Test 4 Memorization Flashcards Preview

Calculus 2 > Test 4 Memorization > Flashcards

Flashcards in Test 4 Memorization Deck (28):
1

What is the standard form of a parabola?

(x-h)^2 = 4p (y-k) (vertical axis) and (y-k)^2 = 4p (x-h) (horizontal axis)

2

What is the standard equation of a circle?

(x-h)^2 + (y-k)^2 = r^2

3

What is the general second degree equation?

Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0

4

What is the standard equation of an ellipse?

(x-h)^2/a^2 + (y-k)^2/b^2 = 1 (Major axis horizontal) or (x-h)^2/b^2 + (y-k)^2/a^2 = 1 (Major axis vertical)

5

What is the equation to determine foci of an ellipse?

c^2 = a^2 - b^2

6

How do you find the vertices of an ellipse?

Add/subtract a from the center

7

How do you find the foci of an ellipse?

Add/subtract c from the center

8

What is the eccentricity (e) of an ellipse?

c/a

9

What is the standard equation of a hyperbola?

(x-h)^2/a^2 - (y-k)^2/b^2 = 1 (Transverse axis horizontal) (x-h)^2/b^2 - (y-k)^2/a^2 = 1 (Transverse axis vertical)

10

How do you find the vertices of a hyperbola?

Add/subtract a from the center

11

What is the equation to determine foci of a hyperbola?

c^2 = a^2 + b^2

12

How do you find the foci of a hyperbola?

Add/subtract c from the center

13

What are the asymptotes for a horizontal transverse axis?

y = k + b/a(x-h) and y = k - b/a(x-h)

14

What are the asymptotes for a vertical transverse axis?

y = k + a/b(x-h) and y = k - a/b(x-h)

15

What is the eccentricity (e) of a hyperbola?

c/a

16

How do you eliminate the parameter?

Solve for t in one equation, substitute into the other equation.

17

What is the parametric form of the derivative?

dy/dx = dy/dt / dx/dt, where dx/dt != 0

18

How do you find the second derivative of a parametric?

d/dt[dy/dx] / dx/dt

19

How do you find the third derivative of a parametric?

d/dt[d^2y/dx^2] / dx/dt

20

What is the formula for arc length in parametric form?

s = integral a to b of: sqrt((dx/dt)^2 + (dy/dt)^2)

21

What do the coordinates in a polar coordinate set denote?

r = radius, theta = angle on unit circle

22

What are the four equations for coordinate conversion of polar coordinates?

x = r cos theta, y = r sin theta, tan theta = y/x, x^2 + y^2 = r^2

23

What is the equation for the slope of the tangent line to the graph of r = f(theta)?

r cos theta + r' sin theta / r' cos theta - r sin theta

24

How do you find tangent lines of a polar function at the pole?

If r(alpha) = 0 and r'(alpha) = 0 then the line theta = alpha is tangent at the pole to the graph of r = f(theta).

25

What is the formula for area of a region in polar coordinates (radial lines)?

A = 1/2 integral a to b of: r^2 d(theta)

26

What is the formula for arc length of a polar curve?

s = integral a to b of: sqrt(r^2 + (dr/dtheta)^2) dtheta

27

What is L'Hopital's rule?

If direct substitution produces an indeterminate form, then Lim x->c f(x)/g(x) = Lim x->c f'(x)/g'(x)

28

What are the indeterminate forms?

0/0, infinity / infinity, 0 * infinity, 1 ^ infinity, 0 ^ 0, infinity - infinity