# 4. (a) Assume a function h is differentiable at some point to. Is it true that... 4. (a) Assume a function h is differentiable at some point to. Is it true that h is continuous on some open-neighbourhood of xo? Provide either a proof or a counterexample. (b) Let f be twice differentiable on R and assume that f" is continuous. Show that for all x ER S(x) = S(0) + s°C)x + [ (x - 1))"(dt. (C) Deduce that for any twice continuously differentiable function f on R and any positive x > 0, x € R, there exists some c € (0, 2) such that 2.r - 2t .22 -f"(t) dt  ##### Add Answer of: 4. (a) Assume a function h is differentiable at some point to. Is it true that...
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• ### 5. (This question shows an alternative definition for the term differentiable, one that is useful when... 5. (This question shows an alternative definition for the term differentiable, one that is useful when you study advanced calculus (in R" instead of R).) Let f: R+R and a ER. Prove that f is differentiable at a if and only if there exists a function L:RR which is continuous at a and satisfies f(x) - f(a) = L(x)(x - a) for all x ER Suggestion: If f is differentiable at a, try to define the L function separately at...

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