Question

Find a function f(x) satisfying f ' '(x) = sqrt{x}, f
' (1)=0 and f(1)=0. You must explain in words what you are doing so
that someone who knows what antidifferentiation is but otherwise
does not have experience can follow your computations. Give your
final answer in what seems to you to be the simplest form.
**Use antidifferentiation, not integration.**

Answer #1

Find a function f(x) satisfying f ' '(x) = sqrt{x}, f
' (1)=0 and f(1)=0. You must explain in words what you are doing so
that someone who knows what antidifferentiation is but otherwise
does not have experience and can follow your computations. Give
your final answer in what seems to you to be the simplest form.

Find F(x) satisfying:
f''(x)= sqrt{x}+x^3+e^x+3
f'(0)=0
f(0)=1

Find the value of C > 0 such that the function
?C sin2x, if0≤x≤π,
f(x) =
0, otherwise
is a probability density function.
Hint: Remember that sin2 x = 12 (1 − cos 2x).
2. Suppose that a continuous random variable X has probability
density function given by the above f(x), where C > 0 is the
value you computed in the previous exercise. Compute E(X).
Hint: Use integration by parts!
3. Compute E(cos(X)).
Hint: Use integration by substitution!

The integral ∫-1(bottom) to 0 ∫sqrt(−1−x2)(bottom) to 0
−4/(−5+sqrt(x^2+y^2)dydx is very hard to do. If you put it in polar
form it's much easier, ∫ba∫dc f(r,θ)r drdθ it's much easier, but
you need to work out the new limits. Find a,b,c,d and the value of
the integral.
a=
b=
c=
d=
∫-1(bottom) to 0∫-sqrt(1−x^2)(bottom) to 0
a/(b+sqrt(x^2+y^2)dydx=

Let f(x,y)=1 for 0<x<1, 0<y<1 and 0 otherwise. Find
the probability density function of Z=max(X, Y)

Let f(x,y)=1 for 0<x<1, 0<y<1 and 0 otherwise. Find
the probability density function of Z=max(X, Y)

Write a script (must be titled “NumIntF”) in MATLAB that
calculates the integration of function f(x)=cos(x) . exp(sin x),
Using numerical integration method. When the user runs the script,
he/she is prompted to input the lower and upper limits for
numerical integration, both in radians, and your program outputs
the integration result. You can use built-in trigonometric
functions and the exponential function, but you are not allowed to
use any built-in function to do the integration. You must use a...

Let the function f and g be defined as f(x) = x/ x − 1 and g(x)
= 2 /x +1 . Compute the sum (f + g)(x) and the quotient (f/g)(x) in
simplest form and describe their domains.
(f + g )(x) =
Domain of (f+g)(x):
(f/g)(x) =
Domain of (f/g)(x):

Given function f(x) = c*|x| on [-3,3] and f(x) = 0 otherwise.
Find c and the corresponding CDF

1) which of the following is a linear approximation of the
function f(x)= sqrt[ 4 ] { x } at a=16.
2) determine the number of inflection points on the graph of
the function f(x)=x^5-x^4.
3) determine the sum of the critical numbers for the function
f(x)=x^3+3x^2-9x.

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