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Question Number 68236    Answers: 0   Comments: 0

Question Number 68235    Answers: 0   Comments: 0

Question Number 68234    Answers: 1   Comments: 5

Question Number 68232    Answers: 0   Comments: 0

Question Number 68222    Answers: 1   Comments: 5

Sketch the shear and moment diagrams of a simply supported beam of 6m.The load on the beam consists of UDL of 15KN/m over the left half of the span.

$${Sketch}\:{the}\:{shear}\:{and}\:{moment}\:{diagrams} \\ $$$${of}\:{a}\:{simply}\:{supported}\:{beam}\:{of}\:\mathrm{6}{m}.{The} \\ $$$${load}\:{on}\:{the}\:{beam}\:{consists}\:{of}\:{UDL}\:{of} \\ $$$$\mathrm{15}{KN}/{m}\:{over}\:{the}\:{left}\:{half}\:{of}\:{the}\:{span}. \\ $$$$ \\ $$

Question Number 68220    Answers: 0   Comments: 0

Let consider (a_n )_n and (u_n )_n two reals sequence defined such as a_0 =1 , ∀ n>1 a_(n+1) =Σ_(p=0) ^n a_p a_(n−p) and Σ_(p=0) ^n a_p u_(n−p) =0 Part1 1)Express ∀ n >1 a_n in terms of n 2) Find the largest domain of convergence of the integer serie {a_n x^n } 3)Determinate ∀ x∈D the sum f(x) of {a_n x^n } 4)Find the radius of convergence of the serie {u_n x^n } 5) Give the relation that between the sum S(x) of the second serie and (x/(f(x))) 6) Can you developp in integer serie g(x)=((πx)/(tan(πx))) Part2 Now do the part 1 but in the order 2)−1)−3)−4)−5)−6)

$$\:\:\:{Let}\:{consider}\:\left({a}_{{n}} \right)_{{n}} \:{and}\:\left({u}_{{n}} \right)_{{n}} \:{two}\:{reals}\:\:{sequence}\:\: \\ $$$${defined}\:{such}\:{as}\:\:\:{a}_{\mathrm{0}} =\mathrm{1}\:,\:\forall\:{n}>\mathrm{1}\:\:{a}_{{n}+\mathrm{1}} =\underset{{p}=\mathrm{0}} {\overset{{n}} {\sum}}{a}_{{p}} {a}_{{n}−{p}} \:\:\:{and}\:\:\underset{{p}=\mathrm{0}} {\overset{{n}} {\sum}}{a}_{{p}} {u}_{{n}−{p}} =\mathrm{0} \\ $$$${Part}\mathrm{1} \\ $$$$\left.\mathrm{1}\right){Express}\:\:\forall\:{n}\:>\mathrm{1}\:\:\:{a}_{{n}} \:{in}\:{terms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{Find}\:{the}\:{largest}\:{domain}\:{of}\:{convergence}\:{of}\:{the}\:{integer}\:{serie}\:\left\{{a}_{{n}} {x}^{{n}} \right\} \\ $$$$\left.\mathrm{3}\right){Determinate}\:\forall\:{x}\in{D}\:{the}\:{sum}\:{f}\left({x}\right)\:{of}\:\left\{{a}_{{n}} {x}^{{n}} \right\} \\ $$$$\left.\mathrm{4}\right){Find}\:{the}\:{radius}\:{of}\:{convergence}\:{of}\:{the}\:{serie}\:\left\{{u}_{{n}} {x}^{{n}} \right\}\: \\ $$$$\left.\mathrm{5}\right)\:{Give}\:{the}\:{relation}\:{that}\:{between}\:{the}\:{sum}\:{S}\left({x}\right)\:{of}\:{the}\:{second}\:{serie}\:{and}\:\frac{{x}}{{f}\left({x}\right)}\: \\ $$$$\left.\mathrm{6}\right)\:{Can}\:{you}\:{developp}\:{in}\:{integer}\:{serie}\:\:{g}\left({x}\right)=\frac{\pi{x}}{{tan}\left(\pi{x}\right)} \\ $$$${Part}\mathrm{2} \\ $$$$\left.{N}\left.{o}\left.{w}\left.\:\left.{d}\left.{o}\:\:{the}\:{part}\:\mathrm{1}\:\:\:{but}\:{in}\:{the}\:{order}\:\:\mathrm{2}\right)−\mathrm{1}\right)−\mathrm{3}\right)−\mathrm{4}\right)−\mathrm{5}\right)−\mathrm{6}\right) \\ $$

Question Number 68219    Answers: 1   Comments: 0

Let consider (a_n )_n and (u_n )_n two reals sequence defined such as a_0 =1 , ∀ n>1 a_(n+1) =Σ_(p=0) ^n a_p a_(n−p) and Σ_(p=0) ^n a_p u_(n−p) =0 Part1 1)Express ∀ n >1 a_n in terms of n 2) Find the largest domain of convergence of the integer serie {a_n x^n } 3)Determinate ∀ x∈D the sum f(x) of {a_n x^n } 4)Find the radius of convergence of the serie {u_n x^n } 5) Give the relation that between the sum S(x) of the second serie and (x/(f(x))) 6) Can you developp in integer serie g(x)=((πx)/(tan(πx))) Part2 Now do the part 1 but in the order 2)−1)−3)−4)−5)−6)

$$\:\:\:{Let}\:{consider}\:\left({a}_{{n}} \right)_{{n}} \:{and}\:\left({u}_{{n}} \right)_{{n}} \:{two}\:{reals}\:\:{sequence}\:\: \\ $$$${defined}\:{such}\:{as}\:\:\:{a}_{\mathrm{0}} =\mathrm{1}\:,\:\forall\:{n}>\mathrm{1}\:\:{a}_{{n}+\mathrm{1}} =\underset{{p}=\mathrm{0}} {\overset{{n}} {\sum}}{a}_{{p}} {a}_{{n}−{p}} \:\:\:{and}\:\:\underset{{p}=\mathrm{0}} {\overset{{n}} {\sum}}{a}_{{p}} {u}_{{n}−{p}} =\mathrm{0} \\ $$$${Part}\mathrm{1} \\ $$$$\left.\mathrm{1}\right){Express}\:\:\forall\:{n}\:>\mathrm{1}\:\:\:{a}_{{n}} \:{in}\:{terms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{Find}\:{the}\:{largest}\:{domain}\:{of}\:{convergence}\:{of}\:{the}\:{integer}\:{serie}\:\left\{{a}_{{n}} {x}^{{n}} \right\} \\ $$$$\left.\mathrm{3}\right){Determinate}\:\forall\:{x}\in{D}\:{the}\:{sum}\:{f}\left({x}\right)\:{of}\:\left\{{a}_{{n}} {x}^{{n}} \right\} \\ $$$$\left.\mathrm{4}\right){Find}\:{the}\:{radius}\:{of}\:{convergence}\:{of}\:{the}\:{serie}\:\left\{{u}_{{n}} {x}^{{n}} \right\}\: \\ $$$$\left.\mathrm{5}\right)\:{Give}\:{the}\:{relation}\:{that}\:{between}\:{the}\:{sum}\:{S}\left({x}\right)\:{of}\:{the}\:{second}\:{serie}\:{and}\:\frac{{x}}{{f}\left({x}\right)}\: \\ $$$$\left.\mathrm{6}\right)\:{Can}\:{you}\:{developp}\:{in}\:{integer}\:{serie}\:\:{g}\left({x}\right)=\frac{\pi{x}}{{tan}\left(\pi{x}\right)} \\ $$$${Part}\mathrm{2} \\ $$$$\left.{N}\left.{o}\left.{w}\left.\:\left.{d}\left.{o}\:\:{the}\:{part}\:\mathrm{1}\:\:\:{but}\:{in}\:{the}\:{order}\:\:\mathrm{2}\right)−\mathrm{1}\right)−\mathrm{3}\right)−\mathrm{4}\right)−\mathrm{5}\right)−\mathrm{6}\right) \\ $$

Question Number 68212    Answers: 3   Comments: 0

Question Number 68210    Answers: 2   Comments: 0

Question Number 68209    Answers: 0   Comments: 0

Question Number 68207    Answers: 1   Comments: 1

solve for x∈C sin x=z (z=a+bi=re^(iθ) )

$${solve}\:{for}\:{x}\in\mathbb{C} \\ $$$$\mathrm{sin}\:{x}={z}\:\:\:\left({z}={a}+{bi}={re}^{{i}\theta} \right) \\ $$

Question Number 68206    Answers: 1   Comments: 0

find S(θ)=Σ_(n=0) ^∞ ((sin^3 (nθ))/(n!))

$${find}\:{S}\left(\theta\right)=\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{{sin}^{\mathrm{3}} \left({n}\theta\right)}{{n}!} \\ $$

Question Number 68203    Answers: 0   Comments: 2

Question Number 68191    Answers: 2   Comments: 0

Question Number 68189    Answers: 0   Comments: 4

Question Number 68188    Answers: 0   Comments: 2

Σ_(n=3) ^∝ 1/n(ln n)^2 is the function converg or diverg ? pleas help me

$$\sum_{{n}=\mathrm{3}} ^{\propto} \:\mathrm{1}/{n}\left({ln}\:{n}\right)^{\mathrm{2}} \:\:\:{is}\:{the}\:{function}\:{converg}\:{or}\:{diverg}\:?\:{pleas}\:{help}\:{me} \\ $$

Question Number 68183    Answers: 0   Comments: 1

Question Number 68178    Answers: 0   Comments: 2

lim_(x→0) (((cosx)^(sin2x) −1)/x^3 )=?

$$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\:\frac{\left({cosx}\right)^{{sin}\mathrm{2}{x}} −\mathrm{1}}{{x}^{\mathrm{3}} }=? \\ $$

Question Number 68171    Answers: 1   Comments: 2

Question Number 68161    Answers: 0   Comments: 7

In my textbook its written: In applying the nth−term test we can see that: Σ_(n=1) ^∞ (−1)^(n+1) diverges because lim_(n→∞) (−1)^(n+1) does not exist. But then why Σ_(n=1) ^∞ (−1)^(n+1) (1/n^2 ) , Σ_(n=1) ^∞ (−1)^(n+1) (1/(ln(n))) converges ?

$${In}\:{my}\:{textbook}\:{its}\:{written}: \\ $$$${In}\:{applying}\:{the}\:{nth}−{term}\:{test}\:{we}\: \\ $$$${can}\:{see}\:{that}: \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} \:{diverges}\:{because}\: \\ $$$${lim}_{{n}\rightarrow\infty} \left(−\mathrm{1}\right)^{{n}+\mathrm{1}} \:{does}\:{not}\:{exist}. \\ $$$${But}\:{then}\:{why}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} \frac{\mathrm{1}}{{n}^{\mathrm{2}} }\:,\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} \frac{\mathrm{1}}{{ln}\left({n}\right)} \\ $$$${converges}\:? \\ $$

Question Number 68151    Answers: 0   Comments: 1

If ∣a∣< 1 and ∣b∣< 1, then the sum of the series 1+(1+a)b+(1+a+a^2 )b^2 +(1+a+a^2 +a^3 )b^3 +... is

$$\mathrm{If}\:\mid{a}\mid<\:\mathrm{1}\:\mathrm{and}\:\mid{b}\mid<\:\mathrm{1},\:\mathrm{then}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{series} \\ $$$$\mathrm{1}+\left(\mathrm{1}+{a}\right){b}+\left(\mathrm{1}+{a}+{a}^{\mathrm{2}} \right){b}^{\mathrm{2}} +\left(\mathrm{1}+{a}+{a}^{\mathrm{2}} +{a}^{\mathrm{3}} \right){b}^{\mathrm{3}} +... \\ $$$$\mathrm{is} \\ $$

Question Number 68150    Answers: 0   Comments: 0

Question Number 68149    Answers: 0   Comments: 2

Explicit f(a)=Σ_(n=1) ^∞ (((−1)^n )/(n(an+1)))

$$\:{Explicit}\:\:\:{f}\left({a}\right)=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}\left({an}+\mathrm{1}\right)}\:\:\:\: \\ $$

Question Number 68145    Answers: 0   Comments: 5

Find the arc length, given the curve x(t) = sin (πt), y(t) = t , 0 ≤ t ≤ 1

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{arc}\:\mathrm{length},\:\mathrm{given}\:\mathrm{the}\:\mathrm{curve} \\ $$$${x}\left({t}\right)\:=\:\mathrm{sin}\:\left(\pi{t}\right),\:\:{y}\left({t}\right)\:=\:{t}\:,\:\:\mathrm{0}\:\leqslant\:{t}\:\leqslant\:\mathrm{1} \\ $$

Question Number 68133    Answers: 2   Comments: 0

solve y′′=y′y

$${solve}\:{y}''={y}'{y} \\ $$

Question Number 68132    Answers: 0   Comments: 3

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