3. Use the definition to show that the function f(x) = is continuous on the interval [c, o0), where c> 0. %3D

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A: According to the guidelines I am answering only first question.

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A: I will use radius of power series and alternating series test.

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A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve the first three ...

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A: Properties of the indices and surds  (ax)y=axy axay=ax-y If ax=ay⇒x=y log a+log b=log (ab)

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Q: ди para t> 0, 0<x<3 ди (0,t) = (3,t)= 0 ди u(x,0) = 3x +1

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A: The given question is related with polynomials. Given that,                  fx = x3 + ax2 + bx + c ...

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Q: Prove (kindly provide reason/s) that for any real numbers m and n, (-m) + (- n) = - (m + n )

A: Let us solve the above problem in the next step.

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A: simplifying the differential equation into linear form.

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Q: (2) I Let (x, y) E R X R. Consider the following functions from R? to R? r((x, y)) = (-y, x) and s(x...

A: We have to find the order of r and s. Here rx, y=-y, x and sx, y=x, -y where x, y∈ℝ. First, we have ...