3 Recall The Theorem From Calculus That States If F Is A Function That Is Differentiable At A Point A In Its Domain T 1 (31.38 KiB) Viewed 62 times
3 Recall The Theorem From Calculus That States If F Is A Function That Is Differentiable At A Point A In Its Domain T 2 (28.25 KiB) Viewed 62 times
3 Recall The Theorem From Calculus That States If F Is A Function That Is Differentiable At A Point A In Its Domain T 3 (27.57 KiB) Viewed 62 times
3 Recall The Theorem From Calculus That States If F Is A Function That Is Differentiable At A Point A In Its Domain T 4 (22.04 KiB) Viewed 62 times
3. Recall the theorem from Calculus that states: If f is a function that is differentiable at a point a in its domain, then fis continuous at a. Below we have take a proof of this theorem, cut it up into sentence fragments, and mixed up the order. a. Using proof frameworks as guidance, identify what the first and last lines of the proof should be, and explain why. b. Next, identify what the second and second-to-last lines of the proof should be. C. Try to finish arranging the rest of the proof in order, creating a proof that differentiability implies continuity
We can evaluate each of these limits separately to see that: Using limit laws, we simplify this limit to This shows that f(x) is continuous at the value x = a. lim, S(x) = f(a) We can write lim --- S(I) = lim - ((142) = 0) (r – a) + Sta))
We assume that f(r) is a function that is differentiable at a value r = a in the domain of for). Therefore, we have shown that lim (r) = f(a). lim-f(x) = lim - 123f0 (-a) + lim,... (f(a)) I lim, (x) = L. (0) + f(a) We want to show that f(r) is continuous at, so we need to show that the limit lim,..) - )
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