Find a parametrization of the tangent line at the point indicated.
r(t) = <1 − t4, 2t, 3t3>
t = 2
L(t) =
<−23t−15,2t+4,36t+24>
Find a parametrization of the tangent line at the point indicated. r(t) = <1 − t4, 2t, 3t3> t = 2 L(t) = <−23t−15,2t+4,36t+24>
Find a parametrization of the tangent line at the point indicated. r(t) = (1 - 4, 4t, 5t), t = 2
2. Find the parametrization of the tangent line to the space curve r(t) = (In(t), e6", –+2) at t= 1.
EXAMPLE 1 (a) Find the derivative of r(t) = (3 + t4)1+ te-y + sin(40k. (b) Find the unit tangent vector at the point t0. SOLUTION (a) According to this theorem, we differentiate each component of r: t 45 cos (4t) r(t) + 3 (b) Since r(0)= and r(o) j+4k, the unit tangent vector at the point (3, 0, 0) is i+ 4k T(0) = L'(0)-- EXAMPLE 1 (a) Find the derivative of r(t) = (3 + t4)1+ te-y +...
Let f(t) = t? and g(t) = 2t + 3. Find f*g. Select one: 1 t4 +3t3 12 123 a. 1 b. t +t3 1 +4 +t3 + 3t? 12 *** +++ Type here to search
(1 point) Find a vector equation for the tangent line to the curve r(t) = (2/) 7+ (31-8)+ (21) k at t = 9. !!! with -o0 <1 < 0
please answer both (12(8 pts) Find parametric equations of the line through the point (2, -1,3) and perpendicular to the line with parametric equations 1-t,y 4- 2t and 3+ t and perpendicular to the line with parametric equations 3+t,y 2-t and z 3+2t. (13)(8 pts) Find the unit tangent vector (T(t) for the vector function r(t) - costi+3t j+ 2sin 2t k at the point where t 0 (12(8 pts) Find parametric equations of the line through the point (2,...
1 point) Suppose that the line l is represented by r(t)- (12+ 2t, 23 +6t, 8 + 2t) and the plane P is represented by 2x + 4y + 52-23. 1. Find the intersection of the line & and the plane P. Write your answer as a point (a, b, c) where a, b, and c are numbers. Answer 2. Find the cosine of the angle 0 between the line l and the normal vector of the plane P Answer:...
2. Consider the surface S with parametrization r(s, t)< st, s,t3 - s >. Find parametric equations and symmetric equations for the tangent plane to S at the point (1, 1,0). 2. Consider the surface S with parametrization r(s, t). Find parametric equations and symmetric equations for the tangent plane to S at the point (1, 1,0).
13. (5 points) parametrization Find an equation of the tangent line to the curve given by the =t- - y = 1+12 at t=1.
(1 point) Find the equation of the line tangent to the graph off at the indicated x value. y = 10 sin-1 3x, x = 0 Tangent line: y =