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Q: Equation of the plane that passes through the point (8, -6, 4) and contains the line of the given eq...

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Q: Let y represent the temperature (in °F) of an object in a room whose temperature is kept at a consta...

A: The object cools from 100°F to 90°F in 10 minutes.

Q: The radius r of a sphere is increasing at a rate of 3 in/min Find the rates of change of the volume ...

A: The radius of sphere is increasing at a rate of 3 inmin. drdt=3 inmin. ........1 Volume of sphere = ...

Q: In Exercises 45–48, calculate the derivative using the values: f(4) f'(4) 8(4) g'(4) -1 10 -2 5

A: f(4) f'(4) g(4) g'(4) 10 -2 5 -1

Q: Fill in the blank/s : If t is a real number and P = (x, y) is a point on the unit circle that corres...

A: given: P=(x,y) is a point on the unit circle that corresponds to t. as we know that x2+y2=r2 is the...

Q: Let M(t) be the mass (in kilograms) of a plant as a function of time (in years). Recent studies by N...

A: (a) The growth rate of a tree having its mass as function of time can be given by formula for some c...

Q: Show that the function is differentiable by finding values of ε1 and ε2 as designated in the definit...

A: Given f(x,y)=x2y

Q: Suppose that a cylindrical can is designed to have a radius of 1 in and a height of 5 in, but that t...

A: Radius of cyclindrical can r1 is 1 in. Height of cyclindrical can h1is 5 in. Radius is off by the am...

Q: Hi, need a step by step break down please

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Q: Find the area bounded by the curve or line: y2+4x-8=0, Y=2x

A: Given that: The equation of the curve y2 + 4x - 8 = 0. The equation of the line y = 2x.

Q: 5b. Explain what this means? (What does the graph look like?) 5х - 2 5. lim X→-4+ x + 4

A: To explain what this means limx→-4+5x-2x+4 and how the graph looks like:

Q: The question has been attached which is number 6. Please solve the problem.

A: We first sketch the region using a graphing calculator. From the graph, we see that x is from 0 to ...

Q: Many areas of Northern California depend on the snowpack of the Sierra Nevada mountain range for the...

A: Concept: The calculus helps in understanding the changes between values that are related by a functi...

Q: The graphs of y = sin-1 x, y = cos-1 x, and y = tan-1 x are shown in the given table. Use transforma...

A: fx=sin-1x-2-π2 The of fx=sin-1x-2-π2 is obtained by horizontally shifting the graph of y=sin-1x to t...

Q: The City Council proposed to utilize a government-owned land with an area of 15,000 square meters. O...

A: Click to see the answer

Q: I need help with number two, thank you!

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Q: Calculate the limit limx→eln(lnx)x−e

A: the given expression is: limx→elnlnxx-e we know that logaa=1

Q: Use the theorem of Pappus to find the volume of a torus (pictured here). Assume that a disk of radiu...

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Q: Limit question.

A: Consider the function f(x)=sin(3x2)2x, if x≠00, if x≠0

Q: 25+64

A: given the two numbers 25 and 64 we need to find the sum of two numbers that is 25+64=?

Q: The question has been attached which is number 5. Please solve the problem.

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Q: Give a geometric description of the set of points (x, y, z) satisfying the pair of equations z = 0 a...

A: given: the set of points (x,y,z) satisfying the pair of equations z=0 and x2+y2=1. as we know that t...

Q: Air pressure at sea level is 30 inches of mercury. At an altitude of h feet above sea level, the air...

A: Hey, since there are multiple subparts posted, we will answer the first 2 question. If you want any ...

Q: Find the derivatives of the function f for n = 1, 2, 3, and 4. f(x) = xn sin x

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Q: This is problem 48 Section 7.3 page 447. Evaluate the given integral. 1 Vx2 + 8x + 3

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Q: Find the difference quotient of f; that is, find f(x+h)−f(x)h/h . f(x)=-6x+5.

A: The function f(x) is, f(x)=-6x+5 The expression for the difference quotient of f is given by: Dq=f(x...

Q: I need to generate a continuous and differentiable function f(x) with the following properties: f(x...

A: Given The f(x) is decreasing at x=−5 The f(x) has a local minimum at x=−3 and f(x) has a local max...

Q: In this problem, p is in dollars and q is the number of units.Suppose that the demand for a product ...

A: Consider the equation 2p2q = 30,000 + 9000p2.

Q: For each of the following, make use of the product rule in finding the derivative of the dependent v...

A: Given, y=(x2-2x+3)(2x2+13x-6)(3x2-4x+1)

Q: Given x^3y+xy^3=2, find y^1 and y^II at the point (1,1) by implicit differentiation twice.

A: x3y+xy3=2To find→y' and y'' Product rule: ddxu⋅v=u⋅dvdx+v⋅dudx

Q: The City Council proposed to utilize a government-owned land with an area of 9,600 square meters. On...

A: Since you have asked multiple questions in a single request, we would be answering only the first qu...

Q: Two cars are approaching an intersection on roads that are perpendicular to each other. Car A is nor...

A: Click to see the answer

Q: Does the function still have a limit at -2, 0 and 32? And are they differentiable at these numbers ?

A: {x2 if x<-2f(x)={x1/5 if -2≤x&...

Q: In this problem, p is in dollars and q is the number of units.Suppose that the demand for a product ...

A: Given that (p+9)q+6=600 ...(1)

Q: Find the slope of the tangent to the curve. (If an answer is undefined, enter UNDEFINED.) 2x2 - 10x ...

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Q: Bacterial population density follows the growth rate rule B'(t)=0.246B(t), where B(t) is in cells/ml...

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Q: -what is the second derivative of i (-1) when i(x) =x^2f(x) -What is the derivative of g(3) when g(x...

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Q: Determine how much time is required for a $500 investment to double in value if interest is earned a...

A: Given information: Consider P is the principal value which is given $500 and the rate of interest is...

Q: no need to draw the graphs, just use numbers/ draw only the lines

A: This graph is decreasing first, that means f'(x)<0 first. Then it is increasing. That means f'(x)...

Q: Graph the given functions, f and g, in the same rectangular coordinate system. Select integers for x...

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Q: 13.7 #1

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