6. Find the curvature of r(t) = ti + t2j +t k.at r = 0.7. Find the curvature of the plane y = -cos() + e8. Find the maximum curvature of y In . nack cuwerune,9. Find the tangential component aT and normal component aN for3ti tj + tk.r(t)10. Let a(t) = 2t i + e j + cos (t) k denote the acceleration of a movirv(0) i+2j- k, find the particle's velocity v(t) at any time t.. (a) Find the domain of f(x, y) =nV2 x(b) Sketch the graph of f(r, y) = 62y.12. Find the limit of show it does not exists.(a)lim(xy)+(0,0) +y8(b)ry ylim(a)(1,0) (1)2+y2

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Asked Jun 12, 2019
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Help w/ #6

6. Find the curvature of r(t) = ti + t2j +t k.
at r = 0.
7. Find the curvature of the plane y = -cos() + e
8. Find the maximum curvature of y In . nack cuwerune,
9. Find the tangential component aT and normal component aN for
3ti tj + tk.
r(t)
10. Let a(t) = 2t i + e j + cos (t) k denote the acceleration of a movir
v(0) i+2j- k, find the particle's velocity v(t) at any time t.
. (a) Find the domain of f(x, y) =n
V2 x
(b) Sketch the graph of f(r, y) = 6
2y.
12. Find the limit of show it does not exists.
(a)
lim
(xy)+(0,0) +y8
(b)
ry y
lim
(a)(1,0) (1)2+y2
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6. Find the curvature of r(t) = ti + t2j +t k. at r = 0. 7. Find the curvature of the plane y = -cos() + e 8. Find the maximum curvature of y In . nack cuwerune, 9. Find the tangential component aT and normal component aN for 3ti tj + tk. r(t) 10. Let a(t) = 2t i + e j + cos (t) k denote the acceleration of a movir v(0) i+2j- k, find the particle's velocity v(t) at any time t. . (a) Find the domain of f(x, y) =n V2 x (b) Sketch the graph of f(r, y) = 6 2y. 12. Find the limit of show it does not exists. (a) lim (xy)+(0,0) +y8 (b) ry y lim (a)(1,0) (1)2+y2

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Expert Answer

Step 1

The curve is given by ti+t2j+t3k.

The formula to calculate the curvature of the curve is given by,

|T"
k =
FOI
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|T" k = FOI

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Step 2

The r’(t) is given by differentiating r(t) with respect to t.

then,

r'(t)i+2rj+3rk
/1+4t +9t°
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r'(t)i+2rj+3rk /1+4t +9t°

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Step 3

T(t) is give...

r'(t)
T(r)(
i+2rj3t k
1+4t 9t
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r'(t) T(r)( i+2rj3t k 1+4t 9t

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