Math 1A Midterm 1 2005-9-29 11:00-12:30pm.You are allowed 1 sheet of notes. Calculators are not allowed. Each question is worth3 marks, which will only be given for a clear and correct answer.1. Find the domain of the functiong(u) =√u+√2-u.2. Sketch the graph ofy=|x2-2x|.3. Find a formula for the inverse of the functionf(x) = 1 +ex3.4. Sketch the graph of a functionfthat satisfies the conditionslimx→0-f(x) = 1,limx→0+f(x) =-1,limx→1-f(x) = 1,limx→1+f(x) =-1, f(2) = 1.5. Evaluate the limitlimx→1x3-1x2-16. How close to 2 do we have to takexso that 5x+ 3 is within a distance of 0.01 from13?7. Find the numbers at whichfis discontinuous, wherefis defined byf(x) =x2ifx≤1,f(x) = 1/xif 1< x <3,f(x) = 1/2 +√x-3 ifx≥3.8. What islimx→-∞(3x+ 1)(4x+ 1)(x+ 1)(2x+ 1)9. A curve has equationy=f(x). Write an expression for the slope of the secant line
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