- #1
gabby989062
- 20
- 0
Homework Statement
Hello, I have some Calculus problems from my latest homework.
1.
The limit as x approaches 3 of sqrt(x+1)
The back of the book says 2. But I'm wondering why it exists as sqrt(3+1) = sqrt(4) = +-2, so since there are 2 values for this, should the limit even exist?
2.
The limit of delta x as it approaches 0 of (sqrt(x + delta x) - sqrt(x)) divided by delta x.
In similar problems, I factored the denominator out of the numerator so I could cancel the denominator so it could never go to 0. But I don't know how to do this for stuff in the radical sign. The book gives no example of this type of problem.
3. Graphical, numerical, and analytical
a. use a graphing utility to graph the function and estimate the limit.
b. use a table to reinforce your conclusion
c. find the limit by analytic methods.
limit as x approaches 1 from the negative side of 2/(x^2-1).
Since it's from the negative side, I just plugged 0.9999999 for x into my calculator, so the bottom approached 0 as a negative number. So I concluded that it is negative infinity. But isn't plugging in 0.999999 considered the numerical method? How do I do this analytically?