digit of a number 2^(2016) and 5^(2016) is?

$$\mathrm{number}\:\mathrm{of}\:\mathrm{digit}\:\mathrm{of}\:\mathrm{a}\:\mathrm{number}\: \\ $$$$\mathrm{2}^{\mathrm{2016}} \:\mathrm{and}\:\mathrm{5}^{\mathrm{2016}} \:\mathrm{is}? \\ $$

Question Number 93908 Answers: 0 Comments: 2

calculste lim_(x→0) ∫_x ^(2x) ((arctan(xt))/(t+x))dt

$${calculste}\:\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\:\:\int_{{x}} ^{\mathrm{2}{x}} \:\frac{{arctan}\left({xt}\right)}{{t}+{x}}{dt} \\ $$

Question Number 93907 Answers: 2 Comments: 4

1) calculate A_n =∫_0 ^(π/2) cos^n x dx 2) calculate ∫_(−∞) ^(+∞) (dx/((x^2 −x+1)^n )) n integr natural

$$\left.\mathrm{1}\right)\:{calculate}\:\:{A}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{cos}^{{n}} {x}\:{dx} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{−\infty} ^{+\infty} \:\frac{{dx}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)^{{n}} } \\ $$$${n}\:{integr}\:{natural} \\ $$

Question Number 93906 Answers: 0 Comments: 0

find ∫_0 ^∞ (e^(−cosx) /(x^2 +1))dx

$${find}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−{cosx}} }{{x}^{\mathrm{2}} +\mathrm{1}}{dx} \\ $$

Question Number 93904 Answers: 1 Comments: 0

∫_0 ^∞ (e^(−ax) −e^(−bx) ) dx

$$\underset{\mathrm{0}} {\overset{\infty} {\int}}\:\left({e}^{−{ax}} −{e}^{−{bx}} \right)\:{dx}\: \\ $$

Question Number 93900 Answers: 0 Comments: 0

y′′+2xy= y

$$\mathrm{y}''+\mathrm{2}{xy}=\:\mathrm{y} \\ $$

Question Number 93899 Answers: 0 Comments: 0

find a function f continue on [a,b] wich verify (∫_a ^b f(x)dx)^2 =∫_a ^b f^2 (x)dx

$${find}\:{a}\:{function}\:{f}\:{continue}\:{on}\:\left[{a},{b}\right]\:{wich}\:{verify} \\ $$$$\left(\int_{{a}} ^{{b}} {f}\left({x}\right){dx}\right)^{\mathrm{2}} \:=\int_{{a}} ^{{b}} \:{f}^{\mathrm{2}} \left({x}\right){dx}\: \\ $$

Question Number 93898 Answers: 1 Comments: 1

let f(x)=2(√(3−x)) and g(x) =x^2 −2x +5 1) calculate fog(x) and determine D_(fog) 2) calculate ∫ fog(x)dx 3) calculate ∫ ((f^(−1) (x))/(f(x)))dx and ∫ ((f^(−1) og(x))/(fog(x)))dx

$${let}\:{f}\left({x}\right)=\mathrm{2}\sqrt{\mathrm{3}−{x}}\:{and}\:{g}\left({x}\right)\:={x}^{\mathrm{2}} −\mathrm{2}{x}\:+\mathrm{5} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{fog}\left({x}\right)\:{and}\:{determine}\:{D}_{{fog}} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int\:{fog}\left({x}\right){dx} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int\:\frac{{f}^{−\mathrm{1}} \left({x}\right)}{{f}\left({x}\right)}{dx}\:\:{and}\:\:\int\:\frac{{f}^{−\mathrm{1}} {og}\left({x}\right)}{{fog}\left({x}\right)}{dx} \\ $$

Question Number 93892 Answers: 0 Comments: 3

let a_(n+1) =(√(2+(√a_n ))) a_0 =(√2) find lim_(n→∞) a_(n+1)

$${let} \\ $$$${a}_{{n}+\mathrm{1}} =\sqrt{\mathrm{2}+\sqrt{{a}_{{n}} }}\:\:\:\:\:\:{a}_{\mathrm{0}} =\sqrt{\mathrm{2}} \\ $$$${find}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{a}_{{n}+\mathrm{1}} \\ $$

Question Number 93874 Answers: 1 Comments: 4

find k if the vector (1^ −2,k) in R^3 be a linear combination of the vectors (3,0,2) &(2,−1,−5)

$$\mathrm{find}\:\mathrm{k}\:\mathrm{if}\:\mathrm{the}\:\mathrm{vector}\:\left(\bar {\mathrm{1}}−\mathrm{2},\mathrm{k}\right)\:\mathrm{in}\:\mathbb{R}^{\mathrm{3}} \\ $$$$\mathrm{be}\:\mathrm{a}\:\mathrm{linear}\:\mathrm{combination}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{vectors}\:\left(\mathrm{3},\mathrm{0},\mathrm{2}\right)\:\&\left(\mathrm{2},−\mathrm{1},−\mathrm{5}\right)\: \\ $$

Question Number 93873 Answers: 1 Comments: 1

find ∫_(−∞) ^∞ (dx/((x^2 +2x+4)^3 ))

$${find}\:\int_{−\infty} ^{\infty} \:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{4}\right)^{\mathrm{3}} } \\ $$

Question Number 93869 Answers: 0 Comments: 2

∫ (dx/(1−tan^2 x)) ?

$$\int\:\frac{\mathrm{dx}}{\mathrm{1}−\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}}\:? \\ $$

Question Number 93860 Answers: 0 Comments: 5

Consider the progression (I_n )_(n∈N) where I_n =∫_0 ^1 ((sin(πt))/(t+n))dt 1\ Show that: ∀n≥0, 0≤I_(n+1) ≤I_n and deduce that the series is convergent. 2\ Show that 0≤I_n ≤ln(((n+1)/n)) and deduce the limit the series (I_n )_(n∈N) 3\ Calculate lim_(n→+∞) (nI_n )

$$\mathrm{Consider}\:\mathrm{the}\:\mathrm{progression}\:\left(\mathrm{I}_{\mathrm{n}} \right)_{\mathrm{n}\in\mathbb{N}} \:\mathrm{where}\:\mathrm{I}_{\mathrm{n}} \:=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{sin}\left(\pi\mathrm{t}\right)}{\mathrm{t}+\mathrm{n}}\mathrm{dt} \\ $$$$\mathrm{1}\backslash\:\mathrm{Show}\:\mathrm{that}:\:\forall\mathrm{n}\geqslant\mathrm{0},\:\mathrm{0}\leqslant\mathrm{I}_{\mathrm{n}+\mathrm{1}} \leqslant\mathrm{I}_{\mathrm{n}} \:\mathrm{and}\:\mathrm{deduce}\:\mathrm{that}\:\mathrm{the}\: \\ $$$$\mathrm{series}\:\mathrm{is}\:\mathrm{convergent}. \\ $$$$\mathrm{2}\backslash\:\mathrm{Show}\:\mathrm{that}\:\mathrm{0}\leqslant\mathrm{I}_{\mathrm{n}} \leqslant\mathrm{ln}\left(\frac{\mathrm{n}+\mathrm{1}}{\mathrm{n}}\right)\:\mathrm{and}\:\mathrm{deduce}\:\mathrm{the}\:\mathrm{limit} \\ $$$$\mathrm{the}\:\mathrm{series}\:\left(\mathrm{I}_{\mathrm{n}} \right)_{\mathrm{n}\in\mathbb{N}} \\ $$$$\mathrm{3}\backslash\:\mathrm{Calculate}\:\underset{\mathrm{n}\rightarrow+\infty} {\mathrm{lim}}\left(\mathrm{nI}_{\mathrm{n}} \right) \\ $$

Question Number 93859 Answers: 1 Comments: 0

Σ_(n=1) ^∞ (1/(n(n+1)))

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

Question Number 93855 Answers: 1 Comments: 0

At what point of the parabola y=x^2 will the tangent a\ be parallel to the line y=4x−5 b\ be perpendicular to 2x−6y+5=0 c\ make an angle of 45^° with 3x−y+1=0

$$\mathrm{At}\:\mathrm{what}\:\mathrm{point}\:\mathrm{of}\:\mathrm{the}\:\mathrm{parabola}\:\mathrm{y}=\mathrm{x}^{\mathrm{2}} \\ $$$$\mathrm{will}\:\mathrm{the}\:\mathrm{tangent}\: \\ $$$$\mathrm{a}\backslash\:\mathrm{be}\:\mathrm{parallel}\:\mathrm{to}\:\mathrm{the}\:\mathrm{line}\:\mathrm{y}=\mathrm{4x}−\mathrm{5} \\ $$$$\mathrm{b}\backslash\:\mathrm{be}\:\mathrm{perpendicular}\:\mathrm{to}\:\mathrm{2x}−\mathrm{6y}+\mathrm{5}=\mathrm{0} \\ $$$$\mathrm{c}\backslash\:\mathrm{make}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{45}^{°} \:\mathrm{with}\:\mathrm{3x}−\mathrm{y}+\mathrm{1}=\mathrm{0} \\ $$

Question Number 93853 Answers: 1 Comments: 0

Find the angle at which the parabola y=x^2 cuts through the line 3x−y−2=0

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{angle}\:\mathrm{at}\:\mathrm{which}\:\mathrm{the}\:\mathrm{parabola} \\ $$$$\mathrm{y}=\mathrm{x}^{\mathrm{2}} \:\mathrm{cuts}\:\mathrm{through}\:\mathrm{the}\:\mathrm{line}\:\mathrm{3x}−\mathrm{y}−\mathrm{2}=\mathrm{0} \\ $$

Question Number 93847 Answers: 0 Comments: 2

log _5 (x−2)+log _8 (x−4)= log _6 (x−1)

$$\mathrm{log}\:_{\mathrm{5}} \:\left(\mathrm{x}−\mathrm{2}\right)+\mathrm{log}\:_{\mathrm{8}} \:\left(\mathrm{x}−\mathrm{4}\right)=\:\mathrm{log}\:_{\mathrm{6}} \left(\mathrm{x}−\mathrm{1}\right) \\ $$

Question Number 93844 Answers: 1 Comments: 0

let f(x)=(√x) and g(x)=(√x) find the domain of (f.g)(x) ? help me sir

$${let}\:{f}\left({x}\right)=\sqrt{{x}}\:\:{and}\:{g}\left({x}\right)=\sqrt{{x}}\:{find}\:{the}\:{domain}\:{of}\:\left({f}.{g}\right)\left({x}\right)\:? \\ $$$${help}\:{me}\:{sir} \\ $$

Question Number 93843 Answers: 1 Comments: 0

Use Horner to solve it . (a^2 −5ab−3b^2 ) : (a−b) find the remainder .

$${Use}\:\:{Horner}\:\:{to}\:\:{solve}\:{it}\:. \\ $$$$\:\:\left({a}^{\mathrm{2}} −\mathrm{5}{ab}−\mathrm{3}{b}^{\mathrm{2}} \right)\::\:\left({a}−{b}\right) \\ $$$${find}\:\:{the}\:\:{remainder}\:\:. \\ $$

Question Number 93837 Answers: 0 Comments: 5

Pg 1205 Pg 1206 Pg 1207 Pg 1208 Pg 1209 Pg 1210 Pg 1211 Pg 1212 Pg 1213 Pg 1214

Contact: info@tinkutara.com