1. Find the limits if it exist. (a) lim cos 2t tcostsin t (b) lim h0...

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1. Find the limits if it exist. (a) lim cos 2t tcostsin t (b) lim h0 (2+ h) - 8 h (c) limx20 2020 [1 + sin (2020x)]. x 0 2. Find the first-order derivative of f(x)=sin() 3. Use the Intermediate Value Theorem to show that f(x) = x +2x - 4 has a root in (1, 2). (Optional: Then use Newton's Method to find the root to five decimal places.) 4. Prove that f(x) = x - sin x is an increasing function. 5. Find the global maximum and minimum values of f(x) = e* 2x on [0, 1]. - 1. Find the limits if it exist. (a) lim cos 2t tcostsin t (b) lim h0 (2+ h) - 8 h (c) limx20 2020 [1 + sin (2020x)]. x 0 2. Find the first-order derivative of f(x)=sin() 3. Use the Intermediate Value Theorem to show that f(x) = x +2x - 4 has a root in (1, 2). (Optional: Then use Newton's Method to find the root to five decimal places.) 4. Prove that f(x) = x - sin x is an increasing function. 5. Find the global maximum and minimum values of f(x) = e* 2x on [0, 1]. -