# Functions, Limits & Continuity

1. Find the doubling time of an investment earning 8% interest if interest is compounded continuously.

2. Find the limit of f(x) = (7x+7)/(4x+4) as x approaching positive infinity and negative infinity.

3. Find the slope of the function's graph at the given point, then find an equation for the line tangent to the graph there.

h(t)=t^3, (2,8)

4. Find the limit of f(x) as x approaches c from the right and find the limit of f(x) as x approaches c from the left for the given function and value of c:

f(x)=(x+8) X (|x=2|)/(x=2), c=-2

5. Find an equation for the line tangent to y= -1-4x^2 at (-2,-17)

6. Find the limit by substitution of the following the limit as x approaches 5pie/6 of x sinx

7. For the given function f(x) and the numbers L, x sub 0, Epsilon > 0, find an open interval about x sub 0 on which the inequality |f(x) - L| < Epsilon holds. Then give a value for delta > 0 such that for all x satisfying o<|x-x sub 0|<delta the inequality |f(x)-L|< Epsilon holds.

f(x)= the square root of 22-x, L=2, x sub zero = 18, and Epsilon = .1

**The terminology on this makes my brain hurt, can you also put this question in simpler terms when you answer it so I can understand similar problems like this in the future?**

8. Find the limit as x approaches 1 from the right of the function 1/(x-1).

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#### Solution Summary

The solution examines functions, limits and continuity.