03/19/19

#### I can't remember a fallacious proof involving integrals and trigonometric identities.?

My calc professor once taught us a fallacious proof. I'm hoping someone here can help me remember it.
Here's what I know about it:
- The end result was some variation of 0=1 or 1=2.
- It...
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#### What are some examples of infinite dimensional vector spaces?

I would like to have some examples of infinite dimensional vector spaces that help me to break my habit of thinking of $R^n$ when thinking about vector spaces.

03/18/19

#### Why are invertible matrices called 'non-singular'?

Where in the history of linear algebra did we pick up on referring to invertible matrices as 'non-singular'? In fact, since
- the null space of an invertible matrix has a *single* vector
- an...
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09/12/18

#### If 20% of the substance disappears in 10 years, what is its half-life? (Round your answer to two

A radioactive substance follows the decay equation dA/ dt= kA. If 20% of the substance disappears in 10 years, what is its half-life? (Round your answer to two decimal places.)

#### Question regarding integral of ln(2x+1) dx

∫ln(2x+1) dx; when I solve for this using u-sub with u = 2x+1, I get 1/2((2x+1)ln(2x+1) - (2x+1)) + C. However, when I solve for it using integration by parts, I get 1/2((2x+1)ln(2x+1)) - x + C....
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08/23/18

#### Does (lnx)^2/x^1.2 converge or diverge in the limits 1 to infinity

Does the integral converge or diverge?
∫1∞(lnx)2/x1.2 dx

04/21/18

#### Finding the work done ( calculus 3 )

Find the work done by the force field F=<z,x,y> on moving a particle from the point (3,0,0) to (0,pi/2,3) along the helix x=3cost, y=t, z=3sint

03/27/18

#### Differential Equations.

I've been trying to solve this problem for hours.
Find the solution of the differential equation
(ln(y))^4 dy/dx=x^4*y
which satisfies the initial condition y(1)=e^2
y=?

03/25/18

#### Differential Equation Question

How would I write this in matrix form (x' = AX)
x' = x
y' = y
Note: Is it supposed to be like this: x' = (1 v 1)(x v y) or x' = (1 + 0 v 1 + 0)(x v y)? Note: the "v" means the value after...
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12/13/17

#### A bucket that weighs 4 lb is lifted vertically at a constant rate of 2 ft/sec by means of a rope of negligible weight. As the bucket rises, water leaks out at a

A bucket that weighs 4 lb is lifted vertically at a constant rate of 2 ft/sec by means ofa rope of negligible weight. As the bucket rises, water leaks out at a rate of 0.2 lb/sec. If thebucket...
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12/13/17

#### show that there is an odd degree polynomial of every odd degree with no critical points

(in other words show that for any odd n there is a polynomial f(x) of degree n with no points x such that f(0)=0

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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06/26/17

#### Find the minimum distance from the origin to the surface

Find the minimum distance from the origin to the surface z2 = (x-1)2+(y-1)2

03/12/17

#### Confusion with differential equation applied as a matrix

http://i.imgur.com/PknZsfZ.png
I'm confused on why the first row has values 0 + yk+1 + 0 and the second row has 0 + 0 + yk+2

#### Is Sin^-1 (x) = - Cos^-1 (x)

In integration, it is given as:
Integration of 1/(1-x^2)^(1/2) = sin^-1 (x)
and
Integration of 1/(1-x^2)^(1/2) = - cos^-1 (x)
Does this imply both are equal?

09/16/16

#### Calculus 2 The Fundamental Theory of Calculus help

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of y=∫cos(u2)du for b=4x and a=cos(x). I don't quite understand what to do here.

09/13/16

#### Solving for t in this equation.

205e0.005t = 280 + t
Please help me solve for t. I would like to know how to do it by hand.

09/11/16

#### Find all the vertical asymptote of secx.

Wouldnt it have an infinite amount ? how do I know though if its a negative infinity or positive?

06/30/16

#### How do you find the roots/zeros of polynomials, with just the equation?

How do you find the roots of polynomial equations with highest powers of either 3 or 4. Step by step directions would helike please.
Well, i have tried those methods. I still cant find an...
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#### Integration question involving cosh^-1???

Evaluate the integral (1/sqrt(x^2 - 5))dx on limits of 3 to 4, using the formula: integral of (1/sqrt(x^2 - a^2))dx.
Recall that this formula was found by using the substitution x = a cosh t, and...
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