a) A flexible string of length is tightly stretched between x = 0, x = π, on x-axis, its ends being fixed at these points. When set into small transverse vibration, the displacement y(x, t) from x-axis of any point x at time t is given by Find the solution of equation which satisfies y(0, t) = 0, y(π, t) = 0, at/t=0 = 0 and y(x, 0) = 0.1 sin x + 0.001 sin 4x for 0 < x≤n. = 4 ax²¹

Q: 1) A circular cylinder with radius r cm and heigh (a) Compute V(2, 5). (b) Find the linear…

A: Given: To explain the given statement as follows, Volume V =π r2h cm3

Q: Find the equation of the tangent line to y = = at x = 1. y - V2 = - V7 (x - 1) A) E (x - 1) -- x y -…

A: The solution is given as

Q: (6) Find the orthogonal trajectories of the family of curves r 4C cos 0, where C being %3D…

A: We have to solve given problem:

Q: The tangent plane to the graph of the function f(x, y) = ey at the point with x = 1, y = -1, a) has…

A: Given: A function fx, y=exy at the point x=1 , y=-1. To Find: Equation of tangent.

Q: Let f(x, y) = x2 – y?. Find (a) The directional derivative of f at (-2, 1) in the direction of v = i…

A:

Q: (a) Compute the directional derivative of f(x, y) = xy² + x³y at the point (4, -2) in the direction…

A: Since you have posted independent questions, so these are considered as multiple questions.According…

Q: 3. If the velocity of an object is v(t)=t^2+2t m/s and at t=2s the position is 5m, use Euler's…

A:

Q: 6) What is the tangent plane of f (x, y) = 5x² – 2xy? + 3xy + 4x at point (xo, Yo) = (1, –2) ?

A: The question is solved in step. 2

Q: 2. Let closed curve C consist of the line segment from (0,0) to (2, 1), followed by the line segment…

A: We will solve both the parts using the basics of integral calculus, in particular double integral,…

Q: An object is traveling along the line y = 2x + 1 heading up and to the right. If the temperature at…

A:

Q: ind the fangent line for... 1x1) = +²+et ( (1) = sh (k) + t at t=0 B) r(e) = sinG + case at 6: T

A: Explaination of the answer is as follows

Q: 7. At which direction the directional derivative of f(x, y, z) = 2x² +4y² +9z² at P(1, 2, 1) has a…

A: To determine the direction in which the directional derivative of fx, y, z=2x2+4y2+9z2 at P1, 2, 1…

Q: Consider the equation ze^(xy) + x^(2)yz + 2xy − z^2 − 5 = 0. Assuming that z = f(x, y),find ∂z∂x .…

A:

Q: Given r"(t) = (e^t, sint, cost),  r(0) = (1, 0, 1),  r'(0) = (0, 2, 2),  solve for r(t).

A:

Q: Let f(x,y) = ex/(1+y2) (a) Find a direction u such that Duf(0,1) = 0. (b) At which point(s) on the…

A:

Q: nd the indicated derivative. 8 dv 7) if v=t+- dt t

A: We are asked to find the derivatives.

Q: b. -2åx + 3d, - åz 2. If E = -xả, + yåy V/m, find the work involved in moving a unit positive charge…

A: We can solve using given information and calculate the work done

Q: solve the differenctil equation by undtermeind coefficients y'' +2y = -18x2e2x   y(x) = ?

A:

Q: 1. Find the orthogonal trajectories of the family of curve a2+3y2 = cy ,where c is an arbitrary…

A:

Q: Show that the displacement u(x, t) in an elastic string of length t fireed at both ends which is set…

A:

Q: 4 a. Consider the i.v.p x' = t^(2) + cos(x), x(0) = 0. Verify that the hypothesis of Cauchy Picard…

A:

Q: (5) Find the equation of the tangent plane to z = 1² + xy +3y* at r = 1, y = 1.

A:

Q: 4 a. Consider the i.v.p x' = t^(2) + cos(x), x(0) = 0. Verify that the hypothesis of Cauchy Picard…

A: a. Verifying Conditions of Cauchy-Picard Theorem  b. Estimating the Interval of Existence

Q: 2) (i) Find the equation for the tangent plane to 2 2 z=f(x, y) = 2 x + 3y at the point (2, 2, 20).…

A: The equation of the plane is z=fx,y=2x2+3y2

Q: Q4 A) Consider the i.v.p x' = t^(2) + cos(x), x(0) = 0. Verify that the hypothesis of Cauchy Picard…

A: The objective of the question is to verify the hypothesis of the Cauchy Picard theorem for the given…

Q: Q4 A) Consider the i.v.p x' = t^(2) + cos(x), x(0) = 0. Verify that the hypothesis of Cauchy Picard…

A: Step 1:   Step 2:To estimate the interval of existence of the solution, we can utilize the theorem's…

Q: Q (2):- Given u = x* + 2y'z and v= y- xz Find the velocity component w(x, y, z)

A:

Q: ) Find the slope of the curve x +y3- 6x²y = 0 at x = 1

A: Slope of a curve: For non- linear functions, the rate of change varies along the given curve. So,…

Q: 4. Given that 1 (230)=1+2²² +² (x, y, z) = 1 + ==x² - Find the followings at (1,-1, 1): (a) The…

A:

Q: the

A:

Q: Let f(x, y) = x³ + 2ry – y² be a func the tangent plane to f(x, y) at the poi

A: Here we have f(x,y)=x3+2xy-y2  we have to find the equation of the tangent plane to f(x,y) at point…

Q: Find an equation for the tangent line to the graph of f(x) = -2x2 + 2x + 3 at the point where x = 1…

A:

Q: Find the arclingth of A) r(6) = 4cos (0) OS OS T ... B) / X (²) = +²+1 2 y(t) = 2³² +2 1≤t≤ 3

A: