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Evaluating a Line
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Calculus
- Material : complex analysisarrow_forwardWHite the veD secsand orde equation as is equivalent svstem of hirst order equations. u" +7.5z - 3.5u = -4 sin(3t), u(1) = -8, u'(1) -6.5 Use v to represent the "velocity fumerion", ie.v =(). Use o and u for the rwo functions, rather than u(t) and v(t). (The latter confuses webwork. Functions like sin(t) are ok.) +7.5v+3.5u-4 sin 3t Now write the system using matrices: dt 3.5 7.5 4 sin(3t) and the initial value for the vector valued function is: u(1) v(1) 3.5arrow_forwardhow do i solve the attached calculus problem?arrow_forward
- Vector-Valued Function r(t) = (5 sin t, 4t, 5 cos t) O 5 Z 0 oy -5 1.0 0.5 0.0 0.0 -0.5 -1.0 Z 2 5 0.5 4 10 1.0 X X Find its length over the given interval. 3 Interval [0, π] O XO -5 2 yo N 0 -10 X 4 -2 -5 5 10 M 5 Narrow_forwarda) Find the value(s) of (1+ i)2/3. b) Show that cos² z + sin? z = 1, for all z = x + iy, , y E R, V-I= i. c) Find a complex valued analytic function f(x, y) = u(x, y) + iv(x, y), whose real part u(x, y) = 213 – 3r?y – 6xy? + y°.arrow_forwardEvaluate z in rectangular formarrow_forward
- Advanced Matharrow_forwardQUICK CHECK 3 Let u(t) = (t,t, t) and v(t) = (1, 1, 1). Compute d (n(t) • v(t)) using Derivative dt Rule 5, and show that it agrees with the result obtained by first computing the dot product and differentiating directly. <arrow_forwardScalar line integrals Evaluate the following line integral along the curve C.arrow_forward
- Evaluating Polar Integrals In Exercises 9-22, change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. μl pV²-3² 11 12. Jo Jo ra I √a²-x² тугилау dy dx JOJOarrow_forwardLet u(x,y)=4x+3x2y−y3. Part (a) Show that u is a harmonic function. Part (b) Find a harmonic conjugate of u.arrow_forwardmathsarrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning