The city wants to build a new stretch of highway to link an

The city wants to build a new stretch of highway to link an existing bridge with an interchange, located 8 km to the south of the bridge. There is 5-km-wide stretch of marshland adjacent to the bridge that must be crossed (see the picture below). Given that the highway costs $19 million per kilometer to build over the marsh and only $7 million per kilometer to build over dry land, how far to the east of the bridge should the highway be when it crosses out the marsh (assume that the city wants to minimize the cost)? Find lim Find .

Solution

This is an overview of the idea of a limit in mathematics. For specific uses of a limit, see limit of a sequence and limit of a function. In mathematics, the concept of a \"limit\" is used to describe the value that a function or sequence \"approaches\" as the input or index approaches some value.[1] Limits are essential to calculus (and mathematical analysis in general) and are used to define continuity, derivatives, and integrals. The concept of a limit of a sequence is further generalized to the concept of a limit of a topological net, and is closely related to limit and direct limit in category theory. In formulas, limit is usually abbreviated as lim as in lim(an) = a, and the fact of approaching a limit is represented by the right arrow (?) as in an ? a.