Question 1: Let u(x, t) be a solution of the problem Ut Uxx = = 0 u(0, t) = u(π, t) = 0 on 0≤t≤T u(x, 0) = sin² x, on 0≤x≤7. - in Qr = {(x, t): 0 < x < , 0 < t < T} Prove that 0 ≤ u(x, t) ≤ etsin x in QT.

Q: Ⓒ Prove that tan' (2)=1; In Inltiz i-iz

A: Since you have uploaded multiple questions, according to our guidelines we have solved first…

Q: Find Domain and Range Sove all points without leavin ℗ x + y² + Z 2 X+ 4+=+/-5 +2Z 3 Sin(x+3y) +2…

A: Domain is the set of points where function is defined. And range is set of images of function.

Q: Which of the following equations is FALSE? * O tan t = tan (t + 2m) where t n/2 + kTI O tan 2t = tan…

A: tant+2π=tant+tan2π1-tant·tan2π    ∵tanx+y=tanx+tany1-tanx tany=tant+01-tant·0=tant Therefore…

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A: As per the guidelines I need to answer only one question at a time. Here all the questions are…

Q: prove that 01a| = 0 => a=o @ 1-al-lal @lak b ⇒-b<a<b @la-bla lal-lb/

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Q: Let u = u(x, t), x, t ≤ R. Solve Ut + 5ux + u = 0 u(x, 1) = = COS X

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Q: Let (w, x, y, z) = wxy + x² tan z and a = (1, -2,3,4). Then w(a): .₂(a) = -6 -2 8 60 -8 1-1 2 , (a)…

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Q: is homeomorphic to R, where f (x) = tan¬1 x. 2'2 1) Check

A: Given: The function is fx=tan-1x To check: The map (-π2,π2)→R is a homeomorphic.

Q: (LO16) Find all of the zeros of f (x) = x³ – 4x² + 2x + 4. A) x = 2, x = 1 ± i C) x = 2,x = 1+ V3 B)…

A: If you like the solution then please give it a thumbs up.. The Answer is:       x=2,x=1±3 So, Option…

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Q: . The average value of f(x)=√(4-x^2) on [-2, 2] is 1/2 True False The function f(x) * f(x) = x² + 1…

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Q: +1²y=y² If the function u = ln (2¹+2²4 - v² ) then a Su rou + you is

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Q: 4) Find ôw/ ôr if w= x=r-s, y= cos(r + s), z = sin(r + s) at the point (r,s)= (1,–1) Ans. 12

A: Find partial derivative using chain rule then put values of x ,y,z in obtained expression then put…

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A: Given:- we are provided with three functions y,z and v where y=sin(x)z=cos(x)v=y+x=sin(x)+xNow, we…

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A: The quadratic equation, y=ax2+bx+c can be expressed in the vertex form as y=a(x-h)2+k, where, the…

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Q: Prove that, cosh-'x = In |x + vx² – 1 for x 2 1 -기/

A: This question is based on Cosine hyperbola.

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Q: 1. Let r = Vx2 + y² + z² and suppose f'(r) = df /dr exists. Prove that V{(r) = L("),

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