Using the definition of continuity and the example below(method for solving the question), show that the following function is continuous q(z) = 1/z^3 at z0 ∈ (0, ∞).

Q: Ql) check the continuity of fX) at X=-1, 0,1.23 -1<x<1 x-4 2x-1, 3x-2 2, x=3 f(x) = 1sxs2 25x53 Q2)…

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Q: 2x²y² {** x² + y² 0 (x, y) = (0,0) (x, y) = (0,0) continuity to determine whether the given function…

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Q: True False Suppose f(x) is continuous everywhere. Must f(x) attain an absolute maximum somewhere on…

A: Extreme value theorem states that if f(x) is continuous on closed interval I, then f(x) attains…

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Q: Consider the function f: RR defined by 1 (a) (b) By using definition, explain whether f is…

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Q: Explain the difference between continuity and uniform continuity with the help of graph when…

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Q: f(x) = x-a, x 1

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Q: (a) Consider the boundary-value problem *(1) + 3ä(1) + ex'(1) = 0 where 0 <8 «1, x(0) = 1 and x(1) =…

A: Perturbation technique

Q: I'm having trouble understanding the continuity questions, please see the attached screen shot.

A: We find left and right hand limit at x=0.Left hand limit = 1

Q: If f is differentiable at xo, prove that f (xo + h) – f (xo – h) – f' (x0) - lim h-0 2h

A: Given that: f is differentiable at xo   To prove: limh→0f(x0+h)-f(x0-h)2h=f'(x0)

Q: f(x)= -2x+3 if x>-1 it メニー」 3+ ax2 if xc-1 if xa-I Is the fanciono continuous at x>-1?

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Q: 1. The function(x)=x-1 has a discontinuity, say where and justify the response. Classify the…

A: Given f(x)=x4-1x-1. to check the discontinuity of f(x).

Q: Please show all work:  Is f(x)= x2+3 continuous at x=1? Why or why not? (A rigorous mathematical…

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Q: if x = 0 f (x) = %3D x* sin(-) otherwise

A: In the given question, concept of continuity is applicable. Continuity Continuity for a graph y=fx…

Q: Q\ Use appropriate functions to guarantee that (). x sin if x # 0 h(x) = 0, if x = 0 is continuous…

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Q: Use the definition of continuity to determine if each function is continuous or discontinuous at…

A: Given function:- fx=x-2x≤-1-xx&gt;-1 Condition to continuity at x=alimx→a-fx=limx→a+fx=fa

Q: x' - 27 x² -9 (c) at x = 3 and x = -3

A: First of all to find critical points put the denominator equal to zero. x2 - 9 = 0 x 2 = 9 x = 3, -3…

Q: Suppose fis a real valued function defined on an open interval I and differentiable at every x eI.…

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Q: Determine if g is continuous at x=0 and if g is differentiable at x = 0 if, let g(x) = {x2sin(1/x)…

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Q: For any R > 0, show f(a) is continuous at R when f(a) sqrt (x) is continuous on (0, +infinity) at…

A: Let R&gt;0.  Suppose fx=x is continuous on 0,∞ at R=b To prove that fx is continuous on R Let b&gt;0…