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Question Number 32765 Answers: 0 Comments: 0

Question Number 32760 Answers: 1 Comments: 0

if y=3x^(4 ) .find the approximate percentage increase in y when x increase by 2(1/2)%.

$$\mathrm{if}\:{y}=\mathrm{3}{x}^{\mathrm{4}\:} .{find}\:{the}\:{approximate}\:{percentage} \\ $$$${increase}\:{in}\:{y}\:{when}\:{x}\:{increase}\:{by}\:\:\:\mathrm{2}\frac{\mathrm{1}}{\mathrm{2}}\%. \\ $$

Question Number 32688 Answers: 1 Comments: 0

Evaluate 1) ∫_(−1) ^0 (x^2 + x 1) dx 2) ∫_1 ^5 (x −1+ (1/x^2 ))dx

$$\mathrm{Evaluate} \\ $$$$\left.\:\mathrm{1}\right)\:\int_{−\mathrm{1}} ^{\mathrm{0}} \left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{x}\:\mathrm{1}\right)\:\mathrm{dx} \\ $$$$\left.\mathrm{2}\right)\:\int_{\mathrm{1}} ^{\mathrm{5}} \left(\mathrm{x}\:−\mathrm{1}+\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\right)\mathrm{dx} \\ $$$$ \\ $$

Question Number 32792 Answers: 1 Comments: 2

the equation 3x− 5=15 represents a straight line. a) find one point on this line. b)find the coordinates of the points when the line cuts the x−axis and the y−axis c)find the gradient of this line.

$${the}\:{equation}\: \\ $$$$\mathrm{3}{x}−\:\mathrm{5}=\mathrm{15}\:{represents}\:{a}\:{straight}\:{line}. \\ $$$$\left.{a}\right)\:{find}\:{one}\:{point}\:{on}\:{this}\:{line}. \\ $$$$\left.{b}\right){find}\:{the}\:{coordinates}\:{of}\:{the}\:{points}\:{when} \\ $$$${the}\:{line}\:{cuts}\:{the}\:{x}−{axis}\:{and}\:{the}\:{y}−{axis} \\ $$$$\left.{c}\right){find}\:{the}\:{gradient}\:{of}\:{this}\:{line}. \\ $$$$ \\ $$

Question Number 32793 Answers: 1 Comments: 0

Given that the point (−3^ ,2) lies on the line y=2x + c.find the coordinates of the point of intersection of this line and the y−axis

$${Given}\:{that}\:{the}\:{point}\:\left(−\bar {\mathrm{3}},\mathrm{2}\right)\:{lies}\:{on}\:{the} \\ $$$${line}\:\:\:\:{y}=\mathrm{2}{x}\:+\:\mathrm{c}.{find}\:{the}\:{coordinates}\: \\ $$$${of}\:{the}\:{point}\:{of}\:{intersection}\:{of}\:{this}\:{line}\:{and}\:{the}\:{y}−{axis} \\ $$

Question Number 32794 Answers: 1 Comments: 0

given that the point (t^ ,0) lies on the curve y=2x^2 −x. find the value of t.

$${given}\:{that}\:{the}\:{point}\:\left(\bar {{t}},\mathrm{0}\right)\:{lies}\:{on}\:{the} \\ $$$${curve}\:{y}=\mathrm{2}{x}^{\mathrm{2}} −{x}.\:{find}\:{the}\:{value}\:{of}\:{t}. \\ $$

Question Number 32707 Answers: 1 Comments: 0

1)find u the value of u if Σ_(n=1) ^4 2u.2^(n−1) =64 2) find k if Σ_(n=1) ^∞ k.((1/3))^(n−1) =(2/3)

$$\left.\mathrm{1}\right)\mathrm{find}\:\mathrm{u}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{u}\:\mathrm{if} \\ $$$$\sum_{\mathrm{n}=\mathrm{1}} ^{\mathrm{4}} \mathrm{2}{u}.\mathrm{2}^{{n}−\mathrm{1}} =\mathrm{64} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{find}\:\mathrm{k}\:\mathrm{if}\: \\ $$$$\:\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \mathrm{k}.\left(\frac{\mathrm{1}}{\mathrm{3}}\right)^{\mathrm{n}−\mathrm{1}} =\frac{\mathrm{2}}{\mathrm{3}} \\ $$

Question Number 32396 Answers: 1 Comments: 0

roots 2x×x+x+3

$${roots} \\ $$$$\mathrm{2}{x}×\boldsymbol{{x}}+\boldsymbol{{x}}+\mathrm{3} \\ $$

Question Number 32220 Answers: 0 Comments: 3

Find the value of a for which the equation sin^4 x+asin^2 x+1=0 will have a solution.

$${Find}\:{the}\:{value}\:{of}\:{a}\:{for}\:{which}\:{the}\:{equation} \\ $$$$\mathrm{sin}\:^{\mathrm{4}} {x}+{a}\mathrm{sin}\:^{\mathrm{2}} {x}+\mathrm{1}=\mathrm{0}\:{will}\:{have}\:{a}\:{solution}. \\ $$

Question Number 32209 Answers: 1 Comments: 0

a boy rides his bicycle 10km at an average speed of 12 km/hr. and again travel 12 km at an average speed of 10 km/hr his average speed for dntire trip is approximately a)10.4km/hr b)10.8km/hr c)12.2km/hr d)11.2km/hr

$${a}\:{boy}\:{rides}\:{his}\:{bicycle}\:\mathrm{10}{km}\:{at}\:{an}\:{average}\:{speed}\:{of}\:\mathrm{12}\:{km}/{hr}. \\ $$$${and}\:{again}\:{travel}\:\mathrm{12}\:{km}\:{at}\:{an}\:{average}\:{speed}\:{of}\:\mathrm{10}\:{km}/{hr} \\ $$$${his}\:{average}\:{speed}\:{for}\:{dntire}\:{trip}\:{is}\:{approximately} \\ $$$$\left.{a}\right)\mathrm{10}.\mathrm{4}{km}/{hr} \\ $$$$\left.{b}\right)\mathrm{10}.\mathrm{8}{km}/{hr} \\ $$$$\left.{c}\right)\mathrm{12}.\mathrm{2}{km}/{hr} \\ $$$$\left.{d}\right)\mathrm{11}.\mathrm{2}{km}/{hr} \\ $$

Question Number 32028 Answers: 1 Comments: 0

If ((2z_1 )/(3z_2 )) is a purely imaginary number, then find the value of ∣((z_1 −z_2 )/(z_1 +z_2 ))∣ .

$${If}\:\frac{\mathrm{2}{z}_{\mathrm{1}} }{\mathrm{3}{z}_{\mathrm{2}} }\:{is}\:{a}\:{purely}\:{imaginary}\:{number}, \\ $$$${then}\:{find}\:{the}\:{value}\:{of}\:\mid\frac{{z}_{\mathrm{1}} −{z}_{\mathrm{2}} }{{z}_{\mathrm{1}} +{z}_{\mathrm{2}} }\mid\:. \\ $$

Question Number 31946 Answers: 0 Comments: 0

Calculate Σ_(j≤k≤i) (−1)^k ((i),(k) ) ((k),(j) )

$$\mathrm{Calculate}\:\underset{{j}\leqslant{k}\leqslant{i}} {\Sigma}\:\left(−\mathrm{1}\right)^{{k}} \begin{pmatrix}{{i}}\\{{k}}\end{pmatrix}\begin{pmatrix}{{k}}\\{{j}}\end{pmatrix} \\ $$

Question Number 31743 Answers: 1 Comments: 0

Find the value of : Σ_(i=0) ^∞ Σ_(j=0) ^∞ Σ_(k=0) ^∞ (1/(3^i 3^j 3^k )). case 1: i≠j≠k. case 2: i<j<k.

$$\:{Find}\:{the}\:{value}\:{of}\::\:\underset{{i}=\mathrm{0}} {\overset{\infty} {\sum}}\underset{{j}=\mathrm{0}} {\overset{\infty} {\sum}}\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\mathrm{3}^{{i}} \mathrm{3}^{{j}} \mathrm{3}^{{k}} }. \\ $$$${case}\:\mathrm{1}:\:{i}\neq{j}\neq{k}. \\ $$$${case}\:\mathrm{2}:\:{i}<{j}<{k}. \\ $$

Question Number 31674 Answers: 0 Comments: 0

let p_n (x) polinom Maclaurin for function f(x)=e^x . How many degree minimal polinom (n) so ∣e^x −p_n (x)∣≤ 10^(−2) , for −1≤x≤1?

$$\mathrm{let}\:\mathrm{p}_{{n}} \left({x}\right)\:\mathrm{polinom}\:\mathrm{Maclaurin}\:\mathrm{for} \\ $$$$\mathrm{function}\:{f}\left({x}\right)={e}^{{x}} .\:\mathrm{How}\:\mathrm{many} \\ $$$$\mathrm{degree}\:\mathrm{minimal}\:\mathrm{polinom}\:\left({n}\right)\:\mathrm{so} \\ $$$$\mid{e}^{{x}} −\mathrm{p}_{{n}} \left({x}\right)\mid\leqslant\:\mathrm{10}^{−\mathrm{2}} ,\:\mathrm{for}\:−\mathrm{1}\leqslant{x}\leqslant\mathrm{1}? \\ $$

Question Number 31671 Answers: 0 Comments: 0

let f diferensiabel on continues x=a and f(a)≠ 0 lim_(n→∞) [((f(a+(1/n)))/(f(a)))]^n value is ?

$$\mathrm{let}\:{f}\:\mathrm{diferensiabel}\:\mathrm{on}\:\mathrm{continues} \\ $$$${x}={a}\:\mathrm{and}\:{f}\left({a}\right)\neq\:\mathrm{0} \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left[\frac{{f}\left({a}+\frac{\mathrm{1}}{{n}}\right)}{{f}\left({a}\right)}\right]^{{n}} \\ $$$$\mathrm{value}\:\mathrm{is}\:? \\ $$

Question Number 31583 Answers: 0 Comments: 0

how to read this ⟨x⟩. p

$${how}\:{to}\:{read}\:{this}\:\langle{x}\rangle.\:{p} \\ $$

Question Number 31569 Answers: 1 Comments: 0

(a,(1/a)),(b,(1/b)),(c,(1/c)),(d,(1/d)) are four distinct points on a circle of radius is 4 units then abcd is equal to ?

$$\left({a},\frac{\mathrm{1}}{{a}}\right),\left({b},\frac{\mathrm{1}}{{b}}\right),\left({c},\frac{\mathrm{1}}{{c}}\right),\left({d},\frac{\mathrm{1}}{{d}}\right)\:{are}\:{four} \\ $$$${distinct}\:{points}\:{on}\:{a}\:{circle}\:{of}\:{radius} \\ $$$${is}\:\mathrm{4}\:{units}\:{then}\:{abcd}\:{is}\:{equal}\:{to}\:? \\ $$

Question Number 31543 Answers: 0 Comments: 2

∫((x^3 +x+1)/(x^2 +1)) dx

$$\int\frac{{x}^{\mathrm{3}} +{x}+\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}\:{dx} \\ $$$$ \\ $$$$ \\ $$

Question Number 31502 Answers: 0 Comments: 3

find f(x)= ∫_0 ^1 ln(1+xt^2 )dt with x>0. 2) give thevalue of ∫_0 ^1 ln(1+t^2 )dt and ∫_0 ^1 ln(1+2t^2 )dt.

$${find}\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{xt}^{\mathrm{2}} \right){dt}\:\:{with}\:{x}>\mathrm{0}. \\ $$$$\left.\mathrm{2}\right)\:{give}\:{thevalue}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{ln}\left(\mathrm{1}+{t}^{\mathrm{2}} \right){dt}\:{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{ln}\left(\mathrm{1}+\mathrm{2}{t}^{\mathrm{2}} \right){dt}. \\ $$

Question Number 31369 Answers: 0 Comments: 0

Question Number 31340 Answers: 0 Comments: 0

Deduce the power series of sin^2 x. Hence show that if x is small then (sin^2 x − x^2 cosx)/x^4 =(1/6) − (x^2 /(360))

$${Deduce}\:{the}\:{power}\:{series}\:{of}\:{sin}^{\mathrm{2}} {x}. \\ $$$${Hence}\:{show}\:{that}\:{if}\:{x}\:{is}\:{small}\:{then} \\ $$$$\left({sin}^{\mathrm{2}} {x}\:−\:{x}^{\mathrm{2}} {cosx}\right)/{x}^{\mathrm{4}} =\frac{\mathrm{1}}{\mathrm{6}}\:−\:\frac{{x}^{\mathrm{2}} }{\mathrm{360}} \\ $$

Question Number 31314 Answers: 0 Comments: 0

let x={(1/n)}_(n=1) ^∞ and y={(1/(n+1))}_(n=1) ^∞ be a sequence of real numbers and l_(2 ) ={x=(x_1 ,x_2 ,x_3 ,...):Σ_(n=1) ^∞ ∣xi∣^2 <∞} a linear space. (1) verify that x and y are in l_2 . (2) compute the inner product of x and y on l_2 please help me solve this question.

$${let}\:{x}=\left\{\frac{\mathrm{1}}{{n}}\right\}_{{n}=\mathrm{1}} ^{\infty} {and}\:{y}=\left\{\frac{\mathrm{1}}{{n}+\mathrm{1}}\right\}_{{n}=\mathrm{1}} ^{\infty} {be}\: \\ $$$${a}\:{sequence}\:{of}\:{real}\:{numbers}\:{and} \\ $$$${l}_{\mathrm{2}\:} =\left\{{x}=\left({x}_{\mathrm{1}} ,{x}_{\mathrm{2}} ,{x}_{\mathrm{3}} ,...\right):\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\mid{xi}\mid^{\mathrm{2}} <\infty\right\} \\ $$$${a}\:{linear}\:{space}.\: \\ $$$$\left(\mathrm{1}\right)\:{verify}\:{that}\:{x}\:{and}\:{y}\:{are}\:{in}\:{l}_{\mathrm{2}} . \\ $$$$\left(\mathrm{2}\right)\:{compute}\:{the}\:{inner}\:{product}\:{of}\:{x}\: \\ $$$${and}\:{y}\:{on}\:{l}_{\mathrm{2}} \\ $$$$\boldsymbol{{please}}\:\boldsymbol{{help}}\:\boldsymbol{{me}}\:\boldsymbol{{solve}}\:\boldsymbol{{this}}\: \\ $$$$\boldsymbol{{que}}{s}\boldsymbol{{tion}}. \\ $$

Question Number 31306 Answers: 1 Comments: 0

Complete the square in y^2 +8y+9k and hence find the value of k that makes it a perfect square.

$$\mathrm{Complete}\:\mathrm{the}\:\mathrm{square}\:\mathrm{in}\:\mathrm{y}^{\mathrm{2}} \:+\mathrm{8y}+\mathrm{9k}\:\mathrm{and}\:\mathrm{hence}\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{k}\:\mathrm{that}\:\mathrm{makes}\:\mathrm{it}\:\mathrm{a}\:\mathrm{perfect}\:\mathrm{square}. \\ $$

Question Number 31281 Answers: 1 Comments: 0

find three nos in AP whose product is equal to the square of their sum.

$${find}\:{three}\:{nos}\:{in}\:{AP}\:{whose}\:{product} \\ $$$${is}\:{equal}\:{to}\:{the}\:{square}\:{of}\:{their}\:{sum}. \\ $$

Question Number 31085 Answers: 0 Comments: 1

calculate ∫∫_(x^2 +y^2 −2x≤0) xdxdy.

$${calculate}\:\int\int_{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:−\mathrm{2}{x}\leqslant\mathrm{0}} {xdxdy}. \\ $$

Question Number 31017 Answers: 1 Comments: 0

solve (√(1+tan^2 x/1+cot^2 x= tanx))

$${solve}\:\sqrt{\mathrm{1}+{tan}^{\mathrm{2}} {x}/\mathrm{1}+{cot}^{\mathrm{2}} {x}=\:\:\:{tanx}} \\ $$

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