MAT 21B Lecture Notes - Lecture 12: Royal Institute Of Technology, Product Rule, Pythagorean Theorem

General Math Terms A product B. digit C. numeral D. compass E. equation F. formula G. negative H. sum I. mean J. statistics K. positive L. percent M. straight-edge N. squareroot O. quotient P. prime numbers Q. difference R. addend S. minuend T. divisor Greater than zero: plus. A number being added to another number. A mathematical sequence whose verb is equal (=). The result of addition. The number doing the dividing in a division problem. An instrument used to construct straight lines. A mathematical expression of a natural law. The result of multiplication. The number from which another number is being subtracted. Any non-negative numeral less than ten. Less than zero: minus. An instrument used to construct circles and arcs of circles. A number that produces another number (it's square) when multiplied by itself. The result of subtraction. A symbol or name of a number. The average: the sum of the elements divided by the number of elements. The result of division. Parts per hundred: hundredths. Natural numbers greater than one that have no other factors except one and themselves. Set of numerical data. Geometry A. chord B. diameter C. radius D. perimeter E. cylinder F. surface area G. right angle H. square I. Hypotenuse J. obtuse angle K. vertex L point M. ray N. bisect O arc P. hexagon Q. pentagon R. polygon S. perpendicular T. rectangle U. rhombus V. triangle W. circumference X cube Y pyramid Z. sphere A six-sided polygon. The common end point of the sides of an angle. An angle measuring more than 90 degree. A long, round object with flat, circular ends. An angle of 90 degree. The side of a right triangle opposite the right angle. The total area of all the surfaces of an object. To multiply a number by itself. A location, the place where two lines cross or intersect. A closed geometric figure made up of three or more line segments. The perimeter of a circle: the distance around a circle. A shape having the same dimensions of length, height, and width. A half-line with a designated end point which extends in only one direction without stopping. A figure having a polygon base and triangular sides which meet in a point at the top. Divide an angle into two equal angles. A part of a circle

2/9x2 + 25 dx Determine the function f(x) given that f'(x) = 1 + sin x and f(0) = 3 The acceleration due to gravity on the moon is 1.62 m/s2 . If a ball is thrown from the surface of the moon upwards with a velocity of 20 m/s, what will its maximum height be? Estimate the net area under the graph of y=x sin x between x = 0 and x = 25 using a Right Riemann Sum with 100 subintervals. Find the average value of f (x)=sin (x) between 0 and 2 pi using the formula involving the integral. Explain why your answer makes sense by considering the graph of y=sin x Show all your work. Evaluate the following integrals Albumin is a protein found in the blood. A common test to see if a person has liver disease is to check that person's albumin levels. If the concentration of albumin in the blood serum is under 32 mg/ml, then liver disease is suspected, as liver disease is the most common cause of low albumin. This test is performed by taking a 1 mL sample of blood serum and running it through an HPLC machine which separates the albumin from the other chemicals in the blood. The output of one such test is displayed below. Does this person have low albumin? HINT: Use the trapezoid method to determine the area under this curve = weight of albumin in the 1 mL sample of blood serum Given that f(x)dx =8 and f(x)dx=-2 c, evaluate the following (f{x)+2x +1)dx 3 f[x)dx The density 'p' of a certain cylindrical rod that has radius 0.1 metres and length 4 metres varies along the length x of the rod by the formula p(x)=3+ 2 x kilograms per cubic meter for 0 x 4. Find the total mass of the rod. HINT: How much weight is there in the differential slice at "x"? It is p(x) times the volume of the slice (pi r2 dx )