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).

Solution Summary

The solution examines functions, limits and continuity.

Determine whether or not each of the following limits exists. Discuss also the continuity of each of the following functions at given point c. Give reasons to your answers.
Please see the attached file for the fully formatted problems.

Detailed step by step calculations of the attached questions regarding complex variables including the domain, limits and continuity of complex functions.
1. For each of the functions below, describe the domain of definition, and write each function in the form f(z) = u(x,y) +iv(x,y)
1) f(z) = z^2 / (z+z)
2) f(z) = z^3
3

Taking the continuity of h(x) as given in#30026,#30028
by using any of the functional limits and continuity theorems prove that the finite sum g_m (x)=sum sign(oo top n=0 bottom) of 1/2^n h(2^n x) is continous on R

Please help with the following mathematics-related problem.
Let f(z) be analytic in a region G and setphi(z,w) = (f(w)-f(z))/(w-z) for w,z E G w does not equal z. Let z0 Ye G. Show that lim (z,w)-->(z0,z0) phi(z,w) =f'(z0).
Complex Variables. See attached file for full problem description

1. Solve log₆x-3=0
2. A business owner is comparing the costs of purchasing inventory and the profit from the sale of the product. The relationship proves to be linear. Which type of variation will describe the data?
Direct as nth power joint regress
Inverse direct
3. Solve x²-25<0
4. What is the

Please help with the following problem. Provide step by step calculations.
True or false:
a)lim x--->2- f(x) = 3
b)limx--->2+ f(x) =0
c)lim x--->2- f(x) = lim x--->2+ f(x)
d) lim x--->2 f(x) exists
e) lim x--->4 f(x) exists
f) lim x--->4 f(x) = f(4)
g) f is continuous at x=4
h) f is continuous at x=0
i) lim x--->3

1. Take the function f(X) = (X-1)/X
a. What does this function equal when X = 0, X = 1, and X =2 ?
b. How about when X =100, X = 1000, and X = 10,000?
c. Describe in words what a graph of this function would look like.
d. What would you say the limit of this function is as X approaches infinity? You can use logic or

Determine where the function f(x)= x + [|x^2|] - [|x|] is continuous.
I think the correct answer is that the function is continuous for its domain but not defined at x=0.
Can someone explain this problem to me and help me understand the greatest integer and absolute value functions?
keywords: continuity