INSTRUCTIONS: ANSWER THE FOLLOWING QUESTION. NO SOLUTION NEEDED AS LONG AS THE FNAL ANSWER IS CORRECT. FOLLOW THE FORMAT.

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Chapter 13, Section 13.9. Question 025 Using Lagrange multipliers, find three positive numbers whose sum is 24 and such that the sum of their squares is as small as possible. Enter the sum of the squares. Minimum value = :l exact number, no tolerance Chapter 12, Making Connections, Question 002bi Use the fact that N () can be expressed directly in terms of r (t) as u (t) NO= where to find N (1) . r (t) = sint . i+ cost . j+ t . k Answer: N() = N . i+Nj . j + Me . k where NE ? Edit Ni = Edit NK = ? EditChapter 12, Section 12.1, Question 003 Find the domain of r() and the value of r(to). r (t) = cos(at )i - Intj + Vt - 14k; to = 15 Enter the domain in interval notation. Round your answer to two decimal places when needed. Domain is: ? Edit r(to) =Chapter 12, Section 12.1, Question 010 Describe the graph of the equation. r = ll sin 4ri-11 cos 4t j O It is an ellipse in the xy -plane, centered at the origin, with major axis of length 11. O It is a circle of radius 11 in the xy -plane, with center at the origin. O It is a circle of radius 4 in the xy -plane, with center at the origin. O It is a parabola in the xy -plane, with vertex at the origin. O It is a circle of radius 11 in the xy -plane, with center at the point (4, 4) .Chapter 12, Section 12.2, Question 001 Find the limit. 12 + 7 lim 1+ +00 612 + 7 " Enter the answer using round brackets. +7 lim Edit 612 + 7 ?Chapter 12, Section 12.2, Question 029 - [r(t) . r2(@)] = r(1). dry+ L . I2(t) and Calculate - [ri (t) . r2 ()] and d - [ri (1) x r2 (1)] first by differentiating the product directly and then by applying the formulas dt dt dt dry dri + dt [ri (1) x12(1)] = ri(1)xdt dt x r2(t). ri (t) = 7ti + 67- j + 7+3 k, r2(t) = # k -[ri (t) . r2(()] = dt ? Edit a dt [n (t) x 12(()] = Edit i+ ? EditChapter 12, Section 12.2, Question 033 Evaluate the indefinite integral. 3te', Int ) di = Edit it ? Edit i+cChapter 12, Section 12.3, Question 006 Find the arc length of the parametric curve. x = 14cost, y = 14sint, z= 48t Outs L = EditChapter 12, Section 12.5, Question 013 Find the curvature and the radius of curvature at the stated point. r () =5 cos fi+ 1l sin tj +4t k; = Enter the exact, simplified answers. K= Edit P Edit