Question

Find a function such that

f '(x)=x+1

and f(0)=6. Then f(x)=

Answer #1

SOLUTION:- To solve the given problem we use following concept :-

1.

2.

3.

4.

1) Find the antiderivative if f′(x)=x^6−2x^−2+5 and f(1)=0
2)Find the position function if the velocity is v(t)=4sin(4t)
and s(0)=0

2) Find the function f if
a) f '' (x) = 6 x + 12 x 2
b) f ''' (t) = et
c) f ' (x) = 8 x 3 + 12 x + 3 , f(1) = 10
d) f'' (x) = 2 - 12 x , f(0) = 9 , f(2) = 15
e) f '' (t) = 2 et + 3 sin t , f(0) = 0 ,
f(π) = 0

Find the Fourier series of the function:
f(x) =
{0, -pi < x < 0
{1, 0 <= x < pi

6. A continuous random variable X has probability density
function
f(x) =
0 if x< 0
x/4 if 0 < or = x< 2
1/2 if 2 < or = x< 3
0 if x> or = 3
(a) Find P(X<1)
(b) Find P(X<2.5)
(c) Find the cumulative distribution function F(x) = P(X< or
= x). Be sure to define the function for all real numbers x. (Hint:
The cdf will involve four pieces, depending on an interval/range
for x....

1)Find F
f”(x)=-2+36x-12xsquer, f(0)=9, f’(0)=18
f(x)=?
2)Find a function f such that f’(x)=3x cube, and the line
81x+y=0 is tangent to the graph of f
f(x)=?

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 the fourier series representation of each periodic
function
f(x) = 0, -4 <x<0
f(x) = 8, 0<=x<=1
f(x) = 0, 1<x<4

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.

Use analytical methods to find all local extrema of the function
f(x)=3x^1/x for x>0.
The function f has an absolute maximum of ? at x=?
The function f has an absolute minimum of ? at x=?

Find f.
f '''(x) = cos(x), f(0) =
5, f '(0) = 6, f
''(0) = 3

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