Calculus Problems: Integrals, Derivatives, and Area Calculation

Let f(x) = -x2 + 2x + 3. The graph of f is shown in the following diagram.

(a) Find ∫(-x2 + 2x + 3) dx

∫-x2 dx + ∫2x dx + ∫3 dx
-x(2+1)/(2+1) + 2x(1+1)/(1+1) + 3x + C
-x3/3 + 2x2/2 + 3x + C
= -x3/3 + x2 + 3x + C

(b) Find the area of the shaded region.

-(2)3/3 + (2)2 + 3(2) – [-(1)3/3 + (1)2 + 3(1)]
-8/3 + 4 + 6 – (-1/3 + 1 + 3)
-8/3 + 10 – (-1/3 + 4)
-8/3 + 10 = (-8 + 30)/3 = 22/3
-1/3 + 4 = (-1 + 12)/3 = 11/3
22/3 – 11/3 = 11/3 u2
Answer: 11/3 = 3.6 u2

2. Let f'(x) = 3x2 – 3. Given that f(2) = 1, find

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Vernier Caliper: Understanding Measurement and Usage

Scale in Millimeters

The degree of precision is calculated by dividing the smallest size of the major scale by the number of divisions of the vernier.

Vernier Markings

The vernier may have the following markings:

Reading Underground Foot Measurements

To see if the tube foot is graduated in the English system or the metric system, look for 10 divisions of the major scale, starting from zero.

  • If this division is not numbered, it means that the instrument belongs to the English system.
  • If compared to Division
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Understanding Data Structure in Statistics

What is the Structure of Information?

Data consists of the unit of analysis, the variable, and the category. Data are the raw materials with which statistics work. Statistical processes transform data into useful information. Data extracted from reality should be the most appropriate data for the objectives of the work to be done.

Example: “Luis is 1.70 Meters Tall”

Identify the data, the unit of analysis, the variable, and the category in the following example: “Luis is 1.70 meters tall.”

In the statement

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RushCard Account Management and Security Procedures

Login Credentials

  • Avaya: 130441 Pass: 1445
  • Windows: luis.colato Pass: G.T.A.07
  • Unirush: lcastillo1 Pass: Rushcard6
  • TSYS: lcastillo Pass: Colato0777
  • VT/Idology: lcastillo1 Pass: Colato0777

Contact Information

  • Dispute: Ext. 404009
  • Tier 2: Ext. 404003
  • Risk Department: 1-877-266-5939 risk@rushcard.com
  • RushCard: 1-866-787-4227
  • PIN IVR: 1-866-787-4150
  • Fax for MHR: 1-866-506-6329

Real-Time Alerts (RTA) Features

  • Deposit notification
  • Low Available Balance
  • Transactions above set limit
  • Close to Spending Limit
  • Rush BillPay
  • Budget
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Primary and Secondary Data Sources: Collection Methods

Primary and Secondary Data Sources

Primary Source

Definition: Data collected directly from the original source.

Description: First-hand data gathered specifically for the current investigation.

Example: Surveys, interviews, and experiments conducted by the researcher for their own research purpose.

Secondary Source

Definition: Data that already exists and was collected for a different purpose.

Description: Second-hand data gathered by others and used for a new analysis.

Example: Reports, academic papers,

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Math Problem Solutions: Equations, Geometry, and Proofs

Math Problem Solutions

Solving Equations

21: Adding the two equations and dividing by 10, we get: x + y = 10. Subtracting the two equations and dividing by -2, we get: x – y = 1. Solving these two new equations, we get, x = 11/2.

Geometry and Circles

30: Let ABCD be the rhombus circumscribing the circle with center O, such that AB, BC, CD, and DA touch the circle at points P, Q, R, and S respectively. We know that the tangents drawn to a circle from an exterior point are equal in length.

  • AP = AS (1)
  • BP
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