help with question 8 please Due Wednesday, April 11, 2018 Math 4A: Worksheet 8 -

Question

help with question 8 please

Due Wednesday, April 11, 2018 Math 4A: Worksheet 8 -Sections 13.1 and 13.2 Nan Instructions: You must show all work (as necessary) to receive full credit. All answers must be simplified and in exact orm, unless otherunse indicated Proper notation must be used. I pages are not stapled, a 3% deduction will be applied. 1. Find the domain of the vector functiorn. t)s (cos t, 12t2-31t+20), VE- b. r(t) (esine, v1-t, In t) 2. Find the limit. sin t a. lim 1-cost b. Jim (tan1ocosk t2+3 3. Find a vector equation and parametric equations for the line segment that joins P(7,-2,-4) and 4. Find a vector function that represents the curve of intersection of the paraboloid zy 5. Sketch the plane curve with the given vector equation. Find r'(t), and then sketch r' (t) for the and the parabolic cylinder x y given value of t. a. r(t) = (e-te2t), t-In 2 b. r(t) (3 sin 2t, 1,3 cos 20), t 6. Find the derivative of the vector function. r(t)=(1-e-t, te2t? a. 7. Find the unit tangent vector T(t) for the given value of t. r(t)= (1, t, t*), t=1 a. b. r(t) (3 cost,4sint,t), t Find parametric equations for the tangent line to the curve with the vector function r(t) (2 cos rt, 2 sin rt, 3t) at the point (1, V3, 1) 8. 9. Evaluate the integral. a. (te iIn(t2)1) dt

Explanation / Answer

r=(2cos(pi*t), 2sin(pi*t), 3t)

r' = (-2*pi*sin(pi*t)), 2*pi*cos(pi*t), 3)

at point (1, sqrt(3), 1)

now from 1st equation,

3t =1

t=1/3

so, r'(1/3) =(- pi*sqrt(3), pi, 3)

so now the required parametric equation will be

x=1-pi*sqrt(3)*t

y=sqrt(3)+pi*t

z=1+3t

i hope you understand the concept

if you still have any doubt then please ask in the comment section

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thanking you

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