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Differentiation#29

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Q: Consider the region bounded above by g(x)=−9x−9 and below by f(x)=x2 −9x−18. Find the area, in squar...

A: Calculation:The given curves are f(x) = – 9 x – 9 and g(x) = x2 – 9x – 18.The area enclosed by two c...

Q: 11

A: Obtain the magnitude value of u as follows.

Q: Help please.

A: The given function is (tan-1x)2.

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

A: Use online graphing calculator to graph of the function.

Q: please explain how to do question 7c

A: The given integral is ∫(1-3x)4dx.

Q: how to find Find the area of the region enclosed by one loop of the curve. r = sin(4θ)

A: The given curve is r= sin4thetaArea of the curve enclosed in the first loop is,

Q: Consider the following velocity function. Complete the sentence: The same distance could have been t...

A: The given velocity function is,

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

A: The function is given as

Q: find the exact length of the curve of the equation below, show all work y = ln(sec(x)), with a range...

A: First, we find the dy/dx

Q: Please help me find the length of the curve

A: We\'ll use arc length formula with a=pi/2, b=2pi/3.

Q: Differentiate y = (s - sqrt(s) ) / s^2 I don't understand what happens on step 3 of the screenshot...

A: Here use quotient rule of differentiation which is,

Q: a. Determine whether the Mean Value Theorem applies to the function f(x)= ex on the given interval [...

A: Definition used: Mean Value Theorem

Q: Find all the roots of the given function.

A: There are two ways to find the roots of this equation:One way is to graph the equation and find wher...

Q: A company orders and uses 6,000 cans of paint each year. Each order has a fixed shipping cost of $15...

A: It is given that,The annual usage of paint cans is 6,000.The fixed shipping cost is $150.Additional ...

Q: Please help

A: Since f(x0,y0) is minimum of f(x,y). Then g(0) is minimum of g(t). That means g(0)<g(t) for t any...

Q: Maximize f(x, y, z) = 2x + 7y +9z on the sphere x + y+z = 67. Additional Materials eBook

A: f(x,y,z) = 2x + 7y + 9z and g(x,y,z) = x2 + y2 + z2 Approach:We will make use of the method of Lagra...

Q: Activity 5 Inverse Functions and their Derivatives 10. When a camera flash goes off, the batteries i...

A: Given:The function is Q(t) = Q0(1−e−t/a), where t is the time in seconds and Q0 is the maximum char...

Q: Find the average value of the function f(x) = e-4x on the interval [0, 1/2 ]

A: Given:The function is f(x) = e−4x .Definition used:The average value of a function f(x) on the inter...

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

A: Please see the picture on the white board. I have used the picture in the question and marked all th...

Q: If y 3 , then dx 5x2-3 10r2 3V/5x2-34 35x2- 3) 5x2-3 10x 3 3(5x2-3)2 10r 3 35x2-3)

A: Find the derivative of the given function.

Q: Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is inf...

A: We first have to factor the numerator and the denominator.

Q: If the formula describing the distance s(in feet) an object travels as a function of time(in seconds...

A: The distance s(in feet) an object travels as a function is s = 100 + 160 t -16t2.It is known that, t...

Q: 5. (4.9) A particle is moving with the given data. Find the position function of the particle: at)si...

A: Acceleration function is given as a(t) = sin(t) + 3cos(t).Integrate the acceleration function to get...

Q: This is solving the 2nd derivative of f(x) = x^2/ 1+e^x, and we have already obtained the 1st deriva...

A: The given function is,

Q: Hello, find the exact value of each of the following under the given conditions. sin alpha=3/5, 0&...

A: We have to find value of tan(alpha-beta).Information is given below:

Q: Differentiate xy^2+tan(y^3)=10y

A: Consider the given expression:

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

A: we are given rate functions as

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

A: The given series is

Q: Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is inf...

A: We have to plug x=5 first in the given expression.

Q: The hyperbolic cosine function, denoted cosh x, is used to model the shape of a hanging cable (a tel...

A: Given information:Tyhe given function is cosh(x).

Q: Question: Find the area of the region bounded by y y0, x1, x-4

A: The area of region bounded by the curve y=(x^2+x-1)/((x)^1/2), x=1,x=4,y=0.

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

A: (a)we are given a function

Q: A mass hanging from a spring is set in motion and its ensuing velocity is given by v(t) = -2 sin (pi...

A: To find the position function we integrate velocity function and use s(0)=2.Answer(A): Position func...

Q: I need help for this.

A: (a) Use the ratio test and compute the interval of convergence as follows.

Q: Find the aveage temperature in the box. Please refer to image. The bounds of x are 0 and ln3 The bo...

A: Given information:The given temperature distribution is T(x,y,z)=15e-x-y-z.

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

A: Given,

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

A: (d) First draw the graph of y = x + 6 and y = x2.Find the intersection points as,

Q: The equation of the line tangnet to the graph of 24e^x at x=2?

A: Find the derivative of the given function.

Q: 1) The substitution u = tanx gives∫(sec2x.tanx)dx = ∫(x)du = 1/2.u2 + C = 1/2.tan2x + CThe substitut...

A: Yes, both integrations are correct by their respective substitutions.Reason:An integral of a functio...

Q: How do I solve this Bernoulli equation using P(x), Q(x) and n as well as u(y)?

A: First, we write it in form of Bernoulli Differential equation.

Q: A fence is to enclose a lot with area 100 square meters. The front of the fence (considered the east...

A: Let the length of the east-west side is = x meter and the length of the north-south side is = y mete...

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

A: a)Analytically complete six rows of a table as below.

Q: Let (0 ifx-5 f(x) 0 ifz 4 and 9(x)-f(t)dt 5 Determine the value of each of the following (d) g(5) (e...

A: The functions are given as

Q: 21 If fx)3then f(x) O 2x-2-1 3x 2x-3r2-3 3x O 2x-3x2-3 6x 2x 3x+2 O 2x-x2-1

A: Find the derivative of the given function.

Q: Let R be the region bounded by y x, x 1, and y 0. Use the shell method to find the volume of the sol...

A: (A)It is given that, the region bounded by y = x2, x = 1 and y = 0.The region around the line y = -8...

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

A: The function is given by,

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...