Unformatted text preview: (a) Suppose that f and g are two functions both continuous on the interval [ a, b ], and such that f ( a ) = g ( b ) = p and f ( b ) = g ( a ) = q , with p 6 = q . Sketch typical graphs of two such functions. Then apply the intermediate value theorem to the function h ( x ) = f ( x )-g ( x ) to show that f ( c ) = g ( c ) for some point c ∈ ( a, b ). (b) Find an example of a function f such that: i. The line y = 2 is a horizontal asymptote of the curve y = f ( x ) and ii. the curve intersects the line y = 2 at an inﬁnite number of points. 1...
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- Winter '08
- Continuous function, Calculus Workshop, PAPER ASSIGNMENTS folder