Limit Definitions
If a point is undefined, then the limit approaching that point is also undefined. True or False?
False
The rate of change is the change in x over the change in y. True or false?
False
How many times does a tangent line intersect a curve?
One
What is the derivative of any constant?
0
What is the limit used to find derivatives?
The limit of [ F(x + h) - F(x) ] / h as h approaches 0.
What is the instantaneous rate of change of x0.5 at x = 4?
1/4
The slope of the tangent line at a point on a curve is the same as the instantaneous rate of change at that point. True or False?
True
What is the derivative of x3?
3x2
What is the derivative of x2 using the limit approach? (I will be checking people's whiteboards to make sure they used the limit approach!)
2x
What theorem guarantees the instantaneous rate of change is equal to the average rate of change at a value c, assuming the function is continuous and differentiable?
Mean Value Theorem
What is the equation for the tangent line of x3 at x=3?
T(x) = 27(x - 3) + 27
Write a formula for the derivative of un
(nun-1)ú
What is the derivative of 5x3 using the limit approach? (I will be checking people's whiteboards to make sure they used the limit approach!)
15x2
What is the average rate of change of x2 over the interval [0,3]?
3
What is an equation for the tangent line of x1/3 at x=8?
T(x) = 1/12(x - 8) + 2
What is the derivative of (u/a)?
(úa - uá) / a2