Graphical limits
On the graph of g(x), find the limit as x approaches 1 from the right (1+).
What is... limit = 0?
Evaluate [look at board] via direct substitution.
What is 1?
Find the limit at infinity for the polynomial: [look at board].
What is -infinity?
For f(x) = x^2 - 3x, find the value of f(a+h) - f(a)
What is 2ah+h^2-3h?
If the graph of f(x) is increasing at c=x, the sign of f'(c) must be this.
What is positive?
Find the value of g(3) where a removable discontinuity occurs.
Evaluate [look at board] by expanding the numerator.
What is 4/3?
For the piecewise function g(x), find the limit as x -> 2.
What is DNE?
Find f(a+h)-f(a) for f(x) = sqrt(x).
What is sqrt(a+h) - sqrt(a)?
Find the average rate of change for V(t)= (10-0.5t)^2 on [0,4].
What is -9 m^3/min?
Determine the limit of g(x) as x -> infinity
Solve [look at board].
What is 0?
Find the limit at infinity for the rational function: [look at board].
What is 3?
Use the limit definition to find f'(-12) for f(x) = 7x+4.
What is 7?
Explain why g'(0) does not exist on the graph in Problem 9.
What is a "sharp turn" or "corner"?
The value of g(1).
What is... x = 3?
Determine the limit: [look at board]
What is -infinity?
According to the definition, a function is continuous at x = c if the limit equals this. *HINT* Refer to the 3 conditions!
What is the function value, f(c)?
Find f'(2) for f(x) 3x^2 +9x-5
What is 21?
Provide the units for the rate of change of volume V (in m^3) over time t (in minutes).
What is cubic meters per minute (m^3/min)?
Identify the x-values where the graph has a removable discontinuity.
What is... x = -1, 1, 3?
Solve [look at board] using the conjugate method.
What is 5/2?
Evaluate the limit as x -> -infinity for [look at board].
What is +infinity?
Find f'(1) for f(x) = -4x^2 +2x-3
What is -6?
Does the tank drain at a constant rate? Justify using rates from [0,4] and [4,8].
What is, "No, the average rates are different"?