# 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.

some questions on limit and continuity

1. Create a function, f(x), and pick a point c such that the limit of f(x) as x approaches c from the right and the limit of f(x) as x approaches c from the left are equal and the function is continuous. Show the values of the limits and explain why the function is continuous. The explanation should be intuitive as well as mathematical. Include a graph of the function.

2. Create a function, f(x), and pick a point c such that the limit of f(x) as x approaches c from the right and the limit of f(x) as x approaches c from the left are equal, the function is defined at the point c but the function is not continuous at c. Show the values of the limits and explain why the function is not continuous. The explanation should be intuitive as well as mathematical. Include a graph of the function.

3. Create a function, f(x), and pick a point c such that the limit of f(x) as x approaches c from the right and the limit of f(x) as x approaches c from the left are equal, the function is not defined at the point c and the function is not continuous at c. Show the values of the limits and explain why the function is not continuous. The explanation should be intuitive as well as mathematical. Include a graph of the function.

4. Create a function, f(x), and pick a point c such that the limit of f(x) as x approaches c from the right and the limit of f(x) as x approaches c from the left are not equal in value. Explain why the limit of f(x) as x approaches c does not exist and why the function cannot be continuous.

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