The acceleration of a truck is given by t2 +t a(t) = cm² / sec when 0

Q: Determine the equation of the tangent line for y = sech(In x) + tan-(x²) tangent at x = e*. A. Yr =…

A: The equation of the  tangent line for the function f(x) at the point x=a is, y-fa=f'ax-a. The…

Q: The linear approximation at x = 0 to sin(2x) is A + Bx where A is: Preview and where B is: Preview

A:

Q: In explicit method of hyperbolic PDES, the second initial condition, the one involving g, gives…

A: Given,

Q: line with a constant acceleration of -8 ms 2. A De in the direction that the particle is initially…

A:

Q: 4. It f(x,)= (x?+Zy^)+Z and ū= a.) Find the derivative of t in the direction Of ū at 13,2) -

A:

Q: The linear approximation at æ = 0 to sin(2z) is A + Bx where A is:| Previev and where B is: |…

A:

Q: Prove the formula.

A: Given a function Arc Sine Hyperbolic (t). We need to find the derivative of the function. Let's…

Q: Find the local linear approximation of f(x) at 4 + x xo = 3, where Ax = x – 3. NOTE: Enter the exact…

A: f(x)=14+x

Q: What is frz, fyy, and fyz of f(x, y) = In(y²")?

A: Given:           f(x,y)=lnyx2          fx=∂∂xlnyx2         Treating y as constant variable…

Q: Use Taylor’s formula to find a quadratic approximation of ƒ(x, y) = cos x cos y at the origin.…

A:

Q: Find the total differential. z = 5x3y9 dz =

A:

Q: If the acceleration of a particle is given by ä = sint i+ cost +e k, find the relity and position…

A: The acceleration of a particle is…

Q: Consider f(x, y) =(ax² + by²). Based on the second derivative test, what are the conditions…

A: Answer

Q: 2. A particle moves along the parabola y = x in the first quadrant in such a way that its…

A: Given: A particle moves along the parabola y = x2 in the first quadrant in such a way that its x -…

Q: A stone, projected vertically upward with initial velocity 112 ft/sec, moves according to s = 112t -…

A:

Q: You would like to use differentials to approximate the change in BMI when weight increases from 55…

A: Given: The function represents body mass index(BMI) is  Bw,h=wh2 where, w means weight in kilograms…

Q: 3. S sec z tan z dz 2 2

A: Given: 3.∫sec23z tan23zdz

Q: What is the largest value that the directional derivative of ƒ(x, y, z) = xyz can have at the point…

A:

Q: The linear approximation at x = 0 to sin(3x) is A + Bx where A is: Preview and where B is: Preview

A: Given function:

Q: tany = C secx

A: The question clearly asks us to find the family of orthogonal trajectories of the given family.…

Q: Find the maximum rate of change of f (x, y) = xy ^ 2 + root (y) at the point (2,1). in which…

A: The maximum rate of change of f(x, y) happens along the direction grad(f) at the given point (2, 1).…

Q: b) Find if Scosy Vt3 + 5 dt + tany = x -sinx b) Find if S* Vt2 + 5 dt + siny = x – x°cosy dx2

A: Solve by differentiation

Q: The directional derivative of f(x, y) = ln(xy) + x² at the point (-1,1) in the direction of from the…

A: We have to find the directional derivative.

Q: Find the set of orthogonal trajectories for r = VA sin (2e)

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Q: Use differentials to approximate V36.1. 3.

A: Consider y = root x.Let take x = 36 and delta x = 0.1.Find delta y as follows.

Q: The linear approximation to 1 over sqrt(5-x) at x=0 is y=?

A: To find the linear approximation at x = 0 to the function 1/sqrt (5–x).

Q: A hollow cylinder has a radius R of the outer surface, radius r of the inner surface and height h.…

A: Given, a hollow cylinder has a radius (R) of the outer surface, radius(r) of the inner surface and…

Q: A particle moves along the x-axis with velocity dx/dt = ƒ(x). Show that the particle’s acceleration…

A:

Q: 2.Evaluate the total derivative of u with respect to x for u = 6x²+4y² + 4z² when y = cosx and z =…

A: We have to find total derivative of u with respect to 'x'    where     u = 6 x2 + 4 y2 + 4 z2  Given…

Q: What is the isogonal trajectories family of curves x² - y² = a which intersects at an angle of ∅ =…

A:

Q: Y2-1 dy

A: Follow the procedure given below.

Q: 2. Suppose that 2 J of work is needed to stretch a spring from its natural length of 30 cm to a…

A: Given data: The work done is 2 J. The change in length is (42-30)=12 cm=0.12 m The expression for…

Q: ) A Cylinder tank of radius 4m and height 10m is initially filled with water. At the bottom of the…

A: Given that radius of a Cylinder tank is 4 meters and Height of tank is 10 meters. A hole is at the…

Q: 2. Use second order derivative to derive the acceleration, a for an object that falls where its…

A:

Q: Find the first-order partial derivative with respect to x of f(x,y) = e5x siny.

A: To find the first-order partial derivative with respect to x, given function, fx,y=e5x sin y

Q: 3. Verify the statement by showing that the derivative of the right side is equal to the integrand…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: (a) The centripetal acceleration of a particular wheel in a locomotive with respect to the angle…

A:

Q: If f has a continuous second derivative on [a, b], then the error E in approximating f(x) dx by the…

A: (a) Trapezoidal Rule. First we need to find the maximum of f''x. In the problem given, fx=7x.…

Q: For the slope field shown, which could be a family of anti-derivatives? TUN | 31 1112+\ll || \ ++~…

A: A slope field shows the slope of a differential equation at certain vertical and horizontal…

Q: Calculate the derivative d In (t)dt dx Ja4 using Part 2 of the Fundamental Theorem of Calculus.…

A:

Q: Solve the nonhomogeneous ODE by variation of parameters. ODE: y" + 4y = cosh 2x

A:

Q: The population of a city is associated by the function P(x,y,z)=x² + 2y² + 2z². If the population of…

A:

Q: Suppose a particle has velocity given by v(t) = sin(t). What is the net displacement of the particle…

A: GIVEN DATA : Velocity of  the particle v(t)=sin(t)        TO FIND : Displace of the particle on 0,…

Q: A bounded, 3B > 0 such that |f(x)| < B Vx € (0, 1), continuous function on (0, 1) with unded…

A: We will find an example

Q: B: Use the Chain Rule to find the derivative of f(x,y) = xy with respect to (t) along the path y =…

A:

Q: Test for homogeneity

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Q: The minimum value of n required to approximate xe dx by composite Trapezoidal rule with an error…

A: Find the minimum value of n required to approximate ∫02xe-xdx by composite Trapezoidal rule with and…

Q: Find the maximum directional derivative of the function f(x.y) = x In y + x2y2 at the point (-1,1).…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.