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Texas A&M University-Corpus Christi - MATH 2414 - Study Guide - Final

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Texas A&M University-Corpus Christi - MATH 2414 - Study Guide - Final

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Math 2414We also discuss several other topics like How do we perceive speech accurately?

Exam 1 Review

EXAM 1 REVIEW

→ TEXTBOOK CHAPTERS 6 AND 7

Common Integrals

Common Derivatives

Common Trig. Identities

(soh - cah - toa)

;If you want to learn more check out What is written and sung by harrison?

= ln |sec x + tan x| + C

If you want to learn more check out What test should be performed to assess if the distribution of the overall response is the same for the two treatment populations?

Don't forget about the age old question of What is the meaning of sociological imagination in sociology?

+ C

ln |sec x| + C

Don’t forget “+C” when indefinite

We also discuss several other topics like What is the difference between two general cell types?

- The first fundamental theorem of calculus

; where F’(x) = f(x)If you want to learn more check out How do the prototype approach and the exemplar approach differ from each other?

- U-substitution: simplifies integrals so anti-derivative is easier to find.

Example:

- Let u = 2t +4; du= 2 dt ⇒ dt = du/2

- Completing the square

- (a+b) 2 = a 2 + 2 a b + b 2
- Ex. x 2 + 6 x + 4

- (x+3) 2 - 5

I. Area between curves: area between the graphs of two functions (Section 6.1)

- Method I: Vertical Strips

- everything with respect to x

- Method II: Horizontal Strips

- A 1:=
- A 2 =
- everything with respect to y

II. Volume: finding the volume of a solid using an integral (Section 6.2)

- Done by “giving” the top and bottom slabs with square cross sections
- Ex: consider a solid with a base bounded by:

- y = 1-x, y = 2x+5, x=0, x=3
- This is not a box, so we break it into pieces and take the limit

- Length = (2x + 5) - (1 - x)
- Width = (2x+ 5) - (1- x)
- Height = Δx (we only know exact value if given)

- Volume:

- Bounds: x = (0, 3)
- Area of Cross Section: [(2 x+ 5) - (1- x)] 2
- Height: dx

- A. disk method (not square cross sections): volume generated when a region is revolved about an axis which is perpendicular to the approximating strip of the region.

- fills in the object with disks (circles with thickness) and adds them up to find volume.