The gradient of the chord of the function y = 4 log10 x over the interval [2, 2.01] is calculated to be 0.8664. From this we can conclude that the instantaneous rate of change of y = 4 log10 x at x = 2 is approximately A 0.87 B 8.7 C 1.74 D -0.87 E impossible to estimate

The gradient of the chord of the function y = 4 log10 x over the interval [2, 2.01] is calculated to be 0.8664. From this we can conclude that the instantaneous rate of change of y = 4 log10 x at x = 2 is approximately A 0.87 B 8.7 C 1.74 D -0.87 E impossible to estimate

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section: Chapter Questions

Problem 33CT

See similar textbooks

Related questions

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)…

Q: Determine the instantaneous rate of change of the function πt ³ √x sin 2 f(x) = LV x3 1 + √t at x=2.…

A: Leibnitz integral rule.

Q: The cost of producing x units of a certain commodity is c(x) = 1000 +5.70x +.7x2. What is the…

Q: Economists have considered the output y of a manuracturing process as a function of the size of the…

A: Derivative of function

Q: Suppose that a company can produce 12000 units when the number of hours of skilled labor y and…

Q: Suppose x and y are functions of third variable t. In the equation x2+y2=45, what are the values of…

A: In the question it is given that x and y are the function of the variable t in the equation…

Q: second. At what rate x changing when x = . O-16 O 16 8 O-8 in such way that the y-value increases at…

A: The given equation is; y=x3-2x2+x-1.

Q: Estimate the instantaneous rate of change at the point indicated. f (x) = ex ; x = e

A: To find the instantaneous rate of change at indicated point:f(x)=ex;x=e. Solution: we know, the…

Q: The Ideal Gas Law is PV = mRT where P is the pressure, V is the volume, m is the constant mass, R is…

Q: Estimate the instantaneous rate of change of f(x)= cos(x-7)+4 at x = π. a) 4. Ax =4 b) Af =1 Ax Oc)…

A: Given function is F(x)=cos(x-pi)+4 where x=pi We are going to find the instantaneous change of this…

Q: Suppose that the sides of a cube are expanding at a rate of 2 inches per minute. How fast is the…

A: Suppose that the sides of a cube are expanding at a rate of 2 inches per minute. How fast is the…

Q: The rate at which a radioactive chemical is delivered into cells is r(t) (measured in miligrams per…

A: NOTE: As method is not specified, question is solved for Riemann left end point approximation.

Q: 2. If f(t) is the rate of change of some quantity, then what does f (t) dt represent?

Q: Given the function f(x) √x f(x) = COS 2 1 + √r dr Determine the instantaneous rate of change at x =…

A: Using Leibniz rule of derivative

Q: The number of per capita cumulative cases of COVID-19 in a particular country can be modeled by g(t)…

A: Let's find.

Q: The cost of manufacturing x cases of cereal is C dollars, where C = 3x + 41x + 2. Weekly production…

Q: What is the rate of change of y with respect to x for this function?

Q: A Cepheid variable star is a star whose brightness alternately increases and decreases. For a…

A: Given: A Cepheid variable star is a star whose brightness alternately increases and decreases. For a…

Q: 1. The heat index (HI) is an estimate of the temperature felt by the human body based on the actual…

A: Note: Here I am assuming T=107°F and rate=2°F Given: HI=-42+2T+10hr-0.22Thr-1.99T2hr2

Q: You are a process control engineer in a water purification plant. In a certain subprocess, water…

A: Mathematical methods used to solve equations or evaluate integrals or solve differential equations…

Q: The combined electrical resistance R of two resistors R1 and R2, connected in parallel, is given by…

A: Consider the following equation: 1R=1R1+1R21R=R1+R2R1·R2R=R1·R2R1+R2 Differentiate the above…

Q: Find the instantaneous rate of change of g(x) = In(x + 3) at x =

Q: A tumor is approximately modeled by the shape of a sphere, given by the following equation: V=4/3πr3…

A: Let x be the diameter of spherical tumor. According to given condition , we have , when x=16mm…

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

Q: If the average rate of change of a function between x = a and x = b is negative, then is the…

A: The rate of change of function between two points of a curve represents the slope of the curve. If…

Q: A honeybee population starts with 100 bees and increases at a rate of n' (t) bees per week. What…

A: Integral formula is ∫abf(x)dx=F(b)-F(a) ∫04n'(t)dt=n(4)-n(0) From the given integral…

Q: The total time required to bake a loaf of bread, B, is a function of the temperature of the oven, T,…

Q: A point moves along the curve y = x ^ 3−3x + 5 so that x = 1/2√t + 3, where t is time. At what rate…

A: Given- y=x3-3x+5 and x=12t+3 To find- The rate of changing when t=4. Concept Used- dydt=dydx·dxdt

Q: 7. Find dy and hence determine the rate of change of y with respect to x for the following…

Q: a) Determine the AVERAGE rate of change of y over each interval −5 ≤ x ≤ 9 −1 ≤ x ≤ 5 −3 ≤ x ≤ 7…

A: a)−5 ≤ x ≤ 9At x=-5, y=48 and x=9, y=41 AVERAGE rate of change of y=41-489--5=-714=-12−1 ≤ x ≤ 5At…

Q: 19. Suppose the rate of change of production of a regular worker at a factory is given by dp…

A: Given problem:- Suppose the rate of change of production of a regular worker at a factory is given…

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

Q: 18. Estimate the instantancous rate of change of the function f(x) = x' +4x - 11x-30 at x = 1. Round…

A: Given, f(x)=x3+4x2-11x-30, x=1

Q: The demand function for an item is given by 100 d(x) = (20 < ¤5 50) 0.01z² + 1 where d(x) (measured…

Q: 9. Suppose an object is moving along a path described by; f(t) = t - 6t, where f (t) is measured in…

A: The objects velocity at t is equal to 4 will be the objects instantaneous rate of change at that…

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

Q: . Use a similar procedure to estimate the instantaneous rate of change of y = 3" at r = 0. Show your…

Q: The domain of the function shown here is [Select ] The derivative of f(x) DNE at x=-1 because […

Q: Estimate the instantaneous rate of change of ƒ(x)= = a) Ax b) 4 Ax = 20000 = 2 c) 4-0 Ax x x-2 at…

Q: Suppose yy varies at a constant rate of change of -0.6 with respect to xx (so that…

Q: A certain radioactive substance is decaying so that at time t, measured in years, the amount of the…

Q: What is the result of integrating a population growth rate betweentimes t = a and t = b, where b…

A: Integrating a population growth rate between a to b that is ∫abRatedt

Q: Suppose that the yield (measured in kg/ ha) of an agricultural crop is represented by the function…

A: We need to find rate.

Q: Calculate the instantaneous rate of change of g at the point (4, 1, 2) in the direction of the vec…

Q: The rate at which a solid substance dissolves [dQ/dt] varies directly as the product of undissolved…

A: Given that 20 lb of substance is initially thrown in tank therefore A=20. Also, saturation…

Q: Suppose both x and y are functions of time (t). Find the rate of change of y with respect to t, that…

Q: The cost in pesos of producing x units of a certain commodity is C(x) = 0.05x2 + 10x + 5000. What is…

Q: Find the gradient of the tangent to the curve xy“ + y+ ( log_(x – 2))² = 14 at the point (3, 2).

Q: A radioactive material, such as one of the thorium isotopes, thorium-234, decays at a rate…

A: We will find the rate of decay as following.

Q: What is the rate of change of y = In x at x = 1 O?

A: Given: y=lnx at x=1

Question

The gradient of the chord of the function y = 4log₁₀x over the interval [2, 2.01] is calculated to be 0.8664. From this we can conclude that the instantaneous rate of change of y = 4log₁₀x at x = 2 is approximately

A 0.87

B 8.7

C 1.74

D -0.87

E impossible to estimate

Expert Solution