373 Answered Questions for the topic Calculus 2

Calculus 2

01/25/18

#### What is the formula for the sequence -3,5,-7,9,-11...

Find a formula for sn for n>1, for the sequence -3, 5, -7, 9, -11 ...

Calculus 2

01/20/18

#### Calculus II Magnitude and Direction of Vectors

I have worked this problem at least 8 different times and keep getting the same answer every single time. Could somebody please explain how to work this problem? Here is the problem: The magnitude...
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#### I'm having trouble with series.

Let f(x)= ∑∞n=0 (x^n)/(n!)
Find f(0)= 1
f(1)= e
f'(x)= f(x)
f''(x)= f(x)
Not exactly sure how we're supposed to go about finding those answers, or how to start.

Calculus 2

12/09/17

#### Sequence and bounds

I found that the limit of the sequence (1+22/n)^n is e^22. I'm told the sequence is bounded because the absolute value of an is < or = to e^22 for all positive integers.
I would like to...
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Calculus 2 Physics

12/08/17

#### How much a force will stretch a spring

Suppose that a spring has a natural length of 20 cm, and that 7 J of work is needed to stretch from a length of 30 cm to 50 cm. How far beyond its natural length will a force of 28 N keep the...
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12/03/17

#### Find the power series of (x^2)ln(3-x) using term by term differentiation/integration?

how would you find the power series representation of x2ln(3-x) using term by term differentiation or integration?

Calculus 2

11/15/17

#### a mouse farm starts with 3 mice, and two months later has 18 mice. Assume the population growth continues exponentially.

Find the function that models the population after t months. Find the population after 9 months. When will the population reach one million mice

#### Determine whether the sequence converges or diverges. If it converges find the limit.

an=e(-1/sqrt(n))
Apparently in converges and the limit is 1 but I'm not really sure how to do this type of problem with a limit of ex
{n2e-n}
Limit converges to 0? How?

11/02/17

#### Consider the curve C given by the equation

Consider the curve C given by the equation: C · · · √ x + √ y = √ a, where a is a constant, a > 0. Let (x0, y0) with x0 > 0, y0 > 0, be a point on C. If (x1, 0) and (0, y1) are x and y...
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10/25/17

#### Given any Cartesian coordinates, (x,y), there are polar coodinates

Given any Cartesian coordinates, (x,y), there are polar coordinates (r,θ) with (-pie/2) < θ ≤ (pie/2).
Find polar coordinates with (-pie/2) < θ ≤ (pie/2) for the following Cartesian...
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10/23/17

#### A ball drops from a height of 20 feet. Assume it goes on forever, find the total distance it travels.

A ball drops from a height of 20 feet. Each time it hits the ground, it bounces up 40 percents of the height it fall. Assume it goes on forever, find the total distance it travels.

Calculus 2 Calculus 3

10/09/17

#### Use substitution x=sin theta to evaluate integrate x^2/(1-x^2)^5/2

Full working out please

Calculus 2

10/03/17

#### Determine the minimum number of terms needed to approximate Tan-1(1.1) so that |S-Sn|<10^-6

I think that i need to use a maclaurin series, but i dont understand how to go about this, if anyway could help, i would appreciate.

Calculus 2 Calculus

09/28/17

#### how would i find the y = version of this expression?

i need to turn xy = yx into a y = version so that i can take its derivative. how would i go about this?

Calculus 2

09/28/17

#### how do you write an expression as a power of e?

For my homework i am to write 5^x^3 as a power of e. how do i go about doing this?

Calculus 2 Calculus

09/28/17

#### Calculate the Laplace Transform of the function f(t)=1

Calculate the Laplace Transform of the function f(t)=1

Calculus 2 Calculus

09/28/17

#### Calculate the laplace transform.

Calculate the Laplace Transform of the function f(t)=0

Calculus 2

09/25/17

#### y=6u^2 - 10u + 4; u= 1/x^2 for x=1/4 and the derivative for x=1/4 is? dy/dx |

dy/dx | x= 1/4 =?

#### Trig Substitution

∫(x^2)/((16-x^2)^(3/2))dx
I keep on getting the wrong answer.

#### Trig Substitution

∫(√x^2-81)/(x^4)dx I can't seem to figure out this problem. Please help.

Calculus 2 Integration

09/06/17

#### How do I integrate (2x+1)/(x^2+16)^2 dx?

I'm suppose to use partial fractions, and I'm given the hint: "Each denominator contains a repeated irreducible quadratic factor".

Calculus 2

09/06/17

#### How do I integrate cosx/(sin^2(x)+9)^2dx?

I'm given the hint: "Make a substitution before using partial fraction decomposition".
edit: squared the denomenator

08/13/17

#### Find the interval of convergence of the power series

Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the interval of convergence is an interval, enter your answer...
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#### Find the Taylor or Maclaurin polynomial Pn(x) for the function f with the given values of c and n.

Find the Taylor or Maclaurin polynomial Pn(x) for the function f with the given values of c and n. Then give a bound on the error that is incurred if Pn(x) is used to approximate f(x) on the given...
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Calculus 2

08/05/17

#### A. Find the local extrema for the revenue function. B. On which intervals is the graph of the revenue function concave upward? Concave downward?

A dairy is planning to introduce and promote a new line of organic ice cream. After test marketing the new line in a large city, the marketing research department found that the demand in that city...
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