Exam #1 Study Guide
Exam #1 Study Guide STAT 1102 - 003
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This 19 page Study Guide was uploaded by Kayla Notetaker on Monday September 28, 2015. The Study Guide belongs to STAT 1102 - 003 at Temple University taught by Ron Kershner in Fall 2015. Since its upload, it has received 154 views. For similar materials see QUANTITATIVE METHODS FOR BUSINESS II in Statistics at Temple University.
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Date Created: 09/28/15
Exam 1 Study Guide True or False A function is a rule that matches one x to one y A vertical line test states that a line passing through a graph twice is a function Domain contains all values of y We can define domain and range using graphs and algebra Horizontal Line Test tests whether or not a function is a onetoone function Piecewise functions have specific values dependent on their domains P V PS P P Find the Domain Algebraically I Y32X 8 v 3 2x 9 Y2x 3xlt1 x 2x21 Consider the function Fx2x1xlt0 17x0 x2 30ltxlt4 12x1x21x24 10 Find f1 and f1 11 Find f3 and f3 12 Find fO and f10 13 Find f5 and f5 Find the domain 14 F9x 2x 3 15 Fx x 2 16 Fx x 4 17 3x 1 7 2x 18 Fx 2x x2 25 19 Fx x 2 x2 X 6 Find the slope of the line 20 Given the points 2 6 and 4 9 find the slope 21 Find the slope given 9 8 and 3 5 Find Equation of Lines 22 Given m 3 and the point 1 5 find the equation of the line 23 Brain Weight the weight B of a human s brain is directly proportional to a person s body weight W a It is known that a person who weighs 120 lbs has a brain that weighs 2 lbs Find an equation of variation expressing B as a function of W b Express the variation constant as a percent and interpret the resulting equation What is the weight of the brain of a person who weighs 170 lbs 24 Given the total fixed cost of 20 000 variable costs of 10unit and a unit price of 90 find a The total profit function b Breakeven point c Cost of producing 100 units 25 Quick copy buys an office machine for 5200 on Jan 2 The machine is expected to last 10 years The salvage valye at the end of 10 years is estimated 1000 Assume a straightline depreciation function of Vt C t C S N where C original cost N number of years of expected life S salvage value a What is the linear function of the straight line depreciation b What is the book value after each of the years 0 1 2 10 26 A computer firm is planning to sell a new graphing calculator For the first year the fixed costs for setting up the production line are 100 000 The variable costs for producing each calculator is estimated at 20 The sales department projects that 150 000 calculators can be sold during the first year at a price of 45 each a What are the cost and revenue functions b What is the profit function c What is the expected profit or loss from an expected sale of 150 000 calculators d Breakeven point True or False 27 For the limfx as x gt a to exist the limfx as x gt a39 and the limfx as x gt a must equal each other 28 Left and right limits can exist without limfx as x gt a existing 29 The limit is the x value that results as x approaches a from either direction Limits Evaluate functions below at limfx as x gt 2 30 FX 6x 3 31 Fx6x3xgt2 2nxsz Find the Iim x 1 fX as and lim x gt1fx as 32 Fx 5 for x gt 1 x 1 forx lt 1 33 Does the limit exist for the function above Find the limits algebraically 34 LimH 1 3x 2 35 lex 1 3x5 4x4 3x 6 36 lex 3 x2 6 x 2 37 Limx gt2 3x2 x 14 x2 4 38 Limx1 x2 5x 4 x2 2x 1 39 Iim x 2x2 9 Determine if the function is continuous 40 Is the function continuous at x 2 fx x2 4x 2 X 2 ix2 41 Is the function continuous at x 3 fx13x4 xlt 3 2x 5x23 42 Is the function continuous at x 2 Fx x2 16x 4 forx 2 7 for x 2 Difference quotient 43 Find the difference quotient for fx x3 44 Find the limit of the difference quotient for x3 45 Find the difference quotient for fx 1 2x 5 46 Find the limit of the difference quotient for fx 1 2x 5 47 Find the difference quotient for fx x2 48 Find the limit of the difference quotient for fx x2 Derivatives 49 Yx3 50 Yx 51 Y 2X 52 1 W 53 Y 34 566 54 Y 80X4 55 Y 7X6 56 Y 6X2 8 57 Y 43Vx2 2x Find the slope of a tangent line Fx x2 6x2 58 Find the slope at x 6 59 Find the slope at x 4 60 Where is the slope of a tangent line to fx 0 Fx x2 3x 61 What is the slope at x 5 62 What is the slope at x 9 63 Find the slope of the tangent line to fx 0 Find an equation of the tangent line to the graph of fx BVXZ at 1 1 64 Find the derivative of the function 65 Find the value of the derivative at the x value given the slope m 66 Use the x y pair given the slope from step two and substitute in the point slope formula The median weight of a boy whose age is between 0 and 36 months can be approximated by the function wt 815 182t 00596t2 0000758t3 Find the following 67 The rate of change of weight with respect to time 68 The weight of the baby at 10 months 69 The rate of change of the baby s weight with respect to time at age 10 months Derivative of a product 7o Fx x2 4x 117x3 X 71 Fx t 23t 4t 7 72 Fx x3x8 73 Fx x3 2x2 x 16 3x2 22x Derivative of a quotient 74 FX 3x7 x3 x 75 FX x x 4 76 FX x3 x10 77 FX X3 9 7x4 6 Extended Power Rule 78 Y 3X2 104 79 Y 5x4 6x2 910 80Y1x3 81 Y 1 x23 5 4x2 82 Y 3x 54 7 x6 83 Y13x82 84Yxx 33 Total revenue Rx 1000x2 01x 85 Where Rx is the total revenue in thousands of dollars from the sale ofx items find the rate at which total revenue is changing when 20 items have been sold Consumer credit Cx 02x4 592x3 5053x2 1892x 11493 86 Where x is the number of years since 1995 87 Find the derivative 88 Interpret the mean of the derivative 89 Using the model in A estimate how quickly outstanding consumer credit was rising in 2010 Higher Order Derivatives 90 Given fx x3 2x2 1 a Find the derivative of fx b Find the second derivative of fx 91 Y 5x4 12x31 a Find the first derivative b Find the second derivative 92 When an object is dropped the distance it falls in t seconds is st 4905t2 a Find vt b Find vt when t 5 c Find at d Find at when t 5
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