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# f07HW6 - ii Show that f is discontinuous at x n = 0 iii...

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MAT 125A Homework 6 M.Fukuda Please submit your answers at the discussion session on November 29th Thursday. You can use theorems in the lecuture unless otherwise stated. When you do so write those statements clearly instead of quoting them by numbers. 1. Use the definition of derivative to calculate the derivatives of the following functions at the indicated points. i) f ( x ) = x 2 cos x at x = 0. ii) g ( x ) = 3 x +4 2 x 1 at x = 1. 2. Let f be f ( x ) = x 2 x Q 0 x R \ Q . i) Show that f is continuous at x = 0. ii) Show that
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Unformatted text preview: ii) Show that f is discontinuous at x n = 0. iii) Show that f is di²erentiable at x = 0. 3. Prove (iii) of Corollary 29.7. 4. Let f : R → R and di²erentiable on R . Suppose sup x ∈ R {| f ′ ( x ) |} = M < 1. Take s ∈ R and de±ne a sequence s n +1 = f ( s n ) n = 0 , 1 , 2 , . . .. Then, show that { s n } is a Cauchy sequence. Hint: Show ±rst that | s n +1 − s n | ≤ M | s n − s n − 1 | . 1...
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