Enter the exact answers. (a) Find the average rate of change of y = - with respect to x over the interval [5, 6]. l'ave = (b) Find the instantaneous rate of change of y = – with respect tox at xo = 5. l'inst =

Q: The tangent line to the graph of y=f(x)at the point (1,11) has the equation y=3x+8 (a) Find f′(1)…

A:

Q: Q2 Use the chain rule to find the derivative of dw w = x2 + y2 with respect to t ). with x = cost -…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: 1. Find the rate of y with respect to x at the point (1, 7) if 7y – ry = 4. dy da

A:

Q: Find the equation of tangent and equation of normal for the implicit function y + 4xy x+y, at the…

A:

Q: 元 Determine the average rate of change of the function y = sin x from x = 0 to x =

A:

Q: 7) Find the instantaneous rate of change of f(x) = ecos(z") + sin(In(8²)) at x = 1.

A:

Q: Find all points on the interval (1, 3) at which the slope of the tangent line equals the average…

A:

Q: Use differentials to approximate the quantity   √17

A:

Q: Let y = x sin(2x). (a) How fast is y changing at x = t? (b) Find an equation of the tangent line to…

A: Given y=x sin(2x)

Q: If the instantaneous rate of change of ƒ(x) with respect to x is positive when x = 1, is ƒ…

A:

Q: Let y=sqrt(2x). Find the rate of change of y with respect to x at x=4.

A: Answer is 1/(2√2).

Q: Calculate the average rate of change of each of the following functions over the interval…

A:

Q: Estimate the true percent relative error for the first derivative of the function, y = cos(sin(x)+…

A: We have to find 1st derivative using central difference method and then calculate true percent…

Q: x sin(2x). (a) How fast is y changing at x = n? Let y = (b) Find an equation of the tangent line to…

A:

Q: A particle is traveling upward and to the right along the curve y = ln x. Its x-coordinate is…

A: Given a particle is travelling upward and to the right long the curve y=lnx. It is given that dxdt=x…

Q: Two students are calculating the instantaneous rate of change of y= sin(x) at x = Student A claims…

A:

Q: 3. Estimate the derivative of the function, f(x) = cos x + tan1 x, at xi= 0.5 using Richardson's…

A: To find the derivative of the function fx at x=x0 by Richardson's extrapolation centered finite…

Q: Find the indicated derivative and simplify. dy 41 Int for y = - dt et

A: Product Rule of differentiation : du.v.wdt =dudt.v.w+u.dvdt.w+u.v.dwdt.

Q: ly 4% confident that the true po ation percentage of people that

A: The margin of error is the amount that is allowed for the error term to vary because of…

Q: 6. Suppose that w = x cos(yz²), where x = sin t, y = t² and z = 2e'. Find the rate of change of w…

A: Using derivative

Q: Let f:[-n, 7] –→ R, where f(x) = 2 sin (2x) – 1. TC Calculate the average rate of change of f…

A:

Q: 17. For f(x) = x*, the instantaneous rate of change is known to be –32 at x = -2. Find the equation…

A: the given function is f(x) = x4 rate of change dydx=-32,          at x =-2

Q: Find the average rate of change of f from 0 to π /6 . f(x)= tan(2x)

A: Given: fx=tan2x To Find: The average rate of change of the given function from 0 to π6

Q: 5. Find the rate of change of the distance D between the origin and a moving point on the graph dx…

A: Given: y=x2+7 then A moving point on the graph is: (x,y)=(x,x2+7) And dxdt=8 cm/sec We have to find…

Q: Suppose x and y are functions of third variable t. In the equation *+y=45, what are the values of…

A: First we will find value of y from given equation And differentiate wrt to t

Q: Suppose y = f(x) is a curve that always lies above the x-axis and never has a horizontal tangent,…

A:

Q: Find the equation of tangent and equation of normal for the implicit function y +3xy =x+y, at the…

A:

Q: What is the instantaneous rate of change for α=arctan(2-r/r) at r=0

A:

Q: Let 7=sin ( y+. *). Find the rate of change of z with respect to x at the point (2, 1) with y held…

A:

Q: Find the (a) approximate error and (b) relative approximate error of the following: The derivative…

A: Note:- For this problem, you don't mention any particular method and anything about h. So, I'll try…

Q: If f(x) = cos(2x), which of the equations below describes the average rate of change of f(x) over…

A:

Q: Find the rate of change of y with respect to x at the indicated value of x. y = csc(x) – 4 cos(x); X…

A: The given function is y = cosecx - 4cosx

Q: The average rate of change of the function y = sinx over the interval [0, ]is 4

A:

Q: Find the slope and the rate of change of the slope with respect to x when t = 90°. x = 2 cos (3t)-3…

A: This question can be solved using the concept of first and second order derivatives at t=90°

Q: Use Richardson extrapolation to estimate the first derivative of Y = sin x at * = π/4 using step…

A: Given the function  y=sinx

Q: 3) Consider the fonction (a) The tangent plare to the graph of fCx,y) at the point Co,0) is (b) At…

A:

Q: Find the instantaneous rate of change of y =- at x = a

A:

Q: 1 By considering the secant through the points where x = 1.2 and x = instantaneous rate of change of…

A:

Q: Determine the instantaneous rate of change of the function πt³ √x sin (TE³ 2 f(x) = x3 1 + √t at…

A:

Q: Find the average rate of change (AROC) of the following functions over the interval [60 ≤x≤180] y =…

A: using , average rate of change…

Q: Consider the function Y3x2-6×+ス a. Find the slope of the tangent lihe to the curve at x=2 be Find…

A:

Q: Find the derivative of the function f(x,y) = tan at the point (3, - 3) in the direction in which the…

A:

Q: Use Richardson extrapolation to estimate the first derivative of y = cos x at x = π/ 4 using step…

A:

Q: The derivative of y=eSinh/x +cosh¬/x equals

A:

Q: 9. Consider the interval [0, 2n] for the function y sec x. State an x- value at which the…

A: Given query is to find value of x for different conditions for instantaneous rate of change.

Q: Let m(x) be the slope of the tangent line to the curve y = 2x° – 6x² + 3x at the point (x, y). Find…

A: We have to find instantaneous rate of change of m(x) at point (2,-2)

Q: (4)The instantaneous rate of change of f(r) = e- at a = 1 is . .. (5) The derivative of f(x) = sec2…

A: (4) We have So we get the instantaneous rate of change of the function at  as .

Q: Given that x and y are functions of time, find the indicated rate of change. iON dx dy = 2, given…

A: Consider the given equation

Q: Let m(x) be the slope of the tangent line to the curve y = 2x³-6x² + 3x at the point (x, y). Find…

A: Given: y=2x3-6x2+3x

Q: Estimate the true percent relative error for the first derivative of the function, y =[e!n(x)72, at…

A: We can solve this using Central difference formula f'(x) = (f(x+h) - f(x-h))/(2h)     x 0.95 1…

Exponential Growth Model

The relation that represents an exponential function is: