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1. Find the derivative of the following functions: *=1/142 y = 1 y=arctan Itz 1 2. Prove that the function f(x) = 0. is differentiable at I = 0 and find f'(0). 3. Suppose that f is continuous at I = 0. Prove that g(z) = xf(x) is differentiable at 0. 4. Suppose that the function f is defined on a, b] and that it is both left differentiable and right differentiable at CE (a,b). Prove that f is continuous at I = C. 5. Suppose that f and g are defined on R and that f is differentiable at I = q, but g is not. Prove or disprove: f + g is not differentiable at I = q. 6. Let f be a function defined on R and suppose there exists M > 0 such that, for any I. y R, If(x) - f(y)| < M/I - Prove that f is a constant function. 7. Suppose that f is differentiable at I = q, and let n € N. Find the limit I 8. Find the derivative of f(x) = log, 2.

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