Enter Title

Position, velocity, and acceleration

100

The acceleration of a particle moving along the x-axis at any time t>0 is given by a(t)=1+e^-t. At t=0 the velocity of the particle is -2 and its position is 3. The position of the particle at any time t is

t²/2-t+e^-t+2

200

The position vector of a particle moving in te xy-plane at time t is given by p=(3t²-4t)i+(t²=2t)j. The speed of the particle at t=2 is

10

300

A particle moves along the x-axis and its position for time t>0 is x(t)=cos(2t)+sec(t). When t=pi, the acceleration of the particle is

-5

400

What month is Julie's birthday in?

July

500

A particle moves on the x-axis in such a way that its position at time t, t>0, is given by x(t)=(lnt)². At what value of t does the velocity of the particle attain its maximum

e

Product, quotient, and chain rule

100

If g(x)=tan²(e^x), then g'(x)=

2e^xtan(e^x)sec²(e^x)

200

What month is Ella's birthday in?

June

300

The graph of f(x)=xsinx defined on 0<x<3.14 has an inflection point whenever

tanx=2/x

400

An equation of the line normal to the graph of f(x)=x/(x-2) at (1,-1) is

x-2y-3=0

500

If h(x)=(f(x))²+f(x)g(x), f'=g(x) and g'(x)=-f(x), then h'(x)=

(g(x))²+2g(x)f(x)-(f(x))²

Implicit differentiation

100

Find dy/dx implicitly for

x/y³=1

dy/dx=1/3(x)^-2/3

200

Name two out of three of Sherry's favorite colors

Purple, white, and black

300

Find dy/dx through implicit differentiation

e^x-sin(y)=x

dy/dx=(e^x-1)sec(y)

400

Find dy/dx by implicit differentiation

7y²+sin(3x)=12-y⁴

dy/dx=(-3cos(3x))/(14y+4y³)

500

Find derivative implicitly

cos(x²+2y)+xe^{y^2}=1

dy/dx=(2xsin(x²+2y)-e^{y^2})/(2yxe^{y^2}-2sin(x²+2y))

Trig and inverse trig functions

100

Differentiate

y=tan(x)sec(x)

dy/dx=sec³(x)+sec(x)tan²(x)

200

Differentiate

y=10tan(x)-2cot(x)

dy/dx=10sec²(x)+2csc²(x)

300

What type of dog is Daisy?

Miniature poodle!

400

Differentiate

y=sin(x)+x²tan^-1(x)

dy/dx=cos(x)+2xtan^-1(x)+x²/(1+x²)

500

Differentiate

y=tan²(e^x)

dy/dx=2e^xtan(e^x)sec²(e^x)

Parametric and Polar equations

100

Find horizontal and vertical tangents of 

x=t+1

y=t²+3t

vertical tangent at t=-3/2

200

Find the equation of the tangent(s) at the pole for 

r=3cosθ 

Tangents are:

θ =π /2 and θ =3π /2

300

When is this function concave up?

x=2+t²

y=t²+t³

(-∞ , 0)

400

What are the names of Ella's cats?

Apollo and Clyde

500

Find horizontal tangents of 

r=1-sinθ 

(2, 3π /2), (1/2, π /6), (1/2, 5π /6)