Suppose f′(x) is continuous with f(9)=8 and f'(9)=-12. Calculate the following limit or determine that it does not exist.

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A: Given that        f(x) = x2 - 5x + 12 Here we have to find f'(x) by using the delta definition of…

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A: Please refer the attached image for complete solution.

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Q: Compute the limit as x goes to 0 of [tan(x) - sin(3x)] / (x^2)

A: limx→0[tan(x)-sin(3x)]x2=[tan(0)-sin(3(0))]02=00

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Q: 5. Use the concept of limits to find derivative of f(z) = (2z + 1)3 at z = -i.

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Q: II) By using the limit definition of derivative, prove the identity J dzf(2)8' (2) = - / da f…

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