Math 2950- Review Sheet for 1st Exam
Math 241WW- Review Sheet for 2nd Exam
The second midterm is Tuesday Oct. 21 and will cover Chapter 14.1-14.7. As a good first step make sure you understand all the quiz problems and homework problems and examples worked out in class.
Definitions/Formulas to know:
• Level curve, level surface, contour map.
• Limit.
• Function continuous at a point, continuous on D.
• Partial derivatives.
• Clairaut’s Theorem on equality of mixed partial derivatives.
• Tangent plane to a surface.
• Linear approximation aka tangent plane approximation of a function.
• Total differential.
• Chain rule.
• Directional derivatives
• Gradient, normal line to surface
• Local and absolute maxima, minima.
• Critical point, saddle point.
• Closed and bounded set.
• Extreme value theorem (p.928).
Skills you should have:
• Determine and sketch domains of functions (p.866 #11-20)
• Sketch graphs of some basic functions. (p.866 #21-29)
• Understand contour maps and match contour maps with sketch of functions. (p.868 #29-46, 55-60)
• Show limit does not exist by finding curves approaching the point with different values.
• Use the squeeze theorem or polar coordinates to show a limit exists.
• Determine points where a function is continuous (p.877 #29-38).
• Calculate partial derivatives, use implicit differentiation. (p.889 #15-41, 45-48)
• Given a function f(x,y), find the tangent plane at a point. Find the linear approximation at a point. (p. 899 #1-6, 11-16)
• Find the total differential. (p. 900 #25-30)
• Apply the chain rule. (p. 907 #1-15, 21-26)
• Implicit differentiation via the chain rule. (p. 908 #27-34)
• Calculate directional derivatives and gradients. (p.920 #4-20) Understand the significance of the gradient.
• Find the maximum rate of change of a function and the direction it occurs. (p. 920 #21-26, 36, 38)
• Find equation of tangent plane and normal line to level surfaces. (p. 921 #39-44)
• Apply the procedure in Section 14.8 to find critical points and determine, using the second derivative test, if they are local maxima or local minima. (p. 931 #5-18)
• Apply the extreme value theorem to find absolute maxima and minima of a continuous function on a closed bounded set. (p. 931 #29-36, 39-43).
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