Calc exam

Cartesian

1. find t from x function

2. plug t into y function

Find k so the two particles collide.

1. Make particle A and B’s x function equal to each other

2. solve to find t

3. Make particle A and B’s y function equal to each other

4. Plug t in to find k

speed of particle

1. square root of (dx/dt)²+(dy/dt)²

2. take derivate of both x and y on particle given

3. if a t is left, plug in what’s given to you

4. plug in derivates

dx/dt (horizontal speed)

1. take derivative of x function

2. plug in t values if needed (solved from setting function equal to x

dy/dt (vertical speed)

1. take derivative of y function

2. plug in t values if needed

max height

1. take derivate of y funciton

2. set equal to 0

3. solve to get t

4. plug t into og function (no derivative)

left hand riemann sum

1. delta x

2. from 0 → n - 1

right hand riemann sum

1. delta x

2. starts at 1 → n

riemann left hand (going down)

overestimate

riemann right hand (going down)

underestimate

estimate for riemann left hand

1. take distance ([x,x]) and divide by n

2. start at velocity 0 and mutliply by the number you got in step 1, adding other velocities as you go

3. stop at n-1

estimate for reimann right hand

1. take distance ([x,x]) and divide by n

2. start at velocity 1 and multiply by the number you got in step 1, adding other velocities as you go

3. stop at n

slope of tangent for particle

1. find derivative of x and y from particle

2. set them y/x

3. plug in t

4. answer is your slope

5. now plug t into of functions to get y1 and x1

6. put into point slope form (y-y1=m(x-x1)

7. plug in values

8. simplify

antid

add 1 to the power and divide by new power

hits ground

set og y function equal to 0. solve for t

h

unchanged og top-bottom