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Q: Hello, How is tan^-1 (tan (6pi/7)=-pi/7 possible? I don't know how it should be a negative or to use...

A: First consider:

Q: Calculate the directional derivative in the direction of v at the given point. fx, v)- tan Cy). -(1,...

A: The partial derivatives of f(x,y) at the point (x,y)=(5,2)are:

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

A: Use Pythagorean theorem,

Q: A particle travels clockwise on a circular path of diameter R, monitored by a sensor on the circle ...

A: Before we get into the question, please recall the theorem that: An angle in a semi circle is always...

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

A: The given function is,

Q: Analysis of daily output of a factory shows that, on average, the number of units per hour y produce...

A: Part (a)The critical values will be where dy/dt = 0. Please see the white board.

Q: Evaluate the following integrals (a) x^5dx (b)(5^2+x^10)dx (c) (12x^5+12x^3-7)dx (d) (x^3-7-(3/x^4))...

A: You have asked a question with multiple sub parts. I will address the first three of them. Please po...

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

A: The given function is,

Q: Kindly help me with this differential equation and identify P(x), Q(x) and v(x).

A: The given differential equation is,

Q: s9-3x then y If y O 89-3x)4 25 O 819-3x)4 25 O 8(0-3x)4 O -24(9-3x)4 O 24(9-3x)4

A: The function is given by,

Q: +2 2 1

A: Consider the integral,

Q: Can somebody help me on how to evaluate the integral.

A: Refer to the question, first evaluate the given integral in indefinite form that is with the limits.

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

A: (a)we are given a function

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

A: We have to find limits.Question is given below:

Q: graph quadratic function f(x) = -3x2- 12x -1

A: Consider the given equation

Q: 1000 Find the marginal cost when q = 10. 9 The average coste for producing q units of a product is g...

A: The average cost c is given by ,

Q: Show that f(x, y) = ln(x2 + y2) solves Laplace's equation, ∂2z ∂x2 + ∂2z ∂y2 = 0...

A: Given Laplace’s equation is

Q: Find the function represented by the following series and find the interval of convergence of the se...

A: The function is given by,

Q: Which of the following is the power series representation for f(x)? A. Σ ( -1): Ο Β. Σ 11k k 0 k 0 Ο...

A: In the given question we have to find the interval of convergence of power series representation for...

Q: Consider an object moving along a line given the velocity v. Assume t is time measured in seconds an...

A: To find the direction we have to graph the function v(t)=2t^2-16t+24;[0,7]And then we check the inte...

Q: 150 100 50 20 40 60 3. Suppose that a population develops according to the logistic equation (c) Use...

A: Given that a population develops according to the logistic equation

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: 12. An oil tanker struck a reef and caused an oil spill in the ocean. Assume that in its early stage...

A: Let r be the radius of the oil spill which is circular in shape.Given,

Q: Find the arc length of the curve below on the given interval 3 /2 on (0,10] y 2x Which of the follow...

A: Click to see the answer

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

A: Consider the geometric series,

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

A: The given interval is [-1,1] and the function is,

Q: 7n 5-4n For the following answer blanks, decide whether the given sequence or series is convergent o...

A: (a)we are given a series as

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: Please help!

A: Recall the quotient rule for derivative:

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

A: Click to see the answer

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

A: To find two positive numbers whose sum is 210 and whose product is a maximum.(a) Analytically comple...

Q: Part d and e

A: (D) When the enclosed region revolve about x=2 line then the radius is on the line joining (2,0) and...

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: 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: Product Radius (inches) Height (inches) Volume (cubic inches) Baking power 1.25 3.65 ...

A: Assuming all the items are in cylindrical shape. Look for the coffee can: The volume V is 62.12 in3;...

Q: I need help please.

A: Rewrite the given series and proceed further.

Q: For the following function f, find the antiderivative F that satisfies the given condition. 2 f(v)= ...

A: Given,

Q: 3 dx = 1 2x 8 In 국 5 -4 In 2 In을 -2 In -8 In LOn LOn

A: Obtain the value of the integral as follows.The given integral is,

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

A: Click to see the answer

Q: Find the equation of the tangent to (x2+/ 5x2-Уг at the point (1,1). 8.

A: Given curve is: (x2 + y2)2 = 5x2 – y2and the given point is (x1, y1) = (1, 1)Equation of tangent wil...

Q: Use the SubstitutionFormula, Integral from a to b f left parenthesis g left parenthesis x right par...

A: Let us assume y=(sec x)/4

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: Please help.

A: The given series is,

Q: Evaluate the integral. Integral from nothing to nothing hyperbolic cotangent StartFraction x Over ...

A: Refer to the integral,Rewrite the hyperbolic cotangent as,

Q: Given f(x) = x^3 + 3x - 2 , find y = (f ^-1 (x))' at the point (2,1)

A: Click to see the answer

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: 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: how do i get number 3

A: Expanded the expression of f(x) first then used the exponent rule to find the derivatives.