If f and g are functions of time, and at time t = 3, f equals 8 and is rising at a rate of 3 units per second, and g equals 6 and is rising at a rate of 8 units per second, then the product fg equals %3D and is rising at a rate of units per second.

Q: In Exercises 35-74, evaluate the integral using the methods covered in thetext so far.

A:

Q: Differentiate. F(x) = (8x +3) F'(x) =] 2.

A: We have to differentiate the function F(x)=8x+32.

Q: Simplify the expressions

A: log319

Q: Linear functions, inverses, and derivatives Consider the general linear function y = f1x2 = mx + b, ...

A: The general linear function, y=fx=mx+b. (a) To find the inverse of fx, y=mx+by-b=mxx=1my-b So replac...

Q: Which of the following statements aretrue, and which are false? If true, say why; if false, give a c...

A: Consider the given information as limfxx→c exit but limgxx→c does not exit.

Q: Find the limits

A:

Q: A spherical balloon is being filled with air at a constant rate of 3 cm3/s. How fast is the radius i...

A: Let,Volume of sphere = VRadius of sphere = rRate at which the volume of sphere is increasing = dVdt ...

Q: The figure shows the graph of f(x) = log x. Use transformations of this graph to graph the function ...

A: Given f(x)=log x and its graph. We need  to use transformation to graph the function h(x)=log x -1 a...

Q: Differentiate. F(x) = (8x +3) %3D F'(x) = O

A: The given function is Fx=8x+32.  

Q: Use the power rule to expand the logarithmic expression:  log6 39

A: Let the given value be y -y = log639Using power rule logarithmic property - logab = blogaImplementin...

Q: Evaluate the integrals . Some integrals do notrequire integration by parts. ∫xex/(x + 1)2 dx

A: We have to solve the integral: ∫x exx+12dx This is special type of integration of the form: ∫exfx+f'...

Q: The graph below shows the velocity of an object moving along a straight line for the time interval o...

A: Solution:- Step-by-step solution of the above question is given below. The figure of above question ...

Q: Find the limit.

A: Limit: x→27lim(x3-1)4We need to find the value of the above limit.Now we should put x=27 at the give...

Q: Integrals Evaluate the following integrals. Include absolute values only when needed.

A: It is given that, ∫sinlnx4x dxWe have to evaluate it.  

Q: Graph each side of the equation cos 1.2x cos 0.8x - sin 1.2x sin 0.8x = cos 2x in the same viewing r...

A: cos1.2x cos0.8x-sin1.2x sin0.8x=cos2x The graph is,

Q: particle P moves clockwise at a constant rate along a circle of radius 10 m centered at the origin. ...

A:     particle P moves clockwise at a constant rate along a circle of radius10 m centered at the origi...

Q: List all numbers in the given set that are : a. natural numbers, b. whole numbers, c. integers, d. r...

A: Let the given set be A - A = -9, -45, 0, 0.25, 3, 9.2, 100(a)Natural Numbers = ?Natural numbers are ...

Q: Determine whether the statement is true or false. If it is true, explainwhy. If it is false, explain...

A: To Determine: If f is continuous on [0, ∞] and ∫1∞f(x)dxis convergent, then ∫0∞f(x)dx is convergent....

Q: A challenging pen problem A farmer uses 200 meters of fencingto build two triangular pens against a ...

A: Dimension of triangular pens is given as x and y So, area of Triangular Pen = 12×height+base        ...

Q: Evaluate the series or state that it diverges.

A: The series ∑k=1∞πkek+1. We have to check whether the series is convergent or divergent.

Q: Find the value or values of c that satisfy the equationƒ(b) - ƒ(a)/b - a = ƒ'(c)in the conclusion of...

A: The function is, fx=x-1 over the interval [1,3]. Thus, a = 1 and b = 3.   Substitute 1 for x in fx=x...

Q: Find an equation for the line with the given property.(a) It passes through the point (3, -6) and is...

A: To find an equation for the line with the given property.(a) It passes through the point (3, -6) and...

Q: Use a convergence test of your choice to determine whether the following series converge.

A: To check the convergence of the given series.

Q: Differentiate the following functions with respect to x

A:

Q: Travel time A projectile is fired at a speed of 840 m/ sec at an angle of 60. How long will it take...

A: Part (a) - Initial speed of projectile = u = 840 m/secAngle of projection = θ = 60°Time of the fligh...

Q: Evaluate

A: The given integral is ∫1∞1-xe-x dx. Evaluate as follows.  

Q: Find the domain and range of the function f(x, y) = √(9 − 6x2 + y2).

A: Given f(x, y) = √(9 − 6x2 + y2)

Q: Evaluating partial derivatives using limits Use the limit definition of partial derivatives to evalu...

A: Given function is f(x,y)=xy

Q: Spherical coordinates Evaluate the Jacobian for the transformationfrom spherical to rectangular coor...

A: Given expressions are: x = ρ sin φ cos θ y = ρ sin φ sin θ z = ρ cos φ The expression for the  Jacob...

Q: Speeding Tickets In a certain state the maximum speed per- mitted on freeways is 65 mi/h, and the mi...

A: Let f(x) be the function that expresses the amount of fine you must pay f(x) depends only on the spe...

Q: Describe the interval(s) on which each function is continuous. f(x) = tan x

A: Given:fx=tanx

Q: Compute the double integral f[148 sin( + ) oyck, where R = {(x,y) /0 5x s %,0 sy s }. х, 3J. R OA 72...

A:

Q: Verify that the function given is a particular solution to the following equation, and find the part...

A: Question is not complete. Kindly update question neat and clear. 

Q: Precalculus Question:

A: Given function is gx=x We have to find the transformed function which is reflected over the y-axis a...

Q: How do I solve this? Right now in math class we are learning about derivatives, product rule, quotie...

A: Given,

Q: As a construction manager, you are asked to build a new road, which will be a perpendicular angle wi...

A: Solution:(x1,y1) and (x2,y2) The objective is to find the slope of the new road that perpendicular a...

Q: Solve the system of equations: 3x - y = -2, 2x2 - y = 0

A: Given: The system of equations  3x-y=-2 2x2-y=0 To find: The solution of given system of equation.

Q: The extreme values of fAx, y) = 4x + 2y? on the region x +y <4 are O A. Maximum = 24, Minimum = 0 B....

A:

Q: Q12 Ans: RM637.60

A: Let 'l' be the length of the box, 'b' be the width, and 'h' be the box's height. Given Data: The len...