Compute the following limit assuming lim f(x) = 8. State the limit law(s) used to justify the computation. X-3 lim [5f(x)] x-3 d Use the table below to find x [5g(x) + 4x] dx X f'(x) g'(x) 1 3 1 252 345 2 3 4 5 4 5 2 1 3 4 |x=1 d (5g(x) + 4x)=(Type an integer or a decimal.) dx X=1 a. Find the derivative function f' for the following function f. b. Find an equation of the line tangent to the graph off at (a,f(a)) for the given value of a. 2 f(x) = 4x - 12x+5, a = 1 a. The derivative function f'(x) = Assume lim f(x) = 16 and lim g(x) = 4. Compute the following limit and state the limit laws used to justify the computation. X-3 x3 lim (f(x) - g(x)) X-3 lim (f(x) - g(x)) = (Simplify your answer.) x3 Find the following limit or state that it does not exist. 2 x - 100 X x-10 lim x-10 Simplify the given limit. 2 x - 100 x-10 lim x-10 = lim x-10 (Simplify your answer.) Find the following limit or state that it does not exist. 7 7 2+h 2 h lim h0 Simplify the given limit. 7 7 2+h 2 h lim h0 = lim h0 (Simplify your answer.) a. Use limits to find the derivative function f' for the function f. b. Evaluate f'(a) for the given values of a. 3 f(s) = 5s +2s; a = -3, -1 a. f'(s) = a. Find the derivative function f' for the following function f. b. Find an equation of the line tangent to the graph off at (a,f(a)) for the given value of a. 2 f(x) = 4x12x+5, a = 1 a. The derivative function f'(x) = Find the derivative of f(x)=x*. f'(x) = | Find the derivative of the following function. f(x) = -2x f'(x) = Find the derivative of the following function. f(x) = 8x + 2x f'(x) =