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Calculus Python

03/03/25

3. For each of the sequences in parts (a), (b), and (c), write a Python function that accepts a positive integer n as input and returns an unrounded decimal approximation of the sequence’s nth term

Use these functions to print the terms of each respective sequence for 2 ≤ n ≤ 15.(a) The sequence of partial continued fractions is defined asa_(1)=1, a_(2)=1+(1)/(1), a_(3)=1+(1)/(1+(1)/(1)),... more

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Calculus

03/02/25

A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a velocity of 33 ft/s. Its height in feet after t seconds is given by y=33t-23t^2.

A. Find the average velocity for the time period beginning when t=1 and lasting: .01s, .005s, .002s, .001s. NOTE: For the above answers, you may have to enter 6 or 7 significant digits

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Calculus Precalculus

03/01/25

The concentration of a drug in the bloodstream

The concentration of a drug in the bloodstream tt hours after injection is given by the function C(t)=0.7te−1.5t,Ct=0.7te-1.5t, where the concentration is measured in milligrams/meter. How fast is... more

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Calculus Math Physics Differential Equations

02/28/25

Becoming a Tutor

I recently joined Wyzant, and I was interested in becoming a tutor instead of looking for a tutor for me. Where can I find that information to sign up to be a tutor? Thank you!

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Calculus Python

02/24/25

2. Use sympy to compute the exact volumes of the following solids S:

(a) S rests on the xy-plane, and its base is the region bounded between f(x) = sin(π/4 · x)and g(x) = cos(π/2 ·x)−1 on 0 ≤ x ≤ 4. Cross-sections of S perpendicular to the x-axisare isosceles... more

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Calculus Python

02/23/25

1. Some functions are too complicated to integrate exactly, even when using sympy or other computer algebra systems. However, there are ways to approximate the definite integrals of such functions.

In this problem, we will be using a Monte Carlo algorithm (named after a famous casino because this algorithm uses random numbers to approximate an answer) to approximate the area under a curve.(a)... more

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Calculus

02/20/25

Evaluate the integral. (Use C for the constant of integration.)

\int (dx)/((x^(2)+4)^((5)/(2)))

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Calculus

02/20/25

Evaluate the integral.

\int_0^(.75) (x^(2))/(\sqrt(9-16x^(2)))dx

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Calculus Python

02/13/25

A jeweler is designing a spherical metal bead with a hole drilled through the center to the opposite side. The bead has radius r millimeters and the hole has a radius of 1 millimeter.

(a) Integrate to find the volume V (r) of the bead, where the axis of rotation is parallel tothe hole.Hint: There are two valid ways of setting this up.(b) Suppose the jeweler needs the bead to be... more

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Calculus

02/07/25

Use calculus to find the area A of the triangle with the given vertices. (0, 0), (5, 3), (1, 4)

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Answers •3

Calculus

02/07/25

A spherical tank with radius 4 m is half full of a liquid that has a density of 900 kg/m3. The tank has a 1 m spout at the top.

Find the work W required to pump the liquid out of the spout. (Use 9.8 m/s2 for g.)

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Calculus

02/06/25

Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis.

y = x2, x = y2; about y = −5

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Calculus

02/06/25

Set up the integral that uses the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.

y = 7x − x2, y = 10; about the line x = 2

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Calculus

02/06/25

Set up the integral that would give the volume V generated by rotating the region bounded by the given curves about the y-axis.

y = x5, y = 0, x = 2Disk/Washer Method

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Calculus

02/06/25

Integrating Square Roots

Evaluate the integral0 ∫ 2pi √((1-cosx)/2) dxI have used (1-cosx)/2 = sin2(x/2) and canceled out the square root and the square on the sin function. I am to the point of 0 ∫ 2pi abs(sin (x/2))dx... more

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Calculus

02/06/25

Integrating Square Roots

Evaluate the integral:0 ∫ 2pi √((1-cosx)/2) dx

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Calculus Math

02/04/25

Question for math problem

When Ibuprofen is given for fever to children 6 months of age up to 2 years, the usual dose is 5 milligrams (mg) per kilogram (kg) of body weight when the fever is under 102.5 degrees Fahrenheit.... more

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Calculus Math Sat Math Differential Equations

02/04/25

Solve the following differential equation by finding an appropriate integrating factor

3xdx+(3x^(2)y+y)dy=0 The answer should be in the form F(x,y)=constant

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Calculus

02/04/25

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.

x=3y^2, x=3; about x=3

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Calculus

02/03/25

Integral of f'(x) given a table with x and f(x)

I was given a table withx= 0,3,5,7,8, and 12f(x)=67,58,51,46,44, and 39 respectivelyThe problem asks me to find the integral from 0 to 12 of f'(x). I know that the integral and derivative cancel... more

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Calculus

02/02/25

Evaluate the function f(x)=3x^2 - 9x + 6 at the indicated values of f(x/2) and f(x^2)

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Calculus Differential Equations

01/30/25

Exercise from Calculus 'Separation of Variables'

At any time t, the rate of growth of the population N of deer in a state park is proportional to the product of N and L-N, where L=500 is the maximum number of deer the park can sustain. When t=0,... more

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Calculus

01/30/25

Find the area of the region(s) between the given curves below on the given interval.

y = 5 cos x, y = 5 − 5 cos x from x = 0 to x = 𝜋

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Calculus

01/29/25

find the area of the region

y=e^x, y=x^2-1, x=-1,x=1I have worked this out and i got e-1/e-4/3 and it says im wrong can someone help and understand what i'm doing wrong. i use the formula integral from -1 to 1 (top - bottom)

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Calculus

01/28/25

Volumes of Revolution

If x ≥ 0, find the volume of the solid obtained by rotating the region enclosed by the graphs about the line y = —5.у = 90 - х. y = x2, x= 0(Use symbolic notation and fractions where needed.).

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3. For each of the sequences in parts (a), (b), and (c), write a Python function that accepts a positive integer n as input and returns an unrounded decimal approximation of the sequence’s nth term

A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a velocity of 33 ft/s. Its height in feet after t seconds is given by y=33t-23t^2.

The concentration of a drug in the bloodstream

Becoming a Tutor

2. Use sympy to compute the exact volumes of the following solids S:

1. Some functions are too complicated to integrate exactly, even when using sympy or other computer algebra systems. However, there are ways to approximate the definite integrals of such functions.

Evaluate the integral. (Use C for the constant of integration.)

Evaluate the integral.

A jeweler is designing a spherical metal bead with a hole drilled through the center to the opposite side. The bead has radius r millimeters and the hole has a radius of 1 millimeter.

Use calculus to find the area A of the triangle with the given vertices. (0, 0), (5, 3), (1, 4)

A spherical tank with radius 4 m is half full of a liquid that has a density of 900 kg/m3. The tank has a 1 m spout at the top.

Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis.

Set up the integral that uses the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.

Set up the integral that would give the volume V generated by rotating the region bounded by the given curves about the y-axis.

Integrating Square Roots

Integrating Square Roots

Question for math problem

Solve the following differential equation by finding an appropriate integrating factor

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.

Integral of f'(x) given a table with x and f(x)

Evaluate the function f(x)=3x^2 - 9x + 6 at the indicated values of f(x/2) and f(x^2)

Exercise from Calculus 'Separation of Variables'

Find the area of the region(s) between the given curves below on the given interval.

find the area of the region

Volumes of Revolution

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