I Calculus Spring 2003 MA113:10-12 Russell Brown Review for test 1 Below are a selection of problems to help prepare you for exam 1. In addition to these problems, you should understand all of the (non-starred) homework problems. Describe how to transform the graph of f (x) = x2 into the graph of g(x) = x2 + 2x + 2. If f and g are odd functions, determine if the following functions are odd or even: f g, f + g and f g. If f (x) is even and f (x) = x3 for x 0, sketch the graph of f . Find the limits, or explain why they do not exist. 1. lim 2. 3. 4. 5. 6. 7. x2 2 x2 x2 + 2 x2 + 4 lim 2 x2 x 4 x2 4x + 4 lim x2 x2 4 x2 + 2 lim x2 (x |x| 2)2 lim x2 x |x| lim x0+ x |x| lim x0 x
State the squeeze theorem. Use the squeeze theorem to nd the limit:
x0
lim x4 cos(1/x2 ).
State the denition of continuity. Find c so that f (x) = is continuous everywhere. State the intermediate value theorem. Use the the intermediate value theorem to show f (x) = x3 + State the denition of derivative. 1 + x2 has a root. x+1 x&g...