12.1.24 Question Help The tangent line to a smooth curve r(t) = f()i + 96)j +...
Find parametric equations for the line that is tangent to the given curve at the given parameter value. Question Help (t)= (5 cost)i+(4 - 4 sin t).i+ (20), t=0 What is the standard parameterization for the tangent line? X y = Z- (Type expressions using t as the variable)
Find parametric equations for the line that is tangent to the given curve at the given parameter value. r(t) = (5+?) 1+ (2t - 1)]+(31') k, t=to = 3 What is the standard parameterization for the tangent line? X = y = ZE (Type expressions using t as the variable.)
Find parametric equations for the line that is tangent to the given curve at the given parameter value. r(t) = In 1+ k, t=to=4 What is the standard parameterization for the tangent line? X= y = ZE (Type expressions using t as the variable.)
Find parametric equations for the line that is tangent to the given curve at the given parameter value. r(t) = (2 cos t) + (9-2 sin t))+(0) What is the standard parameterization for the tangent line? t=0 (Type expressions using t as the variable.)
Suppose the vector-valued function rt-tht) is smooth on an interval containing the point t -to is the line parallel to the tangent vector r()that passes through ()().()).For the following function, find the line tangent to the curve at t to the point to The line tangent to r(t) at r(t) (10 cos t,6 sin 16t,t), to Theline tangent to the curve at t:68COD Suppose the vector-valued function rt-tht) is smooth on an interval containing the point t -to is the...
answer q5,6,7,8 please Find the unit tangent vector T(0) at the point with the gliven value of the parameter t. r(t)-cos(t)I + 8t1 + 3 sin(2t)k, t 0 T(o) Need Help? adHTer Find parametric equations for the tangent ine to the curve with the given parametric equations at the spedfled point. Evaluate the ietegral Need Help?h h SCakETS 13 200 Evaluate the integral. Find the unit tangent vector T(0) at the point with the gliven value of the parameter t....
3. (5 points) (a): Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x=etcost, yr etsint, z=et; (1,0,1) (b): Find the unit tangent vector T, the principal unit normal N, and the curvature k for the space curve, r(t) =< 3 sint, 3 cost, 4t >.
Find the derivative, r'(t), of the vector function. r(t) = eti- j+ln(1 + 7t)k r'(t) = Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. T = 5e, y = te, c = tetp:/5, 0, 0) x(t), y(t), z(t) =
Solve for 14(b,c) and 18 (b,c) please 16. Find a set of parametrie equations t d) r(t)-(4t,3 cos(t).2sin(t) the line tangent to the graph of r(t) (e.2 cos(t).2sin(t)) at to-0. Use the qu tion to approximate r(0.1). tion function to find the velocity and position vectors at t 2. 17. Find the principal unit normal vector to tih curve at the specified value of the parameter v(0)-0, r(0)-0 (b) a(t)cos(t)i - sin(t)i (a) r(t)-ti+Ij,t 2 (b) rt)-In(t)+(t+1)j.t2 14. Find the...
Hi need help for these Questions: a. Given f = yi + xzk and g = xyz2, determine (∇ x f ) . ∇g at the point (1,0,3) b. Point A lies on the curve r(t) = 2 cos t i + 2 sin t j + t k for the range 0 ≤ t ≤ 2π . At point A, the tangent vector is T = - 21/2i + 21/2j + k. Determine the co-ordinates of point A and...