Reference no: EM131082284
Midterm 1 Review Worksheet - Math 1A, section 103
1. What is limx→1 x?
2. Can you prove that limx→1 x = 1 using the ε, δ definition of a limit?
3. Find the domain of the function √x + log(3 - x).
4. Find a formula for the inverse of the function f(x) = 23^x. What is the domain of f-1?
5. Evaluate the limit
limx→5 x- - 25/x - 5.
6. Evaluate the limit
limx→5 2x/x - 5.
7. Show that the equation cos(x) = x has at least one positive real solution.
8. Show that limx→0^+ log10(2x) = -∞ using the definition of a limit.
9. We know that limx→10 log10(x) = 1. Given ε > 0 with ε < 1, find δ so that whenever |x - 10| < δ, we can guarantee that |log10(x) - 1| < ε.
10. Valentine's Day Bonus: Is there a function whose graph looks like a heart? Why or why not? Can you find an explicit equation whose graph looks like a heart? (For instance, the graph of x2 + y2 = 1 is a circle, which is getting close.)
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Determine the nodal displacements at the interfaces
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Find a formula for the inverse of the function
: Can you prove that limx→1 x = 1 using the ε, δ definition of a limit? Find the domain of the function √x + log(3 - x). Find a formula for the inverse of the function f(x) = 23^x. What is the domain of f-1
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