Answer:



Step-by-step explanation:
Given



(0, 1, 0)
The vector equation is given as:

Substitute values for x, y and z

Differentiate:

The parametric value that corresponds to (0, 1, 0) is:

Substitute 0 for t in r'(t)




The tangent line passes through (0, 1, 0) and the tangent line is parallel to r'(0)
It should be noted that:
The equation of a line through position vector a and parallel to vector v is given as:

Such that:
and 
The equation becomes:




By comparison:
and 
The parametric equations for the tangent line are:



5.its correct answer. 6.complimentary 7.supplimentary
We know, S = n/2 [ a + l ]
Here, a = 45
l = 108
Calculation of n:
a(n) = a + (n - 1)d
108 = 45 + (n - 1)1
108 - 45 = n - 1
63 + 1 = n
n = 64
Now, substitute in the expression:
S = 64/2 [ 45 + 108 ]
S = 32 [ 153 ]
S = 4896
In short, Your Answer would be 4896
Hope this helps!
F(1/3)=9(1/3)-2
f(1/3)=3-2
f(1/3)=1