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A: intermediate value theorem: if the function  is continuous on and if  and  then the function has a…

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Q: 2. Proof that fis differentiable at x, thenf is continuos at xo By using f(x) – f(x.) = a(r) + B(r)

A: Here we use basic definition of continuous function.

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Q: 9. Solve Au = 0 in the exterior {r > a} with the boundary condition u = 1 + 3 sin 0 on r = a and the…

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Q: garded as a subset of R. 9.E. y ing theargme ang ), prove that the interval J = { (x, y) : 0 < x <…

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Q: . Use Taylor's neries, to prove that ein z tan (x+ h)3tan" % + (h sin z). sin 3z sin 2z + (h sin zj…

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Q: Let R = [0, 1] × [0, 1] . Estimate ſfr 6(x + y) dA by computing two different Riemann sums, %3D

A: Given, R=0,1×0,1 and ∫∫R6x+ydA let us assume that fx,y=6x,y. Here, we required to calculate Riemann…

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Q: Q5. Usung Maclaurin's thcorem expand, 5tanx as þar as +he term containing x". QC. Prove that , sinx…

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Q: J uore program Use a soft groping of ality aith motrix copobilities to'find the eligenualves the…

A: For any matrix, A , the eigen values are calculated by solving the equation, det(A-λI)=0 . Here , I…

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