Others — Page 1 — Tinkutara Math Forum

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A=∫_0 ^(2α) 2pcos^(−1) (d/(2p))×((Ldβ)/(cos β)) =∫_0 ^(2α) 2(((tan β+(√(tan^2 β−4(atan β−H))))/2))cos^(−1) (L/(l(((tan β+(√(tan^2 β−4(atan β−H))))/2))))×L(dβ/(cos β)) =∫_0 ^(2α) 2(((tan β+(√(tan^2 β−4(atan β−H))))/2))cos^(−1) (((H−(((tan β+(√(tan^2 β−4(atan β−H))))/2))^2 )/(sin β))/( (√((a−b−htan α)^2 +R^2 −h^2 tan^2 (α/2)+((((a−b)tan β)/(1+tan αtan β)))^2 ))(((tan β+(√(tan^2 β−4(atan β−H))))/2))))×(((H−(((tan β+(√(tan^2 β−4(atan β−H))))/2))^2 )/(sin β)))(dβ/(cos β)) =∫_0 ^(2α) 2(((tan β+(√(tan^2 β−4(atan β−H))))/2))cos^(−1) (((H−(((tan β+(√(tan^2 β−4(atan β−H))))/2))^2 )/(sin β))/( (√((a−b−((((a−b)tan β)/(1+tan αtan β)))tan α)^2 +R^2 −((((a−b)tan β)/(1+tan αtan β)))^2 tan^2 (α/2)+((((a−b)tan β)/(1+tan αtan β)))^2 ))(((tan β+(√(tan^2 β−4(atan β−H))))/2))))×(((H−(((tan β+(√(tan^2 β−4(atan β−H))))/2))^2 )/(sin β)))(dβ/(cos β)) =∫_0 ^(2tan^(−1) (R/(a−b))) 2(((tan β+(√(tan^2 β−4(atan β−H))))/2))cos^(−1) ((((H−(((tan β+(√(tan^2 β−4(atan β−H))))/2))^2 )/(sin β))/( (√((a−b−((((a−b)tan β)/(1+((R/(a−b)))tan β)))×((R/(a−b))))^2 +R^2 −((((a−b)tan β)/(1+(R/(a−b))tan β)))^2 tan^2 ((tan^(−1) ((R/(a−b))))/2)+((((a−b)tan β)/(1+((R/(a−b)))tan β)))^2 ))(((tan β+(√(tan^2 β−4(atan β−H))))/2)))))×(((H−(((tan β+(√(tan^2 β−4(atan β−H))))/2))^2 )/(sin β)))(dβ/(cos β))

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Question 229519

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Question 229505

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Question 229496

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Solve y^((2)) (t)−y(t)=cos(t)e^t

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∫(1/( (√(ax^3 +bx^2 +cx+d))))dx

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App has been updated to resolve notification issues faced by new users on latest android version

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Q229401. find C(x,y) of r suppose the bottom left corner of the rectangle is origin

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x^2 +y^2 +z^2 =25 a^2 +b^2 +c^2 =16 ax+by+cz=20 ((a+b+c)/(x+y+z))=?

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An ellipse with semi-axes a and b lies on an inclined plane and can roll down it without slipping. What is the maximum angle of inclination of the plane at which the ellipse can remain in a stable equilibrium?

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All dashed lines are Inversion with respect to the red circle with radius R. Point O is the Inversion Center. Radius of larger Green Circle = r_1 Radius of Inversed Larger Green Circle = R OB × OB′ = R^2 OB × (R + 2R) = R^2 OB = (R^2 /(3R)) = (R/3) r_1 = ((R − (R/3))/2) = (R/3) Radius of Larger Pink Circle = r_2 Radius of Inversed Larger Pink Circle = a (R + a)^2 = (R − a)^2 + R^2 2aR = −2aR + R^2 ⇒ a = (R/4) OC × OC′ = R^2 OC × (R + 2((R/4))) = R^2 OC = (R^2 /((3R)/2)) = ((2R)/3) r_2 = ((R − ((2R)/3))/2) = (R/6)

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Question 229221

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y=x−(x^2 /2)+(x^3 /3)−(x^4 /4)+...∞ prove (dy/dx)=(1/(x+1))

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parabola y=x^2 a chord moves such s way that it cuts an area (4/3) with the parabola every time find the locus of the midpoint of the chord

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h^2 +k^2 =r^2 (((25)/2)−h)^2 +k^2 =((5/2)+r)^2 (13−h)^2 +(6−k)^2 =r^2 solve for h,k &r

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If you need to post hyperlinks please add a plain text message and paste link there. Code should automatically create a clickable link

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Question 229085

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Question 229070

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Question 229012

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2∫_0 ^(2tan^(−1) (R/((a−R)(√2)))) (√((1(sin α+(√2))tan α)^2 +(1+(√(1^2 −((√2)tan α(5−2)−1)^2 ))cot (((((3π)/4)−sin^(−1) ((√(1^2 −((√2)tan α(5−1)−1)^2 ))/((5−1)(√2))))/2))−(1−(√(1^2 −((√2)tan α(5−1)−1)^2 )))tan ((π/4)−sin^(−1) ((√(1^2 −((√2)tan α(5−1)−1)^2 ))/((5−1)(√2)))))^2 ))×((5(√2))/((cos α)^2 ))dα

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∫_0 ^(tan^(−1) (((2×1(5(√2)−1))/( 5(√2)(5(√2)−2))))) 2(1+(√(1^2 −((5−1)(√2)tan α−1)^2 ))cot (((((3π)/4)−sin^(−1) (((√(1^2 −((5−1)(√2)tan α−1)^2 ))/( (√2)(5−1)))))/2))−(1−(√(1^2 −((5−1)(√2)tan α−1)^2 )))tan ((π/4)−sin^(−1) (((√(1^2 −((5−1)(√2)tan α−1)^2 ))/( (√2)(5−1))))))((5(√2))/(cos^2 α))dα

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Question 228907

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mu=mvcos φ+MVcos θ..i mvsin φ=MVsin θ..ii (1/2)mu^2 =(1/2)mv^2 +(1/2)MV^2 ...iii u,sin θ,m&M are given.find V,v,φ in terms of given things

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Question 228898

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Question 228896

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Question 228855

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Question 228845

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Question 228788

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Question 228768

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Solve partial differential equation 1. k∙((∂ )/∂x) (∂u/∂x)=(∂u/∂t) , 0<x<L , k>0 , t>0 condition u(0,t)=0 , u(L,t)=0 , t>0 u(x,0)=f(x) , 0<x<L 2. (∂r/∂t)=−α∇^2 r condition r(t,0)=h(t) , 0≤t≤L r(0,t)=r(L,t)=0 , t>0

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Question 228697

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Question 228687

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Question 228684

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Let f(x)=(1/2)π−(1/2)x (mod 2π) for all ∣x∣<2π g(x)=Σ_(k=1) ^∞ ((sin(kx))/k) , for all ∣x∣<2π f(x) and g(x) are identically equal function. 1)Even though f and g are equivalent functions why is the derivative of f well-defined while the derivative of g is not ?? 2) is it true that continuity implies differentiable?? Does differentiability imply continuity??

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Question 228659

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Question 228632

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Question 228618

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undergraduate level problem 1. For any monotonically decreasing sequence {a_k }_(k=1) ^m , show that Σ a_m converges if and only if Σ 2^m a_2^m converge. additionally prove that Σ (1/m^s ) converges and only if s>1. 2.Provide a counterexample for which lim_(n→∞) ∫_E f_n (x)dx= ∫_E lim_(n→∞) f_n (x)dx does not hold. 3. show that Weiestrass function f(x)=Σ_(k=0) ^∞ a^k cos(b^k πx) , 1+((3π)/2)<ab is continuous function at x∈[−M,M] 4. prove f(x) is not differentiable x∈R 5. 1_Q = { (( 1 , x∈Q)),((0 , x∈R/Q)) :} is Riemann integrable ?? Source:Introduction to Analysis SNU (Seoul National University of Kor)major text books did you try it?? :) and these are the legandary math Bibles of SNU

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Q226485

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f(f(x))=x^2 −x+1 f(0)=?

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Analysis I show that lim_(n→∞) (1+(z/n))^n =e^z . uniformly convergence for all 𝛜>0 there exist N∈N whenever z∈E such that N<n ⇒ ∣f_n (z)−f(z)∣<𝛜 ∼Weiestrass M-test∼ Suppose that {f_n ^ }_(n=1) ^∞ is a sequence real valued function defined on a set E,and that there is a sequence of non-negetive number M_n satisfying the conditions for all n∈N , ∣f_n ^ (x)∣<M_n on a set E more specifically, ∣Σ_(h=1) ^∞ f_h (x)∣<Σ_(h=1) ^∞ ∣f_h (x)∣<Σ_(h=1) ^∞ M_h (Σ_(h=1) ^∞ M_h is convergent to an any arbitrary const.) then, Σ_(h=1) ^∞ f_h (x) is uniformly convergence. Analysis II prove f(t)= (2/π)−(4/π)∙Σ_(k=1) ^∞ ((cos(2kt))/(4k^2 −1)) uniformly convervence where t∈[−π,π] Analysis III Show that g(x)=Π^∞ _(n=1) (1−((x/(nπ)))^2 ) uniformly convergence. where x∈[−M,M]