Evaluate the following limit. lim 3e t - t 5t t+6j+3 tan 6j+3tantk 1 tk) 5t...

Transcribed Image Text:

Evaluate the following limit. lim 3e t - t 5t t+6j+3 tan 6j+3tantk 1 tk) 5t lim 3e - t+6+3tan tk = ti- 3tan=tk) = t (Type an exact answer, using as needed.) -0 Evaluate the following limit. t (-) + ) j 2 lim costi -6 sin t lim costi -6 sin t 2 j+-k = T Evaluate the following limit. lim t0 lim 3 sin t t t e4t-4t-1 5t 4t 3 sin t e -4t-1 -j+ cos t+ 1000 2 (Simplify your answers. Type exact answers.) 5t cos t+ 5t 1 2 -k =i+j+k Differentiate the following function. r(t) = (6t,8 /t. 7) r'(t) = ( For the following parameterized curve, find the unit tangent vector T(t) at the given value of t. r(t) = (cos 8t, 15,2 sin 2t), for 0t, t= - 2 (1)-000 T = 2 Let u(t) = 2ti + (t-1)j - 8k. Compute the derivative of the following function. (t2 + 4t) u(t) Select the correct choice below and fill in the answer box(es) to complete your choice. O A. The derivative is the scalar function B. The derivative is the vector-valued function ()i+(1)j + ()k. Evaluate the following limit. lim 3e t - t 5t t+6j+3 tan 6j+3tantk 1 tk) 5t lim 3e - t+6+3tan tk = ti- 3tan=tk) = t (Type an exact answer, using as needed.) -0 Evaluate the following limit. t (-) + ) j 2 lim costi -6 sin t lim costi -6 sin t 2 j+-k = T Evaluate the following limit. lim t0 lim 3 sin t t t e4t-4t-1 5t 4t 3 sin t e -4t-1 -j+ cos t+ 1000 2 (Simplify your answers. Type exact answers.) 5t cos t+ 5t 1 2 -k =i+j+k Differentiate the following function. r(t) = (6t,8 /t. 7) r'(t) = ( For the following parameterized curve, find the unit tangent vector T(t) at the given value of t. r(t) = (cos 8t, 15,2 sin 2t), for 0t, t= - 2 (1)-000 T = 2 Let u(t) = 2ti + (t-1)j - 8k. Compute the derivative of the following function. (t2 + 4t) u(t) Select the correct choice below and fill in the answer box(es) to complete your choice. O A. The derivative is the scalar function B. The derivative is the vector-valued function ()i+(1)j + ()k.