Find the average velocity of the function over the given interval. 2) h(t) = sin (3t), |0, D) A) B)

Q: A particle moving along R(t) = r cos tî + r sin tj, r > 0, has an instantaneous speed that varies…

A:

Q: z = e*sin y, Mo (1,2) 6

A:

Q: Integrate f(x,y) = x + y over the curve C: x2 + y? = 9 in the first quadrant from (3,0) to (0,3).

A:

Q: Given a particle with the position function r(t) = t/ti+ (Int) j+ eʻk,

A: (a)    r(t)=tt i+lntj+etk Differentiate both sides with respect to t   ddt(r(t))=r'(t) =…

Q: in integating the function fxcos(3r) de using integration by parts, what would you choose for your…

A:

Q: The linear approximation at r 0 to sin(2r) is A+ Br where A is: and where B is:

A:

Q: Evaluate the line integral, where C is the given curve. [x² x sin(y) ds, C is the line segment from…

A:

Q: If f(x) = xe , x >0 and (Y = ln(X)), then the PDF of Y is %3D (In(1)² (In(y))e ye

A: Answer: ⊙ ey-12e2y

Q: 2 dy dx Evaluate the integral: 1+Vx? +,

A:

Q: a) Determine the average value of the function f(t)=t² – 5t + 6 cos at on the given interval –1,

A: As per guidelines, we will solve only first question. Kindly repost other question separately.

Q: In a mass-spring-dashpot system , the mass’s position at time t isy = 4e-t(sin t - cos t), t ≥…

A: Given: y=4e-tsint-cost, t≥0 The average value of y over the interval 0≤t≤2π

Q: Find the total differential. w = = x?yz° + sin(yz) dw =

A: In partial derivatives, the total derivative approximates the function with respect to all of its…

Q: Given a particle is moving in a curve r(t) = cos 8t i + sin 8t j+ 8t k. Find the tangential…

A: The given curve is r(t)=cos 8t i + sin 8t j + 8t k

Q: Consider a rod of length meters with density 8(x)=(2- cos x) kg/m over the interval 0<x<5.

A: Given that The length of rod is π2 and the density of the rod is δ(x)=2-cos(x)  with 0≤x≤π2 To find…

Q: Find the total differential. z = x cos(y) – y cos(x) dz =

A:

Q: A cylinder of radius r and height h has volume V = nr 2h.(a) Use the Linear Approximation to show…

A: Given: A cylinder of radius r and height h has volume V=πr2h a)  show:  ΔVV≈2Δrr+Δhhb)  Percentage…

Q: 1. Integrate using Integration by Parts: I sec? x dx

A:

Q: Use runge-kutta method find an approximate value of y corresponding to x = 0. 1, given that: dy * =…

A: We have function f(x,y)=x+x2y, y0=1, and h=0.1. We have to use the Runge-Kutta method to find an…

Q: Find the velocity, acceleration, and speed of a particle with the given position function. 1. r(t) =…

A:

Q: Evaluate the line integral, where C is the given curve, (x + 9y) dx + x2 dy,  C consists of line…

A: Consider the line integral,

Q: The linear approximation at z = 0 to sin(4z) is A+ Bz where A is: and where B is:

A: Linear approximation is found by L(x)=f(x)+f'(x)(x-a) Differentiate L(x) with respect to x.…

Q: Let y = sin(5x). If Aa 0.1 at z = 0, use linear approximation to estimate Ay Ay 2 Find the…

A: solution

Q: (a) Compute the average temperature of a wire in the shape of a helix c(t) = (cos(t), to, sin(t)), t…

A: To find- Compute the average temperature of the wire in the shape of a helix ct = cost, t10, sint, t…

Q: Find the approximate value for f(r, y) = sin(a7zy + In(y)) at (0.03, 1.04). Take a = 3.

A: We have to find the linear approximation of the given function around suitable point.

Q: Find the total differential. z = 10x6y7 dz = %3D

A:

Q: The differential of with respect to t is obtained by the quotient rule of differentiation. + 8 du d…

A: From the given data:

Q: Find the approximate value for f(z, y) = sin(x5zy+ ln(y)) at (0.03, 1.04). Taken = 3. 00,24 O 0,14 0…

A:

Q: The joint PDF of the r.v. A and B is constant on (a, b): a, b > 0n 0.5 0.5|X<0.5).

A:

Q: Let y = sin(2x). If Aa 0.3 at a 0, use linear approximation to estimate Ay Ay = Find the percentage…

A:

Q: The integrating factor of the linear DE dy + ycot x = sin x dr

A: Given: dydx+ycotx=sinx

Q: Find the total differential z = e−x tan y

A: we have to find the total differential of z = e−x tan y           dz=∂f∂xdx+∂f∂ydy        (1) where…

Q: Calculate the integral | (2x + sin y) dx + x cos y dy 7, where L is any curve from the A(0,0) to B (…

A:

Q: Find the average value of the function f(t)=2t sin[r²) on the interval [0, /7].

A:

Q: he The product of linear integration is where c t $ (2xy – x²) dx + (x + y²)dy, x = y? 30 y = x? ,…

A:

Q: What is the formula for the total distance traveled by an object with a velocity v(t) = O - ¹ sin…

A:

Q: Evaluate the integral a sin y ds where C is the line segment from (0, 3) to (4,6),

A:

Q: SI 1 Evaluate the triple integral S dx dy dz xyz 1

A:

Q: b) f(x): 1 + sec2

A:

Q: Set up an integral that represents the length of the curve. = sin²(t), y = 1 –- 3 sin(t), 0 <t < T…

A: The given problem is solved below.

Q: Apply trapezoidal and Simpson's rules to the integral 1 =[ \1-x² dx h=0,2

A:

Q: Find the total differential. z = x cos(y) -y cos(x) dz %3D

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: a. Apply the Runge-Kutta method of 4th order to find the approximate value of y for x =0.2, dy in…

A:

Q: Find the displacement of the particle with velocity function v (t) = -3 cos (t+) between t 0: %3D t=

A: Consider the function v(t) and the expand it to simplify v(t). Now, refer the value for displacement…

Q: Approximate∫b,a f(x)dx by computing Lf(P), Uf(P), left sum and right sum of the following integral:…

A:

Q: Find the total differential. z = e4x sin(3y) dz =

A:

Q: The linear approximation at and where B is: = = 0 to sin(9x) is A + Bx where A is:

A:

Q: Find the value of 'h' in 8 dx evaluating by 1+x Trapezoidal rule braking in 24 intervals. 1.25 0.25

A:

Q: Find the displacement of an object over the time interval, [0, t/4], given the velocity function,…

A: Here, the velocity function is given and we are required to find the displacement in the given time…