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Q: find the derivative of the question in the picture please show all work

A: Obtain the derivative of the function.

Q: Explain in your own words how to find the volume using the disk method.  Include on example in your ...

A: Suppose that any solid of revolution with disc cross-section.In order to find the volume of these ty...

Q: What is the particular solution for y′=5ex −6x3 +4x such that y(0)=−8? Do not include "y=" in your a...

A: The given differential equation is, y′=5ex −6x3 +4x.

Q: What is the velocity at time t for a car that begins accelerating at a rate of 4 feet per second squ...

A: To determine the velocity from the given conditions

Q: Determine the location and value of the absolute extreme values of f on the given interval, if they ...

A: Calculation:The given function is f(x) = 2(5x)x defined on interval [0.05, 1].In order to find the l...

Q: Find the area of the region described. 18 The region bounded by y and y1 2 9+x The area of the regio...

A: y = 18 / (9 + x2)As a first step we need to find the points of intersection of the curve and the lin...

Q: Calculus Question

A: Let's call the given integral as I. Further let's make the substitution: x2 + 1 = zHence, 2xdx = dzP...

Q: y = t(lnt)2 Find the derivative

A: According to the chain rule of derivative,Using the above rule, where u = t and v = ln t

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: Is y=ex −5x−8 a solution to the initial value problem shown below? y′−5x=3+y y(0)=−7

A: The given differential equation is y=ex −5x−8.The solution of the deferential equation is given as, ...

Q: How do I do this?

A: We are given a function and at a point 

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: Find the point P on the line y = 5x that is closest to the point (52,0).  What is the least distance...

A: Given:The equation of the line is y = 5x.(52,0) is the closest point to the point P which line on th...

Q: Find the area of the surface generated when the given curve is revolved about the given axis. y 10x ...

A: Given:

Q: Question 2 Pratice

A: Part A

Q: Optimization Problem A rectangle is constructed with its base on the diameter of a semicircle with r...

A: a)Let x and y be the base and height of the rectangle, respectively.Given that, the rectangle is con...

Q: A car is traveling at a rate of 23 kilometers per hour when t=7 hours. The acceleration of the car i...

A: To calculate the velocity from the given data 

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

A: The definite integral is given as

Q: differentiate f(t) = t^(1/3)/ (t-3) On the solution guide on the first step for the numerator, we ha...

A: Explanation:Consider the term t1/3.It is known that adding and subtracting a same number to any numb...

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

A: (a)Complete the table below analytically:

Q: Find the relative maxima, relative minima, and points of inflection and sketch the graph for the fun...

A: We have to find the relative maxima, relative minima, and points of inflection and sketch the graph ...

Q: find the exact length of the curve of the equation in the picture below make sure to show all work

A: The given curve equation is,

Q: 3. (4.6) A rectangular flower garden with an area of 30 m2 is surrounded by a grass border 1 m wide ...

A: Given information:A rectangular flower garden with an area of 30 m^2 is surrounded by a grass border...

Q: Use Green's Theorem to evaluate the line integral. Assume curve is oriented counterclockwise. C is t...

A: Let's compare the given integrand with the standard form.(2x + ln 2)dy - (8y2 + sinhx)dx =Q.dy + P.d...

Q: Suppose that the cost funtion for a commodity is  C(x)= 300+6x+1/20x^2 dollars (a) Find the marginal...

A: The given Cost function for a commodity is C(x) = 300 + 6x + (1/20)x2.(a) To find the marginal cost ...

Q: Convert the double integral into a type II double integral

A:

Q: Please help.

A: The given series is,

Q: 2. (4.6) penicillin is sold at a price of $200 per unit. The production cost (in dollars) for x unit...

A: C(x) and P(x) shows the total production cost function and the profit function of penicillin.

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

A: The function is given as

Q: Determine whether the following series converges. Justify your answer 9(4k)! Σ k=1 (kl)* Select the ...

A: Consider the given series:

Q: Consider the following function. Without finding teh inverse, evaluate the derivative of the inverse...

A: Given information:The given function is .

Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by x ...

A: We are given equations as 

Q: For the function y=x-1/3x^3 (a) Find the coordinates of the relative maxima, relative minima or hori...

A: (a) The function is given as

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: How do you solve the limit of this graph?

A: x->-1^- means x is slightly less than -1.

Q: 2 -4 0 such that f(x)-4 0, make a conjecture about the value of 8 that satisfies the preceding ineq...

A: For part a, bAccording to epsilon delta limit.Let f(x) be the function defined on an open interval a...

Q: The problem and graph are imbedded in the image.

A: Given information:An arch is 645cft high and has a 600ft base. It can be modeled by the parabola  

Q: I need help about solving this problem. a) How do I find the time required to reach the maximum amou...

A: Let F be the amount of fertilizer. In 1 minute 1 gallon of solution comes in and 5 gallons of soluti...

Q: Does the series converge absolutely, converge conditionally, or diverge?

A: The given series is

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: Kindly help

A: The Taylor series can be obtain as follows.

Q: Find the derivative of y with respect to x

A: we are given an inverse function 

Q: Marginal Revenue. Suppose the total revenue function for a blender is R(x)= 36x-0.01x2 dollars where...

A: The total revenue function for a blender is R(x)= 36x-0.01x2 dollars where x is the number of units ...

Q: This is #1

A: Part (a)Consider an object moving along a line with the velocity and initial position.

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

A: To find the equation of the tangent line approximation T to the graph of f at the given point.The gi...

Q: a) and b) please

A: Part (a)The population of the town in 2016 is 63,000 and the growth rate is 2.3% per year.

Q: 1. Indefinite and definite integrals including trigonometric functions and ones that will require th...

A: a. Integrate the given indefinite integral with respect to x as follows.

Q: Help with #7

A: Given information:The equation of the curve is  

Q: If l0g x=0.35 and fog6N0.5, evaluate the fo llowig expression.

A: Here, we use the above log rules.

Q: Evaluate the following integral as written. Please refer to attached image.

A: It's  aquestion of double integral. We will first evalaute the integral with respect to x, put the l...

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.