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MAT 1221 Survey of Calculus Exam 1 Info
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Exam 1 Date and Time: 4/24 Thursday (5:30- 6:50 pm) Section 1.5, , B.1, B.2 Total Points: 80 points
Exam 1 This exam is extremely important. The second exam is on 5/15. The last day to withdraw is 5/9. So this exam gives us the critical info for you to make a sound decision.
Calculators Absolutely no share of calculators. Bring extra batteries, extra calculators. It is your responsibility to bring a workable calculator. NO cell phone or PDA Your instructor/TA will not answer any question related to calculators.
Expectations Use equal signs Simplify your answers. Provide units. Check and Double Check your solutions. Show the “formula” steps. For word problems in B.2, show all 5 steps
Steps for Word Problems 1. Draw a diagram 2. Define the variables 3. Write down all the information in terms of the variables defined 4. Set up a relation between the variables 5. Use differentiation to find the related rate. Formally answer the question.
Slope of the tangent line Slope of the tangent line at a point on a graph can be approximated by a limiting process. (The same apply to other rate of change problems in physical sciences.)
x Tangent Lines To define the tangent line at x=1, we pick a point close by. We can find the secant line of the two points We can move the point closer and closer to x=1. y 1
Rate of Change y = distance dropped (ft) x = time (s) Find the average speed from x=2 to x=3.
Derivative For a function y=f(x), the derivative at x is a function f’ defined by if it exists. (f is differentiable at x f’(x)=The slope of the tangent line at x)
Limit Laws Summary
Multiply by conjugate
Constant Function Rule If, then Why?
Constant Multiple Rule If, then where is a constant
Power Rule If, then (n can be any real number)
Sum and Difference Rule If, then
Product Rule If, then
Quotient Rule If then
Extended Power Rule
Important Concepts Left-hand limits and right-hand limits exists if f is continuous at a point if f is differentiable at a point if exists
Important Skills Evaluate limits by using algebra. Finding derivatives using limits and formula. Understand and able to perform implicit differentiation. Solve word problems.
Remarks Portion of points are designated for simplifying the answers. Units are required for some answers.