10. Consider the vector-valued function given by r(t) = (√2t, et, e-t). Compute T, N, and the curvature K.

Q: 3. Sketch the vector-valued function r(t) = (sin(2πt), t, 3 cos(2πt)), indicating direction.

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Q: Find r'(t), r(t), and r'(to) for the given value of to r(t) = (1+t)i + ³j, to = 1 (No Response)…

A: We have to find the values of r't, rt0, r't0 where rt=1+ti^+t3j^, t0=1 and sketch the curve…

Q: 1. Let ř(1) = . Find a vector and parametric equation of the line tangent to F(1) at the point (-…

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Q: 4. Let r(f) = ° 13 i - 6fj + Pk. (a) Find the unit tangent vector T(t) and T(3). | (b) Find the…

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Q: 6. Find a vector which is normal to the currive: 3= 11 at (1,2). x³ + xy + y²

A: We have to find a vector which is normal to the curve: x³ + xy + y³ = 11 at (1,2).

Q: 2. For this entire page, let r(t) = (4 sin(t), 3t, 4 cos(t)) (a) Circle the correct graph for the…

A: The objective of this question is to understand the properties of the vector function r(t) = (4…

Q: 3. Find a vector function that represents the curve of intersection of the paraboloid z =. and the…

A: To find the vector function that represents the curve of intersection of the paraboloid z=x2+y2, and…

Q: Consider the function f(x,y) = 4x² - 5y² - 5 and the point (1,1). a. Find the unit vectors that give…

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Q: The vector function r(t)=sin 2ti−cos 2tj+t√√5k determines a curve C'in space. i. Find the unit…

A: Given: rt=sin2ti-cos2tj+t5k To find: i. The unit tangent vector T and the principal unit normal N.…

Q: 2. Consider the following vector function: r(t) = = a cos wti + a sin wtj + bwtk, where a, b and w…

A: We need to find radius of curvature.

Q: 5. Let 7(t) =. a. Find the domain of the vector function. b. Evaluate lim1 7(t).

A: (a). r→(t)=3et-1t, t3-t2t-2, sin(πt)ln t

Q: Next Consider the two vector-valued functions given by r(t) = (t+1, cos 1+t w(+) = (*, sin() *) . a.…

A: (a) The two vector valued functions intersect if r(a) = w(b) for some t = a and s = b.…