differentiate🫠
Find the derivative of x and y with respect to t and divide y' by x' with respect to t to find dy/dx.
How do you differentiate parametric equations?
d²y/dx² = (d/dt(dy/dx)) / (dx/dt)
What is the formula for the second derivative of a parametric curve?
What is the formula for arc length of a parametric curve?
L = ∫ a -> b √ (dx/dt)² +(dy/dt)² dt
x(t2) = x(t1) + ∫ t1 -> t2 v(t) dt
What is the position of a particle at any given time?
Who's the best math teacher?
Ms. Lerohl
Find dy/dx for x = t2 and y = t2 + 2 when t = √2
1
If x(t) = tan(t) and y(t) = sin(t), find the second derivative at t = π/6 .
-27/32
If a = 0 and b = 2π , and dx/dt = cos(t) and dy/dt = -sin(t), find the arc length.
6.283
|v(t)| = √(x(t))² + (y(t))²
What is the speed formula?
Which teacher teaches multivariable calculus?
Mr. Perna
Find the equation of the line tangent to the parametric curve given x(t) = -t2 + 4t + 12 and y(t) = 1 / (t+1) when t = -2.
y + 1 = (-1/8)x
Given x(t) = t2 - 2t and y(t) = t2 - ln(t), find any value of t that yields a point of inflection
t = 1
Find the length of the parametric curve defined by x(t) = e-t sin(t) and y(t) = e-t cos(t) on the interval 0 ≤ t ≤ 1
√2 - (√2 / e)
r(t) = x(t)i + y(t)j
What is Unit Vector "i-j" form?
Which two math teachers are married?
Mr. Cervone and Ms. Kudlash
Find the tangent line to the parametric curve given by x = cos(t) and y = sin(t) at the point (√2 / 2, -√2 / 2)
y = x - √2
Determine the open t intervals where the curve of the parametric equations x(t) = 2 - t2 and y(t) = t3 + t4 is concave down.
(-3/8, 0)
CALCULATOR REQUIRED
The parametric curve for the Witch of Agnesi on the interval of 0 ≤ t ≤ π can be defined as x(t) = at and y(t) = 2a / (1 + t2). Find the length of the curve over the interval for a = 3.
11.351
NO CALCULATOR
A particle moves along a curve on a plane such that it's velocity vector at any t ≥ 0 is < tcos(t²) , 10t / 5t²>. Find the position vector.
< 0.5sin(t2) , ln(5t2) >
Which math teacher also teaches at Hunter?
Ms. Jung
Find the equation of all lines tangent to the parametric curve x(t) = sin(2t), y(t) = 1 - cos(t) at the point: (0,1).
y = (1/2)x + 1 and y = (-1/2)x + 1
Find the equation of the line tangent to the parametric curve x(t) = 2t - 1, y(t) = t3 -3t2 + 1 at its point of inflection
y = (-3/2)x + 1/2
CALCULATOR REQUIRED
The name "Folium of Descartes" comes from the leaf shape of the curve's loop in quadrant one of a formula that Rene Descartes worked on while challenging Pierre de Fermat to mathematical challenges. The equation located in the image is in parametric form as x(t) = 4t / (1 + t3) and y(t) = 4t2 / (1 + t3). Find the length of the closed loop in quadrant one.
6.557
NO CALCULATOR
If x(t) = tan(4t) and y(t) = cos(2t), find the acceleration vector at t = π/2.
< 0 , 4 >
Which math teacher went to become the principal of a different school?
Mr. Arora