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2. Find the slope and concavity at the given value of the parameter. r = 12...
Find the unit tangent vector T(t) at the point with the given value of the parameter t. r(t) = (2 – 3t, 1 + 4t, 582 + 2x2), t = 4 T(4) = <5,4,720 > 720.02847 x
find dx/dy and d2y/dt2 if possible, and find the slope and concavity (if possible) at the point corresponding to t=3 x=t+2 y=t^2+8t
a) Find the exact value of the slope of the line which is
tangent to the curve given by the equation
r = 2 + cos θ at
. You must show your work.
b) Set up, but do not evaluate, the integral that represents the
length of the curve given by
x = t - t2,
, over the interval 1 ≤ t ≤ 2.
D 4,3/2 y=7
D
4,3/2 y=7
Problem The random variable X is exponential with parameter 1. Given the value r of X, the random variable Y is exponential with parameter equal to r (and mean 1/r) Note: Some useful integrals, for λ > 0: ar (a) Find the joint PDF of X and Y (b) Find the marginal PDF of Y (c) Find the conditional PDF of X, given that Y 2. (d) Find the conditional expectation of X, given that Y 2 (e) Find the...
16. Find all points on the circle x2 + y2 = 676 where the slope is 5/12 (x, y) = _______ (smaller y-value) (x, y) = _______ (larger y-value) 13.Find an equation of the tangent line to the graph at the given point. x2y2 - 9x2 - 4y2 = 0, (-4, -2√3) y = _______ 12. Find the slope of the tangent line to the graph at the given point. (4 - x)y2 = x3, (2, 2)
1 a) Find the domain of r(t) = (2-Int ) and the value of r(to) for to = 1. b) Sketch (neatly) the line segment represented by the vector equation: r=2 i+tj; -1 <t<l. c) Show that the graph of r(t) = tsin(t) i + tcos(t) j + t?k, t> 0 lies on the paraboloid: z= x2 + y². 2. a) Find r'(t) where r(t) = eti - 2cos(31) j b) Find the parametric equation of the line tangent to...
For the curve r(t), find an equation for the indicated plane at the given value of t. 55) r(t) (3 sint+6i+ (3 cos 20t) - 1j+ 12tk; osculating plane at t 2.5m. 12 12 60 +1) + 13 B) y-1) + 169 =0 13 169 12 -6) +. 60 9131)+30) 0 =0 (206-2 56) rt) (t2-6)i+ (2t-3)j+9k; osculating plane at t A) x+y+ (z+9)-0 C) x+ y+(z-9) 0 6. B) z =9 D) z =-9
For the curve r(t), find...
Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x = t4 + 3 y = t3 +t t = 1 y(x) = _______
Find the slope of the tangent line to the Lissajous curve cos(t), y = sin(4t) at t = 1/6. Eliminate the parameter to find the Cartesian equation of the curve x = 41-t, y = (1+t, -1st s 1. Identify what type of curve this is. You do not have to sketch the curve.
Find the slope of the line tangent to the polar curve at the given point. r= 5 sine (25) r=5 sin 0;