The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 3 sin at + 2 cos nt, where t is measured in seconds. (Round your answers to two decimal places.) (a) Find the average velocity during each time period. (i) [1, 2] cm/s (ii) [1, 1.1] cm/s (iii) [1, 1.01] cm/s (iv) [1, 1.001] cm/s (b) Estimate the instantaneous velocity of the particle when t = 1. cm/s

Q: 1. Find the slope and the rate of change of the slope with respect to x when t = 90°. x = 2…

A:

Q: - a. Find the derivative of 3y – 2xy² = sin x + cot y b. Find the derivative of 2y x(3³) – In(²/²) =…

A:

Q: A weight on a spring is bobbing up and down. Its height above the ground at time t is h(t) = 5 + cos…

A: velocity of weight will be 2 detailed solution is given below

Q: 1) Find the equations of the lines that are tangent to Y = 0.5(sin 2t) at the origin the curve COs…

A:

Q: solve all conected Question 3: Find the equation of the tangent line to the curve at the given…

A:

Q: The horizontal distance or range (R) of an object thrown at an angle theta from the horizontal is…

A: This is basic derivative problem

Q: 2.6 Can you show me the steps to solve the problem? Directions: Find dy/dx by implicit…

A: Given,

Q: An equation for the tangent line to the curve In(sec x + y?) = tan(x)+e2" – 1 at the point (x, y) =…

A: Given curveIn (sec x +y2) = tan x +e2x-1We have to find the equation of tangent line at the point…

Q: Given the function fx)=x cosx. Use the centered-divided-difference formula f '(x) = 2h to compute…

A: We will use center difference formula  f'(x)=f(x+h)-f(x-h)2h

Q: 2. A particle is moving along a line with velocity given by the function v(t) =t tanh(ln t)[sech(ln…

A:

Q: Find the equations of the tangent line and normal lines to the graph of the function f(x)= —4 sinx…

A: We have to find

Q: 51-52 Find the given derivative by finding the first few deriva- tives and observing the pattern…

A:

Q: 2. You are given the equation: r2 – xy – y² = 1. dy da a) Find using implicit differentiation b)…

A: We have to find: a dydx using implicit differentiation b equation of tangent line at the point 2, 1…

Q: Question 1 Find the derivative and simplify y cotVt-1 Oy-- Oy= - 2tt-1 1 2t/t-1

A:

Q: 2. An individual's oxygen level, L, at time t E [0, 1], is given by L(t) = 90+10 sin(2t). Use…

A:

Q: 4.1. Find the slope of the line tangent to r = 4 – 3 sin 0 for 0 = ™

A: The given question is based on the tangent and normal topic in which we have to find only the…

Q: Find the equation of the tangent line to the curve y = 4 sin x + 2 cos a at the point (0, 1/2). The…

A:

Q: The temperature of coffee in a large urn fluctuates as coffee is dispensed and more coffee is added.…

A: The given function is: ft=140+10 sint To find the average rate of change in 0,π

Q: 1. Explain two different ways to solve for the derivative of s(0) = 200sin cos

A: Topic = Derivative

Q: What is the approximate value of the first derivative of the y = sinx function at x =pi/4 when you…

A: The first derivative of the function can be obtained using the forward and backward difference…

Q: 11. Consider the equation x + y +e# = e dy using implicit differentiation. dx (a) Find (b) Find the…

A:

Q: I need help with these questions. Please take me step by step

A: The given function is s(t) = –16t^2+96t.

Q: 1) If you pluck a guitar string, pulling it to a height of A and letting go, we can model its motion…

A:

Q: 3T sin (1) A particle moves along the x-axis with velocity given by v(t) 3 t> 0. If the particle is…

A: Given query is to find the position of the partical at indicated time.

Q: find an equation for the line tangent to the curve at the point defined by the given value of t.…

A: Tangent line for a curve at a point is a line which just touches it and is "parallel" to the curve…

Q: -1 The derivative of the function y = sin Va at 1 is equal to 4

A:

Q: 2. Find d using implicit differentiation. Enclose final answers. dx (a) √x=y=√√√x + y = 5 (b) xsin y…

A:

Q: 1. Find S*-3**+ dx by hand and show how to check the result is correct by differentiation.

A:

Q: find an equation for the line tangent to the curve at the point defined by the given value of t.…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: a(t) = -7 cos 2t – 8 sin 2t t Find its velocity and position functions at any time t if it is…

A: Given, The acceleration of a body, at=-7cos2t-8sin2t,  t≥0 At t=0 sec, Velocity,v=4 msec  and…

Q: Breathing is cyclic, and a full respiratory cycle from the beginning of inhalation to the end of…

A:

Q: In a 24-hour period, a human's body temperature will vary ab When at rest (usually at night), the…

A: The derivative of a function of a real variable measures the sensitivity to change of the function…

Q: 14))) What is the approximate value of у= sinx when you calculate the first derivative of the…

A: We will use basic knowledge of numerical methods to answer this question.

Q: Find the equation of the tangent line to the curve 1 y = 3 sin z + 4 cos a at the point (0, 1/4).…

A: Given:     y = 1 / ( 3 sinx + 4 cosx ) Point: ( 0 , 1/4 )

Q: 2. A curve C with equation y = sin2x 0 < x <5, has a stationary point, P. e3x dy (a) Find an…

A:

Q: Consider an oscillating mass that weighs 3100 grams which is attached at the end of a spring with…

A:

Q: (31) Use Newton's Method to make the second approximation x2 to the solution of 2e" = ex. Take x1 =…

A:

Q: The population of foxes in a certain region is estimated to be Ttt P1(t) = 500 + 50 sin in month t,…

A: The population of the foxes in a certain region is given by: p1(t)=500+50sinπt6 in month t. The…

Q: 11) A particle moves along a line so that at time t its position is s(t) = -4 sin 5t, where s(t) is…

A: We will use second derivative test to find time at which maximum veolcity achieved

Q: An equation of the tangent line to the curve y = sin(z) at x = 1/6 is y = -(z – 7/6) . An equation…

A: a.

Q: A particle moves along a circular path in such a way that its x- and y-coordinates at time t are x =…

A: Given Data: The coordinates of the circular path at time t is: x, y=2cost, 2sint The speed of the…

Q: To find the equation of the tangent line to the graph of the equation ln(x) + xe^y = 1 at the point…

A: Given query is to find the tangent line.

Q: 51. The horizontal range R of a projectile launched from ground level at an angle e and initial…

A:

Q: 1 y 4 18) Find the first derivative of y = -sin? x

A:

Q: 2+ cos x 5 (b). Let g(x) = Find equations of the tangent and normal lines to the x sin x graph of y…

A: First find the point corresponding to given value of x then take the derivative of function to get…

Q: Find an equation for the line tangent to the curve at the point defined by the given value of t.…

A: Given,         x=t-sint , y=1-3cost , t=π3

Q: [1.5 Marks] B1: Find the equation of the tangent line to f(x) = 5+4x at a = 2.

A:

Q: 5cos³ (x) Find the derivative of y + tan²(3x² – 4x) – csc(v2x – 1 )and express your sin(3–2x) answer…

A:

Q: 2. Two separate rabbit populations are observed for 80 weeks, starting at the same time and with the…

A:

Q: 3. Consider the function f(x) = sin [3(x-30°)] +4. a) Determine the amplitude, the period, the…

A: Given- Consider the function fx = 12sin3x - 30° + 4.  To find-  Determine the amplitude, the…