Calculus

Delta method versus quotient rule

Delta method versus quotient rule

\(f\left(x\right)=\frac{3}{x^2+1}\)

Applying the quotient rule, notice how the denominator is now squared:

[math=inline]f'\left(x\right)=\frac{\left(0\right)\left(x^2+1\right)-\left(3\right)\left(2x\right)}{

bio_man   24   N/A

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bio_man

Solving for d^2/dx^2

Solving for d^2/dx^2

Need help checking my paper if I did the right process or not
I've attached it

Deckz   76   5 Replies

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bio_man

Use the Delta Method to derive the variance for the quantity [E(Xt^2 )]^3.

Use the Delta Method to derive the variance for the quantity [E(Xt^2 )]^3.

This is a question on my Asset Pricing assignment. I don't know how to calculate this one by delta method.

Wendy   54   1 Reply

bio_man

Find the required derivatives using appropriate formula

Find the required derivatives using appropriate formula

#1. Start w

bio_man   56   1 Reply

Kevin666

How to get the Y' of this function ?

How to get the Y' of this function ?

I really dont know how did the answer turned down to y/x based from my textbook 
Can you show me how it was done ?

Deckz   58   1 Reply

bio_man

How to solve for the derivative of this trig. function ?

How to solve for the derivative of this trig. function ?

see the atrached img. 

Deckz   44   3 Replies

bio_man

Finding the derivative of inverse tangent

Finding the derivative of inverse tangent

From the image, your function is: [mat

bio_man   123   N/A

bio_man

Find the derivative of

Find the derivative of

[math=inline]x\cdot \sin y

bio_man   134   N/A

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bio_man

Delta method question!

Delta method question!

Find the derivative of this by the delta method

\(y=x^2+3x-\frac{2}{x}\)

\(\frac{dy}{dx}=\lim _{\Delta x\rightarrow 0}\left(x^2+3x-\frac{2}{x}\right)\)

Apply [math=inl

bio_man   55   N/A

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bio_man

Chain rule help

Chain rule help

\(y=\sqrt{u^2-1}\)
\(u=4\sqrt{x}\)

Put u into x

\(y=\sqrt{\left(4\sqrt{x}\right)^2-1}\)

Simplify:

\(y=\sqrt{16x-1}\)

bio_man   144   N/A

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bio_man

Rules of differentiation Discussion

Rules of differentiation Discussion

These rules you have nothing to worry about. They're there to make differentiation easier to do, that's all.

Examples:

[highligh

bio_man   42   N/A

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bio_man

Delta method for x√x

Delta method for x√x

If you've been given:

\(x\cdot \sqrt{x}\)

You have to first change it into fractional exponents:

\(x\cdot x^{\frac{1}{2}}\)

Then use the exponent laws t

bio_man   70   1 Reply

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bio_man

Delta method calculus for ³√x²

Delta method calculus for ³√x²

Set:

\(f\left(x\right)=\sqrt[3]{x^2}\)

Apply into limit expression, do not take the limit yet:

[math=inline]\lim _{x\rightarrow 0}\ \frac{\sqrt[3]{\left(x+\Delta x\right)^2}-\sqrt[3]{x^2}

bio_man   92   N/A

bio_man

Cube root of x by the Delta Method

Cube root of x by the Delta Method

\(f\left(x\right)=\sqrt[3]{x}\)

\(\lim _{x\rightarrow 0}\ \frac{\sqrt[3]{x+\Delta x}-\sqrt[3]{x}}{\Delta x}\)

Recall:

[math=inline]a^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)

bio_man   76   1 Reply

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bio_man

Derivative by the delta method

Derivative by the delta method

Determine an equation of the line that is perpendicular to the tangent to the graph of f(x)=1/( x )  at x=2 and that intersects it at the point of tangency.

klcarrasquillo   41   1 Reply

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veronee_madison

Expand (x + Δx)²

Expand (x + Δx)²

Answer:

(x + Δx)² = (x + Δx)(x + Δx)

We 'expand' (aka FOIL) by multiplying each term:

x*x = x²
x*Δx = xΔx
Δx*x= xΔx
Δx*Δx = Δx²

[

bio_man   62   1 Reply

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gaminglifex

Applying Newton's law of cooling and differential equations

Applying Newton's law of cooling and differential equations

Suppose we place a 90 °C cup of coffee into a 20 °C room. If the coffee is in a Styrofoam cup for which k≈−0.05, what is the temperature of the coffee as a function of time?

chementhusiast   65   1 Reply

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austire

Differential equations with exponential growth and decay

Differential equations with exponential growth and decay

The rate of change of the amount of morphine in the human bloodstream is proportional to the amount of morphine present. If initially there is 0.4 mg of morphine in the bloodstream, and only 0.2 mg remains after 3 hours, find an equation for the amou

chementhusiast   34   1 Reply

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zar

Differential equations with exponential growth and decay

Differential equations with exponential growth and decay

Suppose that a rumour spreads according to dP/dt=1.1P. If 3 people know the rumour initially, how many people will know the rumour as a function of time?

chementhusiast   32   1 Reply

Bella_23

How to setup and solve differential equation problems

How to setup and solve differential equation problems

A certain small country has $10000 million in paper currency in circulation and each day $50 million comes into the country's banks. The government decides to introduce new currency by having the banks replace old bills with new ones whenever ol

chementhusiast   42   1 Reply

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bio_man

How to setup and solve differential equation problems

How to setup and solve differential equation problems

A 15 000 ft^3  room has 20 ppm smoke. Fresh air enters at a rate of 1200 ft^3/min and forces the smoky air out. What is the smoke content as a function of time?

chementhusiast   34   1 Reply

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jayjayhussle310

How to setup and solve differential equation problems

How to setup and solve differential equation problems

A tank contains 10 L of water with 4 g/( L )  of dissolved salt. Water containing 2 g/( L )  of salt enters the tank at a rate of 7 L/( min ). The solution is kept thoroghly mixed and drains from the tank at the same rate.

How m

chementhusiast   33   1 Reply

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jamiebonf99

How do I setup and solve differential equation problems

How do I setup and solve differential equation problems

Suppose we have 7000 L of water with 50 kg of salt in it. If we add pure water at a rate Of 2 L/min and add water containing 0.6 kg/L of salt at a rate of 9 L/min, and we know that water flows out at a rate of 11 L/min, then what is the salt content

chementhusiast   42   1 Reply

potatobraiinz

Convert verbal statements into algebraic equations

Convert verbal statements into algebraic equations

If twice a certain number is increased by 9, the result is equal to 2 less than triple the number. Find the number.

After a certain number diminished by 8, the amount remaining is multiplied by 8; the result is the same as if the number we

Goalchi   28   1 Reply

duddy

Solve second-order differential equations when the right side is zero

Solve second-order differential equations when the right side is zero

My first question on Bioforums:

Solve the equation y^′′−3y^′+2y=0.

Solve the equation y^′′−5y′=0.

Goalchi   31   1 Reply

duddy

Solving 2nd order differential equations

Solving 2nd order differential equations

Solve the equation y^′′=x^2  (where x is in radians) if y^′=1 at the point (0, 0).

Please and thanks

chementhusiast   32   1 Reply

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duddy

Write an equation of a curve for a differential system

Write an equation of a curve for a differential system

The slope of a curve at each point is one-tenth the product of the ordinate and the square of the abscissa, and the curve passes through the point (2, 3).

Find the equation of the curve.

chementhusiast   41   1 Reply

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bio_man

Need help solving first-order linear differential equations

Need help solving first-order linear differential equations

First I have:

Write the equation xy^′−e^x+y=xy in the form dy/dx+Py=Q

Next I have:

Solve dy/dx+4y/x=3

Thanks

chementhusiast   47   1 Reply

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bio_man

Differential equations: homogenous equations

Differential equations: homogenous equations

Determine if the following differential equations are homogeneous.

(a) (x^2+y^2 )dx+xy dy=0

(b) (x^2+y^2 )dx+x dy=0

Thanks

chementhusiast   44   1 Reply

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bio_man

How do I deal with first order linear differential equations?

How do I deal with first order linear differential equations?

I have these two questions

Solve y^′+y cot⁡x=csc⁡x

Solve y^′+((1−2x)/x^2 )y=1 given that y=2 when x=1.

Hope someone can helpppppp

chementhusiast   42   2 Replies

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bio_man

Finding derivatives of exponential functions (4 questions)

Finding derivatives of exponential functions (4 questions)

I need help on all four questions:

Derive the function: f(x)=〖10〗^(x^2+2)

Find the first, second, and third derivative of y=2e^3x.

Find the derivative of \(y=e^{\left(x^3+5x^2\right)}\).

Dif

chementhusiast   63   1 Reply

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SIN

Solving homogenous differential equations, how?

Solving homogenous differential equations, how?

The question I have is this:

x dy/dx−y=√(x^2+y^2 ) 

How do I solve it?

chementhusiast   36   1 Reply

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bolbol

How do I use the Runge-kutta method for differential equations?

How do I use the Runge-kutta method for differential equations?

Find an approximate solution to y′=x^2/( y ), with the boundary condition that y=2 when x=3. Calculate y for x=3 to 10 in steps of 1.

Thanks!

chementhusiast   49   1 Reply

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bolbol

What's an improper integral and how do you integrate it?

What's an improper integral and how do you integrate it?

My teacher has given me two functions to integrate:

Q. Evaluate the improper integral  ∫ between 0 and 4 for the function 1/√x dx

Q. Evaluate the improper integral that converges  ∫ between 0 and 2 for the function dx

chementhusiast   43   1 Reply

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bolbol

Finding the area using the prismoidal method?

Finding the area using the prismoidal method?

A curve passes through the points (1, 2.05), (3, 5.83), and (5, 17.9). Assuming the curve to be a parabola, find the area bounded by the curve and the x axis from x=1 to x=5.

chementhusiast   23   1 Reply

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bolbol

Finding solutions to differential equations

Finding solutions to differential equations

Question 1
Is the function y=e^2x  a solution of the differential equation y^′′−3y^′+2y=0 ?

Question 2
Show that the function, 4x^3−3y^4=C, is a solution to the differential equation, dy/dx=x^2/y^3   .

chementhusiast   30   1 Reply

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bolbol

Guidance on how to use Euler's method using differential equations

Guidance on how to use Euler's method using differential equations

Anyone have any resources for this?

chementhusiast   63   1 Reply

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bolbol

How to Find the area underneath a curve using the Simpson's Rules

How to Find the area underneath a curve using the Simpson's Rules

A curve passes through the following data points:

Find the approximate area under the curve using Simpson's rule.

Thanks for the help

chementhusiast   35   1 Reply

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bio_man

Finding the derivative of functions with tangent

Finding the derivative of functions with tangent

Looking for help on these

Q.   Find the derivative of the following:

(a)   \(y=3\tan x^2\)

(b)   \(y=2\sin 3x\cdot \tan 3x\)

chementhusiast   31   1 Reply

bio_man

Calculus 1 - Application problem involving moving parts

Calculus 1 - Application problem involving moving parts

Link L is pivoted at B but slides along the fixed pin P. As slider C moves in the slot at a constant rate of 4.26 cm/s, the angle θ changes. Find the rate at which θ is changing when S=6.00 cm.

Thanks

chementhusiast   25   1 Reply

bio_man