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- Texas
- University of North Texas
- Calculus
- Calculus 1720
- Dulock
- Summer Multivar. Cal

Ore A.

The Fundamental Theorem of Calc

the integral of f from a to be is equal to f(b)-f(a)

What re the 2 ways to represent a curve?

1) by an Equation

2) in parametric form

2) in parametric form

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What is a parametric Equation?

Eq.s that inlude the variable t, which represents a point between any a and b.

t also has a set of x and y coordinates

t also has a set of x and y coordinates

Dimensions of an object=

the # of variables (x,y,z) minus the number of eq.s

How do you plot a parametric graph?

find the value of t and and substitute it into the appropriate equation

x^2+y^2=

1

Eq. of a circle

Eq. of a circle

parametric eq.s involing sin and cos

Use the eq. for a circle and adjust the values of x and y to be parallel to it

Rewrite <a1,a2,a3>

<a1i+a2j+a3k>

How do you add and subtract vectors algebraically?

Combine Like terms

How do you add vectors geometrically?

With Tip to tail method, which you can use if the tips and tails aren't aligned. Just move the vectors within their respective planes

How do you subtract vectors geometrically?

1. draw the first vector "as is"

2. draw the second vector in the opposite direction

2. draw the second vector in the opposite direction

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Scalar Multiplication

Multiplying a vector by a scalar constant, which shrinks or lenghtens the vector accordingly

coordinates of i vector

<1,0,0>

coordinates of j vector

<o,1,0>

coordinates of k vector

<0,0,1>

Magnit./Length of a vector=

the sqrt of a1^2+a2^2

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