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3) Given vector field F(x,y,z)=<y, xz,x? >. Find N dr where T is the path around the triangle with vertices (1,0,0),(0,1,0) and (0,0,1) traced counterclockwise (when viewed from above.)
Let this cluster to be a subspace of V. Find an orthonormal base
for W.
V = R3 ve W =< (1,0, -1),(0,1, -1) >
3. For the equation 24 = r, in 0 <<1,0<t<1, (1,0) = sin(x), on 0 SEST (0,1)=0, u(1. t) = 0, on 0 <t<1, (1) Using the separation of variables, find its solution.
Let Ě = < 2x + y², 8y + z2, 6z + x2 >. Use Stokes' Theorem to evaluate so F. dri where C is the triangle with vertices (1,0,0), (0,1,0), and (0,0,1), oriented counterclockwise as viewed from above.
2. (5 points) Let T: R2 + R3 be a linear transformation with 2x1 - x2] 1-3x1 + x2 | 2x1 – 3x2 Find x = (x) <R? such that [0] -1 T(x) = (-4)
this two graph are one question.
N P(a,b,c) y X Find the equation of the line in the graph if a = 3, b = 8. c = 7. Select one: O a. (x = 3, z = 7} O b. {y = 8, z = 7} O c. {x = 3, y = 8} O d. (x = 3, y = 8, z = 7} N P (a,b,c) у The line when a = 3, b = 8, c...
The graph of the following function is shown in the figure. Find the largest o such that if 0 < x - 11 < 5 then IF(x) - 11 <0.1. Rx) = 21 x 5 1 yel 2+ y09 1+
1. For pdf f (r, y) = 1.22, 0 < x < 1,0 < y < 2, z +y > 1, calculate: EY) and () E (X2)
Question 3 Determine i1. i1 60 >20 i2 11 v2 12 V 111 20 40 330
Solve the following problem อน a( 1,0) = 0, a(2,0) = f(0), 0 < θ <う