Pre Calc
Limits & Continuity
Derivatives
Applying Derivatives
Definite Integrals
100
What is an increment?
The net changes when a particle moves from one point to another.
100
Find f(2) for f(x)= 2x^3 - 5x^2 + 4
f(2)= 0
100
What is the correct way to say the notation dy/dx out loud?
"dy dx" or "the derivative of y with respect to x"
100
What is another name for absolute (global) maximum and minimum values?
Absolute Extrema
100
When does a definite integral exist? (hint: what must a function be in order to be integrable)
The function must be continuous.
200
What is the equation for slope?
(y2-y1)/(x2-x1) or rise/run
200
Find the limit as x approaches -2 for (x-6)^(2/3)
The limit is 4
200
What are 4 ways in which a derivative may fail to exist? (aka when is a function not differentiable?)
corners, cusps, vertical tangents, discontinuities
200
Find the extreme values of the function on the interval & where the occur: f(x)= (1/x) + lnx, x is greater than or equal to 0.5 and less than or equal to 4.
maximum value: (1/4)+ln4 at x=4 minimum value: 1 at x=1 local maximum: (1/2, 2-ln2)
200
Find the average value of y= (x)^1/2 over the interval [0,4]
4/3
300
What is the inverse function of the function f(x)= -2x + 4 ?
-(1/2)x + 2
300
Find an end behaviour model for f(x)= (2x^5 + x^4 -x^2 +1)/(3x^2 - 5x + 7)
(2/3)x^3
300
Find the derivative of: f(x)= (x^2)/(1-x^3)
dy/dx= (x^4+2x)/(1-x^3)^2
300
You are designing a rectangular poster to contain 50 sq. inches of printing with a 4 in. margin at the top and bottom and a 2 in. margin at each side. What overall dimensions will minimize amount of paper used?
18 in. high x 9 in. wide
300
Find the average value of (cosx)^1/2 on the interval [-1,1]
Approx. 0.914
400
Is f(x)= x + 1 an odd or even function?
Neither!
400
Find the limit as x approaches infinity for sin(1/x)
The limit as x approaches infinity is 0.
400
What is the relationship between speed and velocity algebraically?
Speed is the absolute value of velocity. Speed= |v(t)|= |ds/dt|
400
The diameter of a tree was 10 in. During the following year, the circumference increased 2 in. About how much did the tree's diameter increase? The tree's cross section area?
Diameter: (2/pi), approx. 0.6366 in. Cross Section Area: about 10 in.
400
Find the total area between the curve and x-axis. y= 4-x, x is greater than or equal to 0 and less than or equal to 6.
10
500
Sarah invests $1000 in an account that earns 5.25% interest compounded annually. How long will it take her to reach $2500?
approx. 17. 9 years, or 17 years and 11 months
500
Find the points of discontinuity of the function and identify which type of discontinuity it is. f(x)= e^(1/x)
x=0, infinite discontinuity
500
Find dy/dx. x^2 = tany
2xcos^2y
500
y= f(x)= (10)/(1+x^2) If dx/dt= 3 cm/sec, find dy/dt at a point when x=-2
24/5 cm./sec
500
Region R is in the first quadrant enclosed by the x-axis and the graph of the function y= 4x - x^3. Compute the LRAM approximation.
3.75
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