Question

F(x)=3x^{2} -e^{-x}

prove that f(x) has zeroes in the three intervels [-4,-3] [-1,0],[0,1]

Answer #1

prove that this function is uniformly continuous on
(0,1):
f(x) = (x^3 - 1) / (x - 1)

prove that these functions are uniformly continuous on
(0,1):
1. f(x)=sinx/x
2. f(x)=x^2logx

Prove that the function f(x) = x2 is uniformly
continuous on the interval (0,1).

Let X=2N={x=(x1,x2,…):xi∈{0,1}} and define
d(x,y)=2∑(i≥1)(3^−i)*|xi−yi|.
Define f:X→[0,1] by f(x)=d(0,x), where 0=(0,0,0,…).
Prove that maps X onto the Cantor set and satisfies
(1/3)*d(x,y)≤|f(x)−f(y)|≤d(x,y) for x,y∈2N.

Let f:[0,1]——>R be define by f(x)= x if x belong to rational
number and 0 if x belong to irrational number and let g(x)=x
(a) prove that for all partitions P of [0,1],we have
U(f,P)=U(g,P).what does mean about U(f) and U(g)?
(b)prove that U(g) greater than or equal 0.25
(c) prove that L(f)=0
(d) what does this tell us about the integrability of f ?

Evaluate the following integral. ∫ (x3 − 3x2)( 1 x −
3) dx
(A) − 3 4 x4 + 14 3 x3 − 3 2 x2 + C
(B) − 3 4 x4 + 4 x3 − 3x2 + C
(C) − 3 4 x4 + 10 3 x3 − 3x2 + C
(D) − 3 4 x4 + 10 3 x3 − 3 2 x2 + C
(E) ( 1 4 x4 − x3)( 1 x − 3) + ...

Let f(x) = x3 + 3x2 − 9x − 27 . The first
and second derivatives of f are given below.
f(x) = x3 + 3x2− 9x − 27 = (x − 3)(x +
3)2
f '(x) = 3x2 + 6x − 9 = 3(x − 1)(x + 3)
f ''(x) = 6x + 6 = 6(x + 1)
a.) Find the x-intercepts on the graph of f.
b.)Find the critical points of f.
c.) Identify the possible inflection points...

The polynomial f(x) given below has 1 as a
zero.
f(x)=x3−3x2+4x−2?

A uniform random variable on (0,1), X, has density function f(x)
= 1, 0 < x < 1. Let Y = X1 + X2 where X1 and X2 are
independent and identically distributed uniform random variables on
(0,1).
1) By considering the cumulant generating function of Y ,
determine the first three cumulants of Y .

Show that there is a solution to the equation e^x=3-2x in the
interval(0,1)

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