e. n=1

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A: Mean value theorem states that:If f(x) is continuous on the closed interval [a,b] and differentiable...

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A: It is given that,

Q: A forest ranger is in a forest 2 miles from a straight road. A car is located c miles down the road....

A: Consider the given diagram:

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A: To evaluate the given limit 

Q: 31. | V36 — 9х2 dх

A: Use trigonometric substitution x=2sint.

Q: Calculus Question

A: Given,

Q: Consider the function f(x, y) = (a) Find f(0, 0) and f(0, 0) fx(0, 0) fy(o, 0)= (b) Determine the po...

A: According to the given information the given function is:

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A: Given,          A crate open at the top has vertical sides, a square bottom, and a volume of 256 cub...

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A: Given information:

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A: Substitute the point (-3,-1) in the given equation.

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A: To determine the value of x.

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A: To verify the hypotheses of the mean value theorem and find all numbers c that satisfy the conclusio...

Q: Find the length of the curve 9y =8x5 from x 0 to x 12 when y> 0. The length of the curve is(Type an ...

A: Given that,

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A: To determine a point on the ellipsoid where the tangent plane is perpendicular to the line.

Q: How do you find the derivative of an inverse trig function?

A: Note that, there are six trigonometric functions which also have inverses. There are general formula...

Q: The population of a city is 40,000.The city grows continuously by 2.4% per year. If this trend​ cont...

A: 2.4%= 0.024So growth rate = 1+0.024=1.024Every year the popukation grows by 1.024

Q: A piece of wire 18 m long is cut into two pieces. One piece is bent into a square and the other is b...

A: Let x m make a square.So each side= x/4 mArea of the square = (x/4)^2= x^2/16 m^2

Q: A voltage V across a resistance R generates a current I=V/R. If a contant voltage of 6 volts is put ...

A:

Q: Find the slope of x cubed plus y cubed minus 84 xy equals 0x3+y3−84xy=0 at the points left parenthes...

A: The given curve is,

Q: see attachment

A:

Q: Determine if the series below converges or diverges. If it converges, determine what to do.

A: To discuss the convergence or divergence of the given series

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A: Given:

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Q: Hi Please help me with number 2.  Please refer to limit theorems on the "APEX Calculus Version 4" ch...

A: Given,

Q: see attached

A: To find the first four terms of the given sequence substitute the value of n = 1, 2, 3 & 4 and g...

Q: Hi Please help me with number 1.  Please refer to limit theorems on the "APEX Calculus Version 4" ch...

A:  In the given question it is needed to find the derivative of the function f(x) = 7x-3 using the def...

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A: The given function is

Q: The temperature at any point (x, y) in a steel plate is T = 500 - 0.6x2 - 1.2y2, where x and y are m...

A: Partial differentiation with respect to x. Treat every other variable as a constant.

Q: Brain weight B as a function of body weight W in fish has been modeled by the power function B = 0.0...

A: Given that,

Q: How do you perform integration by parts?

A: Integration by parts is,

Q: please answer only question 57. the guidelines and question are provided in the images.

A: Given function is

Q: Calculus Question

A: The spherical balloon is filled with helium gas at the rate of 3 cubic feet per second.

Q: Exercise 3: Use the squeeze theorem to prove lim0 sin(x-1) = 0

A: To prove:

Q: Determine whether there is a relative maximum, a relative minimum, a saddle point, or insufficient i...

A:

Q: Differentiate the function. h(x) 13 csch (x3) Give your answer in exact form. 39x2 39х h(x) = 6 х

A:

Q: Find the derivative of the following function.: y=ln(x2+4)2π

A: The given function is,

Q: Sketch the solid described by the given inequalities: 0<=r<=2, -pi/2<=theta<=pi/2, 0<...

A: First draw the first two inequality 0<= r <=2 and –pi/2<= theta <= pi/2 in the xy-plane....

Q: A baseball team plays in a stadium that holds 54000 spectators. With the ticket price at $11 the ave...

A: Given that a baseball team plays in a stadium that holds 54000 spectators. With the ticket price at ...

Q: 21. In 3x dx

A: Given integral is

Q: Find the limit of the Function if it exists? lim (x,y) to (0,0) ytanx /3x^2 +y^2

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Q: Can you help me on #29.

A: Given:

Q: 60

A:

Q: Calculus Question

A:

Q: show work to prove if the serie is convergent or divergent?   as n=> infinity   an= (ln(3n)) / (3...

A: The given series is,

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A: We need to compute the following derivative.

Q: The radioactive element carbon-14 has a half life of 5750 years. A scientist determined that the bon...

A: Given:The radioactive element carbon-14 has a half-life of 5750 years and the bones from a mastodon ...

Q: A rectangular sheet of cardboard 3 m by 8 m is used to make an open box by cutting squares of equal ...

A: According to the given question:Length of cardboard = 8mBreadth of cardboard = 3mA square of equal s...