3.K = |r'(t) x r''(t)|/|r'(t)|^(3/2)
r(t) = [2t ln(t) t^2]
r'(t) = [t 1/t 2t]
r''(t) = [1 -t^-2 2]
K = ln(4)+15
9.s(t) = integral(a,t)|r'(u)|
r(t) = [t^2 2t^2 t^3]
r'(t) = [2t 4t 3t^2]
s(t) = 1/27((20+9t^2)^(3/2)-20^(3/2))
11.r(t) = [2t+3 4t-3 5-t], t=4
r'(t) = [2 4 -1]
v(4) = sqrt(4+16+1)
= sqrt(21)
13.r(t) = [t lnt (lnt)^2]
r'(t) = [1 1/t 2lnt*1/t]
sqrt(1+(1/1)+2ln(1)*1/1]
= sqrt(2)
15.r(t) = [sin3t cos4t cos5t]
r'(t) = 3cos3t -4sin4t -5sin5t]
sqrt((3cos3(pi/2))^2+(-4sin4(pi/2))^2+(-5sin4(pi/2))^2)
= 5

1.r'(t)=[8t 9]
T(t) = 1/sqrt(64t^2+81)[8t 9]
T(1) = [8/sqrt(145) 9/sqrt(145)]
5. r'(t) = [-pisin(pit) picos(pit) 1]
T(t) = 1/sqrt(pi^2+1)[-pisin(pit) picos(pit) 1]
T(1) = [0 -pi/sqrt(pi^2+1) 1/sqrt(pi^2+1)]
7. K = |r'(t) x r''(t)|/|r'(t)|^(3/2)
r'(t) = [0 e^t 1]
r''(t) = [0 e^t 0]
K = e^t/(1+e^2t)^3/2
11. K = |r'(t) x r''(t)|/|r'(t)|^(3/2)
r'(t) = [-t^-2 -2t^-3 2t]
r''(t) = [2t^-3 6t^-4 2]
K = 2sqrt(74)/27
17. K = |r'(t) x r''(t)|/|r'(t)|^(3/2)
K = 48/210*(sqrt(41)/125)
21.K = |r'(t) x r''(t)|/|r'(t)|^(3/2)
r'(t) = [0 cost/sint 1/cost]
k = secht

3. r'(t)=[3t^2 -1 8t]
r''(t) = [6t 0 8]
a(1) = [6 0 8]
v(1) = [3 -1 8]
5.r'(theta) = [cos(theta) -sin(theta) -3sin(3theta)]
r'(theta) = [-sin(theta) -cos(theta) -9cos(3theta)]
v(pi/3) = [1/2 sqrt(3)/2 0]
a = [-sqrt(3)/2 -.5 9]
15. v(t) = [t^2/2+3 4t-2]
r(t) = [t^3/6+3t 2t^2-2t]
17. r(t) = [t 1 t^3/6]
v(t) = [1 t^2/2]
31. Slowing down

1. f(2,2) = 18, f(-1,4)=-5
3. h(3 8 2)=6, h(3 -2 -6) = -1/6
7. y=4x^2
21. H - 3x+4y=12-C
V - (12-3a)-4y=z
23. V-z=a^2+4y^2=x^2+4a^2
33.Contour map starts deeper in center and 
slowly extends outwards with decreasing steepness
utilizing an elipctical shape
35. Countour map slowly extends outwards from center but
this time extending in a rectangular shape

9. lim(x,y)->(1,2)(g(x,y)-2f(x,y))=1
11.lim(x,y)->(2,5)e^(f(x,y)^2-g(x,y))=e^2
15.(1+m^3)/m^2
21.Limit DNE b/c the function values are dependnet
upon the value of m
23.lim(x,y,z)->(0,0,0)(x+y_z)/x^2+y^2+z^2=inf
27.-16e
31.1/5=.2
35.-48