In Problems 20 to 31, evaluate each
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- 5. Prove that the equation has no solution in an ordered integral domain.arrow_forwardCompute sin z dz , where a is the piece of the parabola with equation y = a?, which lies between the points 0 and -1+i.arrow_forward. Given f(x, y) = sin(x²) + xy³, find Duf(x, y) where u is in the direction of (1,2). What is Duf(-2, 1)? What does this represent?arrow_forward
- Differentiate, T. (cb-da-db T (ch btd with respect to T ●arrow_forward14. Consider the two vector-valued functions given by 1 r(t) = (t+1, cos 1+t and w(s) = (s, sin (), ). a. Determine the point of intersection of the curves generated by r(t) and w(s). To do so, you will have to find values of a and b that result in r(a) and w(b) being the same vector. b. Use the value of a you determined in (a) to find a vector form of the tangent line to r(t) at the point where t = a.arrow_forwardThis is Vector Calculus. Please answer thoroughly with clear answers and explanations. This is a 4 part question split into two different posts. PLEASE ONLY ANSWER PARTS A AND B. Thank youarrow_forward
- c. r(t) = cos (t - /2)i + sin (t d. r(t) = (cos t)i – (sin 1)J• 20 %3D %3D niz mil e. r(t) = cos (r)i + sin (12)j, t0 v 38. Motion along a circle Show that the vector-valued function %3! r(1) = (2i + 2j + k) + cos t il + sin i + j+ k V3 describes the motion of a particle moving in the circle of radius 1 centered at the point (2, 2, 1) and lying in the plane x + y - 2z = 2. 39. Motion along a parabola A particle moves along the top of the s bai 1 smit %3Darrow_forwardEvaluate √(2² + yz sin(xyz))dx+(y²+xz sin(xyz))dy+(x+xysin(xyz))dz where C is the curve following the outline for the triangle from (1,0,0) to (0,1,0) to (0, 0, 1) and back to (1,0,0).arrow_forwardEvaluate ſ Im(2) dz over the line segment that joints the point 2+ 3i to 4+7i by using the parametrizations (a) z(t) = (2+3i)(1 – t) + (4 + 7i)t, 0arrow_forwardGiven vector r(t)= (t2,t3,t) a. Find dr(t)/dt b.Find the unit tangent when ? = 1 c. Evaluate the integral from -2 to 1 of r(t)dt (Picture of question is provided for letter c.arrow_forwardA net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by v = (x - y, z + y +7,z²) and the net is decribed by the equation y = √1-x²-2², y 20, and oriented in the positive y-direction. (Use symbolic notation and fractions where needed.) 1.45-1 yasarrow_forward2.4 Prove that the contour integral |(e* – z)dz = -12i where C is the triangle with points 0, 3i and -4 oriented anticlockwise.arrow_forwardarrow_back_iosarrow_forward_ios
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,