Position, velocity, and acceleration
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
If g(x)=tan2(ex), then g'(x)=
2extan(ex)sec2(ex)
Find dy/dx implicitly for
x/y3=1
dy/dx=1/3(x)-2/3
Differentiate
y=tan(x)sec(x)
dy/dx=sec3(x)+sec(x)tan2(x)
Find horizontal and vertical tangents of
x=t+1
y=t2+3t
vertical tangent at t=-3/2
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
What month is Ella's birthday in?
June
Name two out of three of Sherry's favorite colors
Purple, white, and black
Differentiate
y=10tan(x)-2cot(x)
dy/dx=10sec2(x)+2csc2(x)
Find the equation of the tangent(s) at the pole for
r=3cosθ
Tangents are:
θ =π /2 and θ =3π /2
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
The graph of f(x)=xsinx defined on 0<x<3.14 has an inflection point whenever
tanx=2/x
Find dy/dx through implicit differentiation
ex-sin(y)=x
What type of dog is Daisy?
Miniature poodle!
When is this function concave up?
x=2+t2
y=t2+t3
(-∞ , 0)
What month is Julie's birthday in?
July
x-2y-3=0
Find dy/dx by implicit differentiation
7y2+sin(3x)=12-y4
dy/dx=(-3cos(3x))/(14y+4y3)
Differentiate
y=sin(x)+x2tan-1(x)
dy/dx=cos(x)+2xtan-1(x)+x2/(1+x2)
What are the names of Ella's cats?
Apollo and Clyde
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
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
Find derivative implicitly
cos(x2+2y)+xey^2=1
dy/dx=(2xsin(x2+2y)-ey^2)/(2yxey^2-2sin(x2+2y))
Differentiate
y=tan2(ex)
dy/dx=2extan(ex)sec2(ex)
Find horizontal tangents of
r=1-sinθ
(2, 3π /2), (1/2, π /6), (1/2, 5π /6)