Calculus

Integrating an exponential function

Integrating an exponential function

How to integrate this one ?
(e^x)-1/(e^x)+1

Deckz   130   5 Replies

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bio_man

Find the derivative using delta method

Find the derivative using delta method

1/Square root(x+1)

Mathus   96   4 Replies

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bio_man

Who can help me on my integral calculus. Our topic is on algebraic substitution :((

Who can help me on my integral calculus. Our topic is on algebraic substitution :((

help please ( message me if u want to help

ghostar   96   1 Reply

bio_man

Derivative of transcedental function

Derivative of transcedental function

find y'' if y=cos3xsin2x,   and if x=60°
         y'=cos3x•d/dx(sin2x)+sin2x•d/dx(cos3x)
         y'=cos3x•cos2x•2+sin2x(-sin3x)•3
&nbs

Deckz   109   1 Reply

duddy

Finding the derivative of the given function

Finding the derivative of the given function

f(t)=[2/squareroot(t)]+[6/cuberoot(t)]

The answer my book was :
(-t^1/2+2t^2/3)/t^2


Yet i'm getting different answer, can someone try it ? Hoping we got same answer  

Deckz   120   4 Replies

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Deckz

How to plot the graph of product of trignomatric and exponential function of base e without table

How to plot the graph of product of trignomatric and exponential function of base e without table

 plot e^x cosx without point table

tamim   51   1 Reply

bio_man

Integrate dy/square root of y+4 minus 2

Integrate dy/square root of y+4 minus 2

Integrate dy/square root of y+4 minus 2

Allen z   52   1 Reply

bio_man

Calculus differential equation (not sure which type)

Calculus differential equation (not sure which type)

A population r(t) of rabbits (at time t) satisfies
dr/dt = kr (1 − (r/r∗)) − αfr                                       (1)
where k > 0 i

yungdumb   102   5 Replies

duddy

The population of a

The population of a

1.The population of a certain state (in thousands) at t years since 1991 is modeled by the polynomial p(t)=-0.24t^2+111t+6766.

a. Find the average growth rate from 1991 to 2001 analytically.
b. Find the instantaneous growth rate in 19

yoyoyo12345   38   3 Replies

bio_man

12.Determine analytically, showing all work, all values of x (if any) at which the the func on f(x)

12.Determine analytically, showing all work, all values of x (if any) at which the the func on f(x)

1. Find analytically the equation of the line that is tangent to g(x)=sqrt（-x-3 ）and parallel to the line y=-1/2x+2. Use the limit definition of the derivative and find the point of tangency by hand, showing all work. Verify your results by sketching

ccnnieeee   59   1 Reply

bio_man

What is the integral of √(a-y) /√y

What is the integral of √(a-y) /√y

What is the integral of √(a-y) /√y

Rentz   51   1 Reply

bio_man

Determine whether or not of the following statements are true or false, and give explanations or cou

Determine whether or not of the following statements are true or false, and give explanations or cou

1. Determine whether or not of the following statements are true or false, and
give explanations or counterexamples for each.

If a < b and f ( a ) < L < f ( b ), then there is some value of c in ( a , b ) for which f ( c ) =

chansamhua   102   10 Replies

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bio_man

If f(x) = g(x) for all values of x except possibly for x = 2 and limx→2 g(x)=5 , then

If f(x) = g(x) for all values of x except possibly for x = 2 and limx→2 g(x)=5 , then

1. If f(x) = g(x) for all values of x except possibly for x = 2 and limx→2 g(x)=5 , then
a. f(2)=5
b.limx→2 f(x)may not equal 5
c.limx→2f(x)=5

2.If f(x)={4x+1 if xnot equals to , x+b if x=0} and limx→0 f(x)=f(0) , then

ccnnieeee   91   5 Replies

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bio_man

For the position function s(t) = −16t^2+110t : a) Complete the following table with the ...

For the position function s(t) = −16t^2+110t : a) Complete the following table with the ...

For the position function s(t) = −16t^2+110t :

a) Complete the following table with the appropriate average velocities (show work and
give up to 3 decimal places)
Time Interval    [0.99, 1]        &n

ccnnieeee   63   3 Replies

duddy

Use a reference triangle to find the exact value of cos[arctan(-3/10)]

Use a reference triangle to find the exact value of cos[arctan(-3/10)]

1. Use a reference triangle to find the exact value of cos[arctan(-3/10)]
2.y= arctan(1/x),  Use a reference triangle to find cos y.

ccnnieeee   52   3 Replies

duddy

1. The position of an object moving along a line is given by the function s(t) = t^2-2t .

1. The position of an object moving along a line is given by the function s(t) = t^2-2t .

1. The position of an object moving along a line is given by the function s(t) = t^2-2t .
What is the average velocity over the interval [0, 2] ?
2. The position of an object moving along a line is s(t) = t^2-2t . Approximate the instantane

ccnnieeee   54   4 Replies

bio_man

Find the derivative of the inverse trig fn below

Find the derivative of the inverse trig fn below

I literally don't know how to solve it because every time i'am getting a wrong answer so I need help Guys

b=arcsec[(a^2+1)/(a^2-1)]

Inverse trig fn   67   1 Reply

bio_man

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   122   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   129   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   103   1 Reply

bio_man

Find the required derivatives using appropriate formula

Find the required derivatives using appropriate formula

#1. Start w

bio_man   94   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   125   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   90   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   196   N/A

bio_man

Find the derivative of

Find the derivative of

[math=inline]x\cdot \sin y

bio_man   228   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   153   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   240   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   101   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   130   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   171   N/A

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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   122   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   79   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   95   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   89   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   55   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   57   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   79   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   52   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   55   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   80   1 Reply

potatobraiinz