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Q: A theorem states that one local extremum implies an absolute extremum. Verify that the following fu...

A: The given function is,

Q: 1. Estimate the volume of the solid that lies below the surface z = xy and above the following recta...

A: You have asked two unreleated questions in the same post. Further your first question has multiple s...

Q: You are given the four points in the plane A=(8,−8), B=(10,4), C=(12,−1), and D=(16,1). The graph of...

A: We have given the four point in the plane A, B, C and D.The total integral is to be the sum of the a...

Q: Find y' if x^y = y^x .

A: Given,

Q: Evaluate the integral in cylindrical coordinates. Please see attached image.

A: To calculate the value of the integral in cylindrical coordinates which is shown below,

Q: Use the derivative f' to determine local minima and maxima of f and the intervals of increase and de...

A: When f'(x)>0 then f(x) is increasing. Answer: f(x) is increasing in (-4pi/3,-pi)U(-2pi/3,-pi/3)U(...

Q: Need a,b, and c please!

A: The given equation is s = –0.2t2 + 12t and the velocity is v =12 m/s. a. Obtain the velocity v of th...

Q: I did the test points but not sure how to answer??? It’s positive when less than 3, less than 0 and ...

A: To determine when the motion is in the positive direction and when it is in the negative direction.

Q: Find the point on the plane 4x+5y+x=11 that is nearest to (2,0,1). What are the values for x, y, and...

A: The equation of the plane is

Q: How can I get the result? Which is the result?

A: The given function is,

Q: The consumer price index (CPI) measures how prices have changed for consumers. With 1995 as a refere...

A: Given:The rate of change of CPI in dollars per year is dC/dt= 0.009t2 − 0.096t + 4.85, where t repre...

Q: A train is initially traveling at a rate of 5 miles per hour. The acceleration of the train is 5 mil...

A: Given: The acceleration of the train is 5 miles per hour squared. That is, a(t) = 5.The initial velo...

Q: curves. Find the volume of the solid generated when R is revolved about the x-axis Let R be the regi...

A: Use disk method to find the volume of the solid generated when R is revolved about the x-axis is cal...

Q: Is y=e2x +4x+3 a solution to the differential equation shown below? y′−2y=−8x−2

A: To test if the given function is a solution of the given differential equation

Q: Let R be the region bounded by the following curves. Find the volume of the solid generated when R i...

A: The given curves are y=x, y=4x, y=16.The graph of the region formed by these curves is,

Q: b. Find the area of the region bounded by Y = xe ax and the x-axis on the interval 0,41, where a> 0....

A: Area of region which is bounded by f(x) and x-axis on [0,4] computed as follows.

Q: Find the slope of the secant line between x=2 and x=5 on the graph of the function f(x)=−2x2+2x+3.

A: We have to find the slope of the secant line between x=2 and x=5 on the graph of the function f(x)....

Q: Use the graph off and f' to find the critical points and inflection points of f, the intervals on wh...

A: Finding the critical point

Q: 3. Given the function g(x) 8x defined on [-1, 1], determine if the function satisfies the Mean Value...

A: Given,

Q: Help please...

A: The Taylor series of f(x)=cotx at x=(7π)/6 is given by;

Q: Help with #7

A: Given information:The equation of the curve is

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the...

A: Given curve:and region bound are:We need to find the volume of solid obtained by the given curve for...

Q: Find the values of the convergent series [from k=4 to infinity] E (2/3)3n-1 (-4/7)2n+3 *that E just ...

A: Given information:The given convergent series is

Q: How can I get the result?

A: We used a calculator to find the values for the table. And rounded each value to 4 decimal places. ...

Q: 34. If a, b, andc are all positive constants and y(x) is a solution of the differential equation ay"...

A: Given that the differential equation is

Q: If a cup of coffee has temperature 95°C in a room where the temperature is 20°C, then, according to ...

A: The equation for the temperature of the coffee after t minutes is,

Q: For y= (x^4/4)-(x^3/3)-2 (a) Find y' =f'(x). (b) Find the critical values. (c) Find the critical ...

A: We are given a function

Q: Help with #5

A: Given curve: r(t) = (2cost)i + (2sint)j + tkRecall the expressions for unit tanget and principal uni...

Q: A van is accelerating at a rate of 7 meters per second squared. The initial velocity of the van is 6...

A: Given: The van is accelerating at a rate of 7 meters per second squared. That is, a(t) = 7.The initi...

Q: Find a particular solution to the differential equation below that passes through the point (−3,−5)....

A: The given differential equation is y’ = 5x–5.

Q: Limit as x approaches 2 of (x3-8)/(x-2)

A: Obtain the value of the limit as follows.

Q: 2.5 Continuity 3. We would like to find a value of k to make the piecewise function f(x) continuous ...

A: 3)Answer: a) If I was to graph f(x) then the left part of 3 is changed when k is changed. As the k i...

Q: Kindly help

A: Given information:The given intergal is

Q: All boxes with a square base, an open top, and a volume of 210 ft cubed have a surface area given by...

A: Approach:As a first step we will differentiate the given function and equate it to zero to find all ...

Q: How do I show the correct solution for the differential equation? I know the answer is D.

A: First we separate the variables

Q: Find the area of the region described. -4x and xIn 3 The region bounded by y e. ye X The area of the...

A: We first draw a rough sketch of y=e^x, y=e^-4x and x=ln 3And find the region bounded by them.

Q: I don’t understand what I am doing wrong. Please help me find the tangent line equation!

A: To calculate the slope and equation of the tangent line from the provided value of parameter which i...

Q: How do I solve the initial value problem using P(x), Q(x) and v(x)?

A: First we find P(t) and Q(t) by comparing with y\'+P(t)y=Q(t).

Q: How can I get the result? Which is the result?

A: (a)we are given a function

Q: Because a new employee must learn an assigned task, production will increase with time. Suppose that...

A: To find the number of units completed in t hours by the new employee, integrate the rate of performa...

Q: Find the position and velocity of an object moving along a straight line with the given acceleratio...

A: Obtain the velocity as follows.

Q: Use the derivative f'(x) = (x - 3)(x + 4)(x + 4) to determine the maxima and minima of f and the int...

A: f will be increasing if f'(x)>0. From the graph of f'(x) we see f'(x)>0 when x>3 [because a...

Q: Find the power series representation for g centered at 0 by differentiating or integrating the power...

A: Consider the geometric series,

Q: Which is the result?

A: We are given a function as

Q: b) and c) I tried doing it the same way I did the first one...

A: we are given rate functions as

Q: Answers for 10-12

A: We will solve Q-10

Q: How can I get the result? Which is the result?

A: The given function is,

Q: please show ALL your steps

A: we are given a function

Q: x24x 3 + x 1 = xp 7x2 - 2x + C In)x - 1C Inx C 6x 3 Inlx 1 + C 2 5x + 2 Inx 1 C

A: Consider the integral is

Q: Assume a person invests $12000 at the end of each year for 30 years at an annual interest rate of r....

A: Part (a)The future value amount should be equal to A = $ 1,000,000.Please see the white board.The mi...