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Q: 2. Verify that the given function u=e* sin y is harmonic and then find a harmonic conjugate of u.…
A: For function to be harmonic, del^2(U) = 0.
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A: We can answer both the question in the following steps.
Q: 4. j(x) = x² sec x %3D
A: We can solve question no 4 as below.
Q: dy xev-x*); y(0) = 0 %3D dx
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Q: Q8. The general solution of the differential equation dy x-1 %3D -2 is dx y+2' Y #
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A: Given query is to the derivative of the expression.
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A: 1. =∫2sin(3x) sin(4x) 2 dx=∫12-cos3x+4x+cos(3x-4x) dx=∫12-cos7x+cosx dx=∫12[cos(x)-cos(7x)] dx
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Q: To apply this test we must first find Y'(N). Doing so gives the following result. kN Y(N) 16 + N2…
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Q: 0; x 0
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Q: 3. Find the interval fconvergence of the Sevies : 1-3(x-4) + 9 x-4)-..
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Q: Blowing Soap Bubbles Carlos is blowing air into a spherical soap bubble at the rate of 7 cm³/sec.…
A: V=(4/3)πr3 now differentiate it with time dV/dt = 4πr2dr/dt 7 = 4(22/7)*9*9(dr/dt) dr/dt =…
Q: Find the area bounded by the curve 2x2 + 4x + y – 0 and the line y + x = 0
A: To find the area of region bounded by the given curves.
Q: a) E}Ej³ b) Σ59/2 250 c) E}soj 100
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Q: ential equation of the family of curves y B are arbitrary constants
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Q: nd the implicit differentiation by using Total Derivatives a unction, x³ cos(2y) – 3x4 + 2e3y
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Q: Evaluate the integral over the rectangle R: (a) |/ ev dA, 0 < ¤ < In 2, 0 < y < In 2 R (b) dA, 0 < x…
A: As we know that; The Power rule; ∫xndx=xn+1n+1+C ; n≠-1 And ∫eax+bdx=1aeax+b+C (a). Given:…
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Q: e component form of u + v given the lengths of u and v and the angles that u and v make with the…
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A: Note: As per the company policy we are supposed to solve only one question, so kindly repost…
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Q: Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat…
A: Given dr=0.08 cm, d=65 metres r=d/2=65/2=32.5 metres Now convert r into centimeters r=32.5*100=3250
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Q: find dx/dt at x=1 if y=3x^2+3 and dy/dt=1
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Q: Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b). (Select all…
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Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u, v,…
A: To find the volume of the parellelepiped having given adjacent sides u,v and w.
Q: . Evaluate the limit of a function using the concept of Special Limits. et-1 t2-3t+5 + t2-1 1. lim t
A: Given that a limit problem and we solve this problem by using general property of limit. Here i…
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Q: Let y 3T. Find the change in y, Ay when x 2 and Ax 0.3 Find the differential dy when a 2 and da 0.3
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Q: 3. For f(x) = rV9-x, find a). domain, b). f', the intervals on which f is increasing or decreasing;…
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Q: Match the integral expression on the left to an equal expression on the right. Ssin(3x)sin(4x)dx -…
A: Let's find.
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Q: The integral expression J xcos-(2x)dx can be evaluated using integration by parts of the form…
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Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…
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Q: The integral expression J xcos (2x)dx can be evaluated using integration by parts of the form…
A: This is a problem of integration. Based on the uv formula we will solve the question.
Q: Given the following vectors a = (-1,–2),5 = (-3,-4),6 = 2,-1), d = (-4,3) %3D Use the dot product…
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- Consider the following parametric equations: x=t^2+5t+4, y=4t. Find dy/dx, d2y/dx2, and the line tangent to the curve at point t=0.Solve for the critical points of parametric equation x=t^3-1, y=t^2+tConsider the graph ofr(t) = 2t^2i + t^2j + t^3 kDetermine parametric equations of the tangent line to the curve at the point where the curve intersects the planex − 2y − z = 8.
- Determine the total distance covered from t = 1 to t = 3 from the given parametric equations: x = t^3, y=2t-1, z = 4t^2If I have a pair of parametric equations x=20cos(t) and y=10sin(t) How can I increase the speed of the particle moving in these path x2/400 + y2/100=1consider the parametric curve x=t2 , y=9t-t3 . find dy/dx at t=2.
- Consider the following parametric curve: x(t) = 3t^2 −6 and y(t) = 3t^4 −3t^2 +12t +10 Find the equation of the tangent line to to the point along the curve at(−3,−2).Consider the parametric equations:x = 4t + 4 sin t y = 4t + 4 costFind the value(s) of t for which the tangent to the parametric curve has the same gradient asthe line y = x.Determine the exact length of the curve for the parametric equation x = tsint and y = tcost for 0 ≤ t ≤ 1.
- Consider the parametric equation x = t2 - 1 and y = t2 + 2t. (a) find (dy)/(dx) and (d2y)/(dx2). (b) Set up, but do not evaluate, and integral representing the arc length over the interval 2 ≤ t ≤ 4.Find the equation for the line tangent to the parametric curve: x = t^3 - 9t y = 9t^2 - t^4 at the points where t = 3 and t = -3. For t = 3, the tangent line (in form y=mx+b) is y = ? For t = −3, the tangent line is y = ?