2. Differentiate each function. a. f(x) = e b. g(x) = x + e- c. h...

 

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2. Differentiate each function. a. f(x) = e b. g(x) = x + e- c. h (x) = 2xe2x d. s(t) = 3. Determine the value of f'(0) for each of the following functions. a. f(x) = x + 2x + 3e* 2+ez ex b. f(x) 1-e2t+1 t = -3x c. f(x) = e d. f(x) = ex+1 +ex 7. Determine all points at which the tangent to the curve y = (x + 1)e is horizontal. 8. Use the definition of the derivative to evaluate the following limit: e-1+h h 9. Let f(x) = e-2x lim h0 e a. Determine f'(x), f" (x), f(3) (x), and (4) (x). b. Use part a) to determine a general formula for the nth derivative of f(n) (x). 2. Differentiate each function. a. f(x) = e b. g(x) = x + e- c. h (x) = 2xe2x d. s(t) = 3. Determine the value of f'(0) for each of the following functions. a. f(x) = x + 2x + 3e* 2+ez ex b. f(x) 1-e2t+1 t = -3x c. f(x) = e d. f(x) = ex+1 +ex 7. Determine all points at which the tangent to the curve y = (x + 1)e is horizontal. 8. Use the definition of the derivative to evaluate the following limit: e-1+h h 9. Let f(x) = e-2x lim h0 e a. Determine f'(x), f" (x), f(3) (x), and (4) (x). b. Use part a) to determine a general formula for the nth derivative of f(n) (x).