Solve the following problems completely. Estimate (1.02) V0.99 using a local linear approximation of f(r) = (3 – 2r) /T.

Q: The atmospheric pressure at altitude h (kilometers) for 11 ≤ h ≤ 25 is approximately…

A: Given: P(h)=128e-0.157h

Q: (2) From assumption (c), the velocity (v) at time (t) of the water droplet is 3. v' + t+ro If the…

A: This is a linear differential equation which have to be solved using integrating factor

Q: Find the supply function x = f(p) that satisfies the initial conditions. dx 10 x = 160 when p = $1…

A:

Q: Estimate v99 by using a linear approximation of f(x) = /x about the value c = 100. Round your answer…

A: We use the power rule. Then we find f(x) and f'(x) at x=100

Q: For the position function, s(t)=-16t2+103t​, complete the following table with the appropriate…

A: Consider the position function, s(t) = 16t2+103t.

Q: Answer part D.

A: As we consider the approximation of function have already done in  above parts,(D) When change in x…

Q: If the velocity is given by : (-t^2 i + 2t^2 j+ t^2 k) then the normal component of the acceleration…

A: Given: Velocity: vt=-t2i+2t2j+t2k. Then, v't=-2t i+4t j+2t k Find the normal component of the…

Q: Solve the following initial value problem for y as a function of x dy 3+ /39 Vx² - 2- 25 = 1, x> 5,…

A: Here we have to use the following formula 1)  ∫dxx2-25=ln x+x2-25+c2)  lnab=ln(a)-ln(b)

Q: Please answers part c, d

A: As per norms, the first three questions are answered. The questions concern the linear approximation…

Q: The total derivative of f(x,y) = e2x +5y is df =

A: Consider the following function: fx,y=e2x+5y Total derivative of function:…

Q: Solve the following differantial equation using finite difference method. d²x(1) + x(t) = 0 dt? dx…

A:

Q: Find the amount of medicine to which the body is most sensitive by finding the value of M that…

A: Given

Q: Suppose that a particle moving along the x-axis encounters a resisting force that results in an…

A: Definition used -                   v=∫adts=∫vdt

Q: The acceleration function of a particle moving along a line is given by: a ( t ) = 2 t + 3 in m / s…

A:

Q: The value of the instantaneous velocity at t = 1 is

A: Consider the position function To calculate the instantaneous velocity

Q: Consider J(0) = 30* + 1. Let e = 0.001, compute the numerical approximation to the derivative at 0 =…

A: The given problem is to find the derivative of the given function at point 2 with given accuracy…

Q: In the given question , consider a particle moving along the x-axis, where x (t) is the position of…

A: Givenx(t)=t3-6t+9t     0≤t≤5

Q: Suppose the position function of a moving object is given by s (æ) = Væ. Then the average velocity…

A: Given that: To find:

Q: ) Suppose that the acceleration function of a particle moving along a coordinate line is a(t) = t –…

A: a)Givena(t) = t - 3Now average acceleration is given by ∫aba(t)dtb-aHere a=0 and…

Q: A particle moves along the x-axis with velocity given by v(t) = 6t – 6t for time t > 0. If the…

A:

Q: e f² = ¹² Use Simpson's Rule to estimate dx with a maximum error of 0.1.

A: Simpson Rule According to Simpson's Rule, ∫abfxdx=∆x3fx0+4fx1+2fx2+........+4fxn-1+fx2

Q: 1. (a). Find the linear approximation to f(x) = VT at r = 81, (b). use it to approximate V85. (c).…

A:

Q: Evaluate the second derivative of e22.1.png а f(x) acos(b/x) x2 if a = 345 and b = 0.6 at x = 5…

A: Given: Let us consider the given, fx=acosbxx2 where a=345 & b=0.6 at x=5 using BDA with ∆x=0.06.…

Q: A particle moves along the x-axis with velocity given by v(t) = 10t + 12 for time t> 0. If the…

A: For the given velocity  v(t) = 10t +12 for t>=0 if the position is x =2  at time t = 0  Position…

Q: For what function P is the integrating factor α(x) equal to x?

A: We know that , integrating factor of the differential equation is

Q: A particle moves along the x-axis with velocity given by v(t)=3t^2-6tv(t)=3t2−6t for time t\ge…

A: Answer and explanation is given below..

Q: Given the function s(t)= -16t2 + 128t, what is the average velocity at time interval [1,2]? Then…

A: The given function is,

Q: For what function P is the integrating factor α(x) equal to ex?

A: Here the given integrating factor

Q: 1. The position of a particle at time t is given by s(t) = t³ – t2. Using a table, estimate the…

A:

Q: A particle moves along the x-axis with velocity given by v(t) = 10t + 12 for time t> 0. If the…

A: Given: The velocity of the particle along x-axis is vt=10t+12 The particle is at the position x=2 at…

Q: A particle moves along the x-axis with velocity given by v(t) = 6t2 – 18 for time t > 0. If the…

A:

Q: If the velocity is given by : (-t^2 i + 2t^2 j+ t^2 k) then the normal component of the acceleration…

A:

Q: The movement of a particle from time t=0 to t=4 is given by the equation s(t)=−5t2−10t−6. What is…

A:

Q: Given the following function, determine the maximum rate of change of it at the point P(0,0, 1/2).…

A:

Q: The accompanying graph plots the best quadratic fit, a(t) = − 0.70t^2 + 1.44t + 10.44, to the data…

A:

Q: If the position of a particle on the x-axis at time t is-5t", then the average velocity of the…

A:

Q: If s(t) is the position on the x-axis of a particle at time t, then the quantitys(t + h)−s(t) / h…

A: If s(t) is the position on the x-axis of a particle at time t,

Q: A particle moves along the x-axis with velocity given by v(t) = 6t² + 1 for time t > 0. If the…

A:

Q: A particle moves along the x-axis with velocity given by v(t) = 6t² – 10t for time t> 0. If the…

A:

Q: A particle moves along the x-axis with velocity given by v(t) = 3t2 + 12t – 6 for timet > 0. If the…

A:

Q: 33. The atmospheric pressure at altitude h (kilometers) for 11 <h< 25 is approximately P(h) =…

A:

Q: Given y = V4x+5, find the differential dy when x = 7 and dx = 0.3. Round your answer to three…

A: Take derivative with respect to x and put the given values.

Q: Calculate the error of approximation with Ea for the following functions when x = 2, Ax = dx = 0.08

A: If the input of a function y=f(x) changes, its output also changes. The derivative of a function is…

Q: Q2: Use bisection to determine the drag coefficient needed so that an 80-kg parachutist has a…

A: Solution :-

Q: What is the derivative of r(t)=e^(4t)costi+e^(4t)sintj+e^(4t)k

A: Differentiate both sides with respect to t.

Q: Approximate v10 using a linear approximation. Round to 5 decimal places. つ

A: Here is the solution

Q: Find the antiderivative of the given derivative. ds = 14t(5t2 – 1)3 dt S=

A:

Q: Given y = = V4x + 5, find the differential dy when.x 7 and dx = 0.3. Round your answer to three…

A:

Q: Given the graph of the linear function y = k(t) with k(6) = 24. %3D y 2A A 6 t 8.1 Show how you use…

A: 8.1) Given:     y=kt with k6=2A Area ∫06ktdt        Substitute kt=2A            =∫062A dA