Here's the question:
Let f be the function satisfying f'(x)=x\sqrt{f(x)} for all real numbers where f(3)=25.
a. Find f''(3)
b. Write an expression for y-f(x0 by solving the differential equation \frac{dy}{dx} = x\sqrt{y} with the initial condition of f(3)=25.
For a, I got...
Calculus Logarithmic Functions help please!
The question is:
A particle moves alonge the x-axis with position at time t given by x(t) = e^(-t) sin t for 0 ≤ t ≤ 2π.
1. Find the time t at which the particle is farthest to the left. Justify your answer.
2. Find the value of the constant A...
When does 226Ra become "safe"?
Hi, I was working on an assignment which deals with radioactive decay.
Half life of 226Ra is 1600 years (it varies from source to source, but this is the one I chose), and the equation I got for half-life is y=Ce^(-0.000433216988t), C being the initial value and...
Hi
Currently, I have to write a research paper about application of calculus in one of these eight branches of sciences: geology, gravitation, immunology, oceanography, oncology, optics, sonics, and zoology. Can you give me an example of specific process in one of these sciences which...
Mark44: Actually, I would be thankful if you can explain how the antiderivative of arcsin (x) works, because I have trouble understanding the concept. Thanks.
Hi. I'm having trouble trying to understand the relationship between inverse trig functions, especially arcsin x, and pythagorean identity. I know that because cosx=sqrt(1-(sinx)^2), derivative of arcsin x is 1/(cos(arcsin x)) = 1/(sqrt(1-(sinx)^2)arcsinx)) = 1/(sqrt(1-x^2). But how does...
What are good sources to find a model for catenary used to build suspension bridges?
I know that the equation for catenary is a*sin(x/a). what does a stand for?
Thanks.
Hi, can you help me solve these three questions? Please show each step. Thanks.
1. solve for x: arcsin(6x-pi)=1/8
2. Find an equation of the tangent line to the graph of y = arcsin (6x) at the point ((1/(6sqrt2),(pi/4))
3. Find the indefinite integral of 1/sqrt(81-100x^2)
When I apply the Fundamental theorem of calculus in the last step, for LaTeX Code: \\int_8^{10} u^{-\\frac{1}{2}} du , do I use 8 and 10 as my a and b or do I use 5 and 7?
HallsofIvy: thanks for your help, but what you gave, i think, is indefinite integral, rather than a definite integral. from what i know, because definite integral is a limit, it has to end in a certain number, without a variable. thanks again for your help though