Limits question

maths toppers answer

Not sure why my previous answer was deleted...

If you substitute , then gives , so the limit is equal in value to

Since , we can write

Because is continuous at all , we can pass the limit to the argument of the exponential function. That is,

so that the limit we're interested in is equal to

For all natural numbers , we have

so

and this makes the overall limit take on a value of

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step-by-step explanation:

the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).