The position of a mass on a spring is given by s = f(t) = 3e−t cos(6t + 8). a. Find lim s(t). t→∞ Interpret this in terms of the dynamics of the mass-spring system. b. Find the velocity and acceleration of the mass.

Q: Find the arclength of y 3x + 4 on 0 < x < 1

A:

Q: Find the arclength of y = 2a/2 on 1 <a< 2

A:

Q: A membranc of uniform density area is stracthed on a Circular frame of radius A to uniform stress…

A:

Q: 4. Find the arc length of function y = x2+ x- 2, -2 SXS1

A: Given: y=f(x)=x2+x-2  and -2≤x≤1 We have to find the arc length of the functionf(x).

Q: Give the number of oscillations occurring per second for a spring-mass system that obeys the simple…

A:

Q: Find the tangent to the folium of Descartes  x  3+ y 3= 6xy  at the point (3,3)

A: Consider the given curve: Here the objective is to find the tangent at point p (3, 3).

Q: Find the arclength of y = 2x + 3 on 0 < x < 3

A: Find the differentiation of the function and then substitute the function in the arc length equation…

Q: (b) Calculate the arc length of the curve y from x = 1 and x = 2. +

A:

Q: 22. Calculate the arc length of the graph of (a) y = f(x) = 1⁄2x³ + x-¹ over [1,3]. Hint: (b) y = 1…

A:

Q: Let y(t) be the solution of dy/dt = 0.3y(2 − y) with y(0) = 1. Determine limt→∞ y(t) without solving…

A:

Q: Let f(x) = x³/2. Determine the length of the arc swept over x E la, b).

A:

Q: Find the arclength of y = 2x3/2 on the interval x is greater than or equal to 1 and less than or…

A: Equation of given curve is y=2x32 Differentiate with respect to x. dydx=232x32-1=3x

Q: find the total length of the arc of the function 6xy = x^4 + 3, x=1 to 2.

A:

Q: Find the gardientoff at the indicatedpoint. frx,y)=D5sin x+Cos3y ;

A: Given: f(x,y)=5sinx2+cos3yπ2,0

Q: Find the arclength of f(x)=x on [0,1].

A:

Q: Find the arclength of y = 2x + 5 on 0 < x < 4

A:

Q: Let y(t) be the solution of dy/dt= 0.3y(2 − y) with y(0) = 1. Determine lim t→∞y(t) without solving…

A:

Q: Find the arclength of y = 3r/2 on 1 < a < 3

A: As we know that the expression for the arclength is:   l=∫x1x21+dydx2dx...(1)   Given: y=3x32x→1 to…

Q: Use the Chain Rule to find az/as and az/at. as az at || || z = arcsin(x - y), x= s² + t², y = 3 -…

A: Given z = arcsin(x-y)x = s2 + t2y = 3 - 4st

Q: Find the arclength of y = 2a + 4 on 0 < a < 4

A:

Q: Compute the trapezoidal approximation T5 to the arc length s of y = tan x over [0, 4].

A:

Q: Set up an integral that represents the arc length of the function y=2x^4+4x from the point (0,0) to…

A:

Q: Find the speed of the cycloid c(t) = (2t – 2 sin t, 2 – 2 cos t) at points where the tangent line is…

A:

Q: Find the arclength of y = 2x/2 on 1 < x < 3

A:

Q: Let y = tan(5x + 3). Find the differential dy when æ = 2 and dæ = 0.3 Preview Find the differential…

A:

Q: A force of F = 14x – x N stretches a nonlinear spring by x meters. What work (in J) is required to…

A:

Q: dz dz Use the chain rule to find and as at arcsin(x – y), x = s² + t², y = 4 – 9st Z = az as az at

A:

Q: Let f(x) = x3/2. Determine the length of the arc swept over r E (a, b).

A:

Q: Find work done from the followingW = G- sec²(3x)- V8) dx witch Gx +9 h used to stretch a spring from…

A:

Q: Find the point on the cycloid c(t) = (t − sin t, 1 − cos t) where the tangent line has slope 1/2.

A:

Q: 4. Use the arc length formula to show that the length of a linear function f(x) = mx +c on the…

A:

Q: 1- cos(Vr² + y?) lim (x,y)→(0,0) • (a) Va2 + y?

A:

Q: - Find the arc length of f(x) = (-) (x² + 2)ž on the interval [0,9)

A:

Q: Find the arclength of y = 3x + 1 on 0 <x < 3 %3D

A:

Q: Construct (a) slope field for the DE: y'+4 y'=x (b) tabulate the values at these 5 points ( 0,0 )(…

A: We have to sketch the slope field for the differential equation y'=x2-4y2. Then we  will tabulate…

Q: Find the arclength of y = 3x2 -5 on x is greater than or equal to 0 and less than or equal to 2

A:

Q: Find the arclength of y = 4x + 3 on 0 < x < 2

A:

Q: If y = 1+ sin t ,x = cost at t = Findy by using Chain Rule, then choose the correct answer: dt

A: Given that: y=1+sintx=cost

Q: Find the arc length from (x1, y1) to (x2, y2) on the graph of f(x) = mx + b.

A: Given Data The first point on the graph is (x1, y1). The second point on the graph is (x2, y2). The…

Q: Find the arclength of y 2x +1 on 0 < x < 2

A:

Q: Find the exact arclength of y = 2x3 for 0≤ x ≤ 2:

A:

Q: Find the arclength of y = 2x/2 on 1< x < 3

A:

Q: Let y tan(3x + 6). Find the differential dy vwhen a 2 and da 0.4 Find the differential dy when z 2…

A:

Q: Find the point on the curve F(t) - (5 sin t)i + (5 con t)j+ 12tk at a distance 20 units along the…

A: Let's find.

Q: Find the length of the catenary y = a cosh from x = 0 and x = a X1.

A:

Q: Find the arclength of y = 2x/2 3/2 on 1 < x < 3

A: We know that the arclength of a curve y=f(x) on a≤x≤b is given by L = ∫ab1+f'(x)2 dx

Q: 1. Find the arc length of the curve f(x) = 3 4 (x + 2)2 on the interval [0, 4]. 3

A: Find the arc length

Q: Find the arclength of y = 2x +1 on 0 < 1< 3

A:

Q: 1.) Use the arc length formula to find the length of the curve y = 3x + 2 on the interval 0 ≤ x ≤ 3.

A: Given data  y=3x+2 Interval ÷ 0≤x≤3 Formula for arc length is given by  L=∫ab1+dydx2dx