5. Let f(x) = ²+1 when x > 0, and f(x) = = - cos x when x < 0. Does f admit an extension f on R, which is continuous at x = 0? Explain why. x-1 6. Let f, g be two continuous functions on R so that limx→0- ƒ(x) = 1, g(0) = 10, limx→1 g(x) = 2. Decide the value of limx→0 9 ○ f(x) if it exists.

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A: Given : fx = exex+sinx+x2

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A: Since you have asked multiple question and have not specified any question in particular, I will…

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A: To prove the given limit

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A: f(x) be a differentiable function with the propertiesf(1)=8 and limx→∞f(x)=5.

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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…