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Math 1100 Practice Exam 1. Are the following functions? (a) State the denition of a function. (b) 0 = x2 + y2 4y + 1 (c) 0 = yx4 + x2 + 2 2. For the following prolbems you will discuss the continunity of the function. (a) State the 3 criterion for a function f (x) to be continous at a point c. In addition state what it means for a function f (x) to have a nonremovable discontinutity at a point. What does it mean for a function to have a removable discontinunity at a point. (b) Where is the function f (x) = xx2 24 continous on the real line. Where are it's discontinunities? What types of discontinunities does this function have (justify your answer). (c) Show that limx!0 jxj does not exist. (to get full points calculate the upper and lower limits) Is this function continous? ( (d) Is the function f (x) = x + 1 ifx 0 continous at x=0? x ifx < 0 3. State the limit detion of derritive of a function f (x) 4. Use the limit denition of derritive from section 2.1 to nd the derritive of the following functions (a) Find the derritive of f (x) = x1 (b) Find the derritive of f (x) = 9998876654 (c) Find the derritive of f (x) = x2 5. Find the derritive of the following functions. (a) f (x) = x(x + 2)2 + x 21 3 +5x2 x 10 (b) g(x) = xx47+6 x3 9x 8 1 6. Suppose that a wight is dropped from a clip 400 feet high and it's height function is given by h(t) = 16t2 +400. At what times does the object hit the ground? With what velocity, and acceleration does the object hit the ground? 7. Suppose that you sell math text books to students for 120 dollars a book, and you buy these text books for 15 dollars a textbook from a club which has a one time membership fee of 500 dollars. What is your cost, revenue, and prot functions. Now nd marginal cost, marginal revenue, and marginal prot. Comments: you will be tested on sections 1.4, 1.5, 1.6, 2.1, 2.2, and 2.3. This test is a good simulation for some of the problems that you will see on the exam aswell as concepts that will be on the exam. I will also put one or two problems from the selected solutions to homework on the exam, and in addition you should review your homeworks (make sure your answers are correct). You also review your notes and the text book. 2