MATH 115 PRACTICE
MIDTERM 1
A) If
f(x) = x B) If
x then f(x) is
continuous at x = -2 C) If a
function f has a limit L at x
= c, and f(c) = L, then the function is
differentiable at x = c.
A) Evaluate
the following limits if they exist: i)
ii)
iii)
iv)
B) At what points is f(x)
not continuous? C) At what points is f(x) not differentiable?
A)
B)
C)
A(t) = 200 e where t represents the time in years after 1968 and A
represents the kg of algae in the lake. A) Is
this model a differentiable function? Explain. B) Use a
graphing calculator to graph this function.
Over what domain is this a reasonable model? C) Approximate
(with the assistance of your graph) the slope of the tangent line when t
= 20 and when t = 40.
D) What
do your answers from part C mean in terms of the algae in Lake Tahoe?
P = -.03x A. Find the additional profit when rentals increase from 25 to 26 units. B. Find the marginal profit when x = 25.
(Any constructive remark will be worth full credit.) |