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Question Number 27567    Answers: 0   Comments: 0

f(x)=3x^2 (a)Find the critical number (b)Find the interval on which f increase and decrese (c)Find the local extrem value of f (d)using the 2^(nd) derivative, find local extrem

$$\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{3x}^{\mathrm{2}} \\ $$$$\left(\mathrm{a}\right)\mathrm{Find}\:\mathrm{the}\:\mathrm{critical}\:\mathrm{number} \\ $$$$\left(\mathrm{b}\right)\mathrm{Find}\:\mathrm{the}\:\mathrm{interval}\:\mathrm{on}\:\mathrm{which}\:\mathrm{f} \\ $$$$\mathrm{increase}\:\mathrm{and}\:\mathrm{decrese} \\ $$$$\left(\mathrm{c}\right)\mathrm{Find}\:\mathrm{the}\:\mathrm{local}\:\mathrm{extrem}\:\mathrm{value}\:\mathrm{of}\:\mathrm{f} \\ $$$$\left(\mathrm{d}\right)\mathrm{using}\:\mathrm{the}\:\mathrm{2}^{\mathrm{nd}} \:\mathrm{derivative}, \\ $$$$\mathrm{find}\:\mathrm{local}\:\mathrm{extrem} \\ $$

Question Number 27564    Answers: 0   Comments: 4

Question Number 27563    Answers: 0   Comments: 0

The absolute value of ∫_(10) ^(19) ((cos x)/(1+x^8 )) dx is

$$\mathrm{The}\:\mathrm{absolute}\:\mathrm{value}\:\mathrm{of}\:\underset{\mathrm{10}} {\overset{\mathrm{19}} {\int}}\:\frac{\mathrm{cos}\:{x}}{\mathrm{1}+{x}^{\mathrm{8}} }\:{dx}\:\:\mathrm{is} \\ $$

Question Number 27561    Answers: 0   Comments: 1

a penduum bob is operated by a thread of breadth 100cn and the bob is pulled aside untill the string makes an angle of 60°. calculate (i)the velocity of the bob when the string is vertiv

$${a}\:{penduum}\:{bob}\:{is}\:{operated}\:{by}\:{a}\: \\ $$$${thread}\:{of}\:{breadth}\:\mathrm{100}{cn}\:{and}\:{the} \\ $$$${bob}\:{is}\:{pulled}\:{aside}\:{untill}\:{the}\:{string} \\ $$$${makes}\:{an}\:{angle}\:{of}\:\mathrm{60}°.\:{calculate} \\ $$$$\left({i}\right){the}\:{velocity}\:{of}\:{the}\:{bob}\:{when} \\ $$$${the}\:{string}\:{is}\:{vertiv} \\ $$

Question Number 27559    Answers: 2   Comments: 1

Change in Q#27507 Solve simultaneously: 2(√x)+y=13 x+2(√y)=10

$$\mathrm{Change}\:\mathrm{in}\:\mathrm{Q}#\mathrm{27507} \\ $$$$\mathrm{Solve}\:\mathrm{simultaneously}: \\ $$$$\mathrm{2}\sqrt{\mathrm{x}}+\mathrm{y}=\mathrm{13} \\ $$$$\mathrm{x}+\mathrm{2}\sqrt{\mathrm{y}}=\mathrm{10} \\ $$

Question Number 27547    Answers: 0   Comments: 0

let give A=(_(1 −1) ^(1 1) ) find A^n and e^A .

$${let}\:{give}\:{A}=\left(_{\mathrm{1}\:\:\:\:\:\:\:\:\:−\mathrm{1}} ^{\mathrm{1}\:\:\:\:\:\:\:\:\:\:\mathrm{1}} \right)\:\:\:\:\:{find}\:{A}^{{n}} \:\:\:{and}\:\:{e}^{{A}} \:\:\:. \\ $$

Question Number 27538    Answers: 0   Comments: 0

Question Number 27536    Answers: 0   Comments: 0

m_1 s_1 (x−𝛉)=m_2 s_2 (𝛉−y) ; x=? ;y=? 𝛉=? solve it as an equation....

$$\boldsymbol{\mathrm{m}}_{\mathrm{1}} \boldsymbol{\mathrm{s}}_{\mathrm{1}} \left(\boldsymbol{\mathrm{x}}−\boldsymbol{\theta}\right)=\boldsymbol{\mathrm{m}}_{\mathrm{2}} \boldsymbol{\mathrm{s}}_{\mathrm{2}} \left(\boldsymbol{\theta}−\boldsymbol{\mathrm{y}}\right)\:\:\:;\:\boldsymbol{\mathrm{x}}=?\:;\boldsymbol{\mathrm{y}}=?\:\boldsymbol{\theta}=? \\ $$$$\mathrm{solve}\:\mathrm{it}\:\mathrm{as}\:\mathrm{an}\:\mathrm{equation}.... \\ $$

Question Number 27531    Answers: 0   Comments: 5

(√(1−cos θ/1+cos θ))=?

$$\sqrt{\mathrm{1}−\mathrm{cos}\:\theta/\mathrm{1}+\mathrm{cos}\:\theta}=? \\ $$

Question Number 27530    Answers: 0   Comments: 0

5/6.6/8.7/9.11/13.....asending order

$$\mathrm{5}/\mathrm{6}.\mathrm{6}/\mathrm{8}.\mathrm{7}/\mathrm{9}.\mathrm{11}/\mathrm{13}.....{asending}\:{order} \\ $$

Question Number 27525    Answers: 1   Comments: 1

x=7×4(√(3 ))thenx+1/x=?

$${x}=\mathrm{7}×\mathrm{4}\sqrt{\mathrm{3}\:}{thenx}+\mathrm{1}/{x}=? \\ $$

Question Number 27524    Answers: 1   Comments: 0

If x is real, the maximum value of ((3x^2 +9x+17)/(3x^2 +9x+7)) is

$$\mathrm{If}\:{x}\:\mathrm{is}\:\mathrm{real},\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\frac{\mathrm{3}{x}^{\mathrm{2}} +\mathrm{9}{x}+\mathrm{17}}{\mathrm{3}{x}^{\mathrm{2}} +\mathrm{9}{x}+\mathrm{7}}\:\:\mathrm{is} \\ $$

Question Number 27520    Answers: 0   Comments: 0

Question Number 27539    Answers: 2   Comments: 1

Question Number 27517    Answers: 0   Comments: 0

Question Number 27557    Answers: 0   Comments: 1

proove that π = 3.142

$${proove}\:{that}\:\pi\:=\:\mathrm{3}.\mathrm{142} \\ $$

Question Number 27514    Answers: 1   Comments: 0

The president of a republic wishes to assign the premiership,the vice-premiership,and six other cabinet posts to a selected group of 8,comprising of 6 career diplomats and 2 business men.If none of the business men can be made premier or vice premier,in how many ways can the 8 posts be assigned to the 8 people?

$${The}\:{president}\:{of}\:{a}\:{republic}\:{wishes} \\ $$$${to}\:{assign}\:{the}\:{premiership},{the}\: \\ $$$${vice}-{premiership},{and}\:{six}\:{other} \\ $$$${cabinet}\:{posts}\:{to}\:{a}\:{selected}\:{group} \\ $$$${of}\:\mathrm{8},{comprising}\:{of}\:\mathrm{6}\:{career} \\ $$$${diplomats}\:{and}\:\mathrm{2}\:{business}\:{men}.{If} \\ $$$${none}\:{of}\:{the}\:{business}\:{men}\:{can}\:{be} \\ $$$${made}\:{premier}\:{or}\:{vice}\:{premier},{in} \\ $$$${how}\:{many}\:{ways}\:{can}\:{the}\:\mathrm{8}\:{posts} \\ $$$${be}\:{assigned}\:{to}\:{the}\:\mathrm{8}\:{people}? \\ $$

Question Number 27513    Answers: 1   Comments: 0

Using only the integers 4 to 8, how many even numbers can be formed if each must lie between 4000 and 9000?

$${Using}\:{only}\:{the}\:{integers}\:\mathrm{4}\:{to}\:\mathrm{8}, \\ $$$${how}\:{many}\:{even}\:{numbers}\:{can}\:{be} \\ $$$${formed}\:{if}\:{each}\:{must}\:{lie}\:{between} \\ $$$$\mathrm{4000}\:{and}\:\:\mathrm{9000}? \\ $$$$ \\ $$

Question Number 27555    Answers: 0   Comments: 0

Question Number 27507    Answers: 1   Comments: 4

2(√(x ))+y=9....(1) x+ 2(√y)=3....(2) solve the simultaneous equation

$$\mathrm{2}\sqrt{{x}\:}+{y}=\mathrm{9}....\left(\mathrm{1}\right) \\ $$$${x}+\:\mathrm{2}\sqrt{{y}}=\mathrm{3}....\left(\mathrm{2}\right) \\ $$$$ \\ $$$${solve}\:{the}\:{simultaneous}\:{equation} \\ $$

Question Number 27503    Answers: 1   Comments: 0

If x=cy+bz ,y=az+cx & z=bx+ay prove that(x^2 /(1−a^2 ))=(y^2 /(1−b^2 ))=(z^2 /(1−c^2 )) .

$$\mathrm{If}\:\mathrm{x}=\mathrm{cy}+\mathrm{bz}\:,\mathrm{y}=\mathrm{az}+\mathrm{cx}\:\&\:\mathrm{z}=\mathrm{bx}+\mathrm{ay} \\ $$$$\mathrm{prove}\:\mathrm{that}\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{1}−\mathrm{a}^{\mathrm{2}} }=\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{1}−\mathrm{b}^{\mathrm{2}} }=\frac{\mathrm{z}^{\mathrm{2}} }{\mathrm{1}−\mathrm{c}^{\mathrm{2}} }\:. \\ $$

Question Number 27502    Answers: 0   Comments: 1

find ∫_0 ^(π/2) ((ln(1+xsin^2 t))/(sin^2 t))dt with −1<x<1 .

$${find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{ln}\left(\mathrm{1}+{xsin}^{\mathrm{2}} {t}\right)}{{sin}^{\mathrm{2}} {t}}{dt}\:{with}\:−\mathrm{1}<{x}<\mathrm{1}\:. \\ $$

Question Number 27500    Answers: 0   Comments: 2

find ∫∫_Δ (√(4 −x^2 −y^2 )) dxdy with Δ={(x,y) ∈R^2 / x^2 +y^2 ≤2x}

$${find}\:\int\int_{\Delta} \sqrt{\mathrm{4}\:−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} \:}\:\:{dxdy}\:{with} \\ $$$$\Delta=\left\{\left({x},{y}\right)\:\in\mathbb{R}^{\mathrm{2}} /\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:\leqslant\mathrm{2}{x}\right\} \\ $$

Question Number 27498    Answers: 0   Comments: 0

find S_n = (C_n ^0 )^3 +( C_n ^1 )^3 +....(C_n ^n )^3 .

$${find}\:\:{S}_{{n}} \:=\:\:\left({C}_{{n}} ^{\mathrm{0}} \:\right)^{\mathrm{3}} \:\:+\left(\:{C}_{{n}} ^{\mathrm{1}} \right)^{\mathrm{3}} +....\left({C}_{{n}} ^{{n}} \right)^{\mathrm{3}} \:\:. \\ $$

Question Number 27497    Answers: 0   Comments: 0

let give I_n = n ∫_1 ^(1+(1/n)) f(x^n )dx with f is numerical function integrable on[1,e] .prove that lim_(n−>∝) I_n = ∫_1 ^e ((f(t))/t) dt.

$${let}\:{give}\:{I}_{{n}} =\:{n}\:\int_{\mathrm{1}} ^{\mathrm{1}+\frac{\mathrm{1}}{{n}}} {f}\left({x}^{{n}} \right){dx}\:{with}\:{f}\:{is}\:{numerical} \\ $$$${function}\:{integrable}\:{on}\left[\mathrm{1},{e}\right]\:.{prove}\:{that} \\ $$$${lim}_{{n}−>\propto} \:\:{I}_{{n}} \:=\:\int_{\mathrm{1}} ^{{e}} \:\:\frac{{f}\left({t}\right)}{{t}}\:{dt}. \\ $$

Question Number 27496    Answers: 0   Comments: 0

let give f(x)= ∫_0 ^∝ (1/(√t)) e^(−(1+ix)t) dt calculate f^′ (x) prove that ∃λ∈R/(x+i)^2 (f(x))^2 = λ then find ∫_0 ^∝ e^(−t^2 ) dt .

$${let}\:{give}\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\propto} \:\:\frac{\mathrm{1}}{\sqrt{{t}}}\:{e}^{−\left(\mathrm{1}+{ix}\right){t}} {dt} \\ $$$${calculate}\:{f}^{'} \left({x}\right)\:{prove}\:{that}\:\exists\lambda\in{R}/\left({x}+{i}\right)^{\mathrm{2}} \:\left({f}\left({x}\right)\right)^{\mathrm{2}} =\:\lambda \\ $$$${then}\:{find}\:\:\int_{\mathrm{0}} ^{\propto} \:\:{e}^{−{t}^{\mathrm{2}} } {dt}\:. \\ $$

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