Show that a constant function f1x2 = b has an averagerate of change of 0. Compute the average rate of changeof y = 24 - x2 on the interval 3 - 2, 24. Explain how this can happen.

Q: Use Intermediate Value theorem to show that sin¹x + 3x - 4 has a zero in the interval [0, 1].

A: Given function, f(x)=sin-1(x)+3x-4 Here sin-1(x) is continuous and 3x-4 is linear equation which is…

Q: Use the inverse function theorem to find the derivative of g(x) Step 1 f(x) = 9¹(x) = Step 2 Step 3…

A: Quotient Rule of Differentiation : ddxuv=v.dudx-u.dvdxv2 .

Q: Let R be the region bounded by y = 0, y = √√x, and x = 4. According to the disk method, the integral…

A:

Q: Differential equations -Separable dy_ x + 1 dx y

A:

Q: Let r(t) = (2t³ + 4, − 5e-4t, − 3 sin( – 5t)). Find f(t)dt (don't include the +C)

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

Q: a) with this function Hal-log, X. Use the properties of the reciprocal "cartesion graph of f" and of…

A: a) Given the function f(x) = log(x2). Then inverse of f, f-1 is found out as follows:  Let…

Q: 2. Sketch the graph of a function, f, that is continuous everywhere, with the possible exceptions of…

A:

Q: 211. S 3x +4 (x²+4)(3x) -dx

A:

Q: A business has found that it can sell 780 items if it sets its price to $68.69. However, if it…

A:

Q: (ƒ-¹ of ¹)(-2) 78. (g-¹g-¹)(8)

A:

Q: 203. 1를 2-xdx 2 x² + x xx

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

Q: adym by implicit differentiation. х2 + y2 = 36 Find dy C

A: to find out the implicit differentiation for the given function.

Q: Determine the equation of the plane containing the point and the line. (-7, 10,-3), r(t) = (1 - 4t,…

A:

Q: Consider the space curve r(t) = (2t — 4, — 3t — 4, – t – 1). a. Find the arc length function for…

A: As per our guide line if multiple questions are posted we are supposed to answer only the first one…

Q: Let c be a constant and let f and g be differentiable functions on R². Use the gradient rules…

A:

Q: Find all the critical numbers of y=x²-2x²-3, then determine the local minimum and maximum points by…

A:

Q: arametric equations for the line through Po = (5,-1, 1) perpendicular to the plane 6x + 14y - 15z =…

A: Given query is to find the value of y and z.

Q: Suppose f and g are differentiable functions with the values shown in the table below. For each of…

A: Given table:- x f(x) g(x) f'(x) g'(x) 2 3 4 5 -2

Q: The following table shows the average returns for some of the largest mutual funds commonly found in…

A:

Q: 1 5 6 7 8 Previous y 6 S 44 3 24 -6-5-4-3-2-1 -24 031 3 acer -1 Find g-¹ (2). Type your answer...

A: See this solution in below.

Q: Suppose that the dollar cost of producing x appliances is c(x) = 1500 + 130x − 0.4x² a. Find the…

A: We need to find costs.

Q: If f1x2 = int12x2, find(a) f11.22 (b) f11.62 (c) f1 - 1.82

A: Given information fx =int2xorfx = 2x

Q: Consider the region R: Bounded y = x^2 and y = sqrt(x). As well as, y = x^2 and y = 4 and x = 0.…

A:

Q: 3 Consider the functions f(x) = x³ - 4 and g(x)=√x+4. (a) Find f(g(x)). (b) Find g(f(x)). (c)…

A:

Q: Sketch the graph of y = 2x.

A: Given the equation of a line:- y=2x

Q: A circular oil slick is expanding with radius, r in feet, at time t in hours given by r = 12t -…

A: Concept: The radius of the circular oil slick is r The area of the circular slick is  A=πr2

Q: 197. 3x 2 x² + 2x - 8 -dx

A: Note:As per our answering guidelines we  are supposed to answer only one question if multiple…

Q: Find the vertical asymptotes, if any, and the value of x corresponding to holes, if any, of the…

A:

Q: Differential equations -Separable dy/dt=3+5y

A: We can solve the differential equation in the below steps.

Q: Find the curvature of the curve r(t) = (4 cos(t), 4 sin(t), 3t) at the point t = Give your answer to…

A:

Q: ear approximation to the function f(x) = cos(6x) at a = π/2 is Br where and where Ris

A: Topic:- calculus

Q: Find 7'' (t), given 7'(t) = (te²t, − cos(5t + 5), 3t ln( − t)). ř'(t) = x, 4 cos(2t) = -6e-2t x,…

A:

Q: Find the two x-intercepts of the function f and show that f'(x) = 0 at some point between the two…

A:

Q: Find the linear approximation L(x) of the function ¹ƒ(x) = x² + 2x³ at a = -1.

A:

Q: f(x) = 5; df dx = 5x

A: Given query is to find f(x) is the solution of the differential equation or not.

Q: Use cylindrical shells to find the volume of the solid formed by rotating area bounded by the gra…

A:

Q: Find y' by (a) applying the Product Rule and (b) multiplying the factors to produce a sum of simpler…

A:

Q: Problem 4. dx √²-3x+2° x² - 3x + 2 (a) Compute the following integrals x + 7 (b) / √2+1 dx

A: Concept: In mathematics, integration is a technique for combining or adding the parts to arrive at…

Q: graph each function using the techniques of shifting, compressing, stretching, and/or reflecting.…

A: Given, fx=x2-1

Q: La- (1 − x − 4x³ + 2x³) dx - -

A:

Q: Find all critical numbers of the function ƒ(x) = sin²6x + cos6x¸ 0 < x < / Select one: a. b. C. O d.…

A:

Q: The instructions for the given integral have two parts, one for the trapezoidal rule and one for…

A:

Q: The integrand of the definite integral is a difference of two functions. Sketch the graph of each…

A: To represent the integral on graph.

Q: nd Vw. w = xe³y sin 5z TE: Give your answer in unit vector notation; that is, in terms of i, j, and…

A: Topic:- application of derivatives

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i, j…

A:

Q: To find the partial fraction decomposition of and solve for A, B, and C. 4x (x - 1)(x + 3)' Bx + C x…

A:

Q: The displacement from equilibrium of an object in harmonic motion on the end of a spring is 1 y =…

A:

Q: Suppose a designer has a palette of 13 colors to wor with, and wants to design a flag with 2…

A: We have to find out

Q: volume is described as follows: 1.  the base is the region bounded by x=−y^2+6y+74  and…

A:

Q: Part A What average force is required to stop a 990 kg car in 7.6 s if the car is traveling at 87…

A:

Exponential Growth Model

The relation that represents an exponential function is: