Question

Suppose that f and g are infinitely differentiable functions defined on R. Suppose that Pf is...

  • Suppose that f and g are infinitely differentiable functions defined on R. Suppose that Pf is the second order Taylor polynomial for f centered at 0 and that Pg is the second order Taylor polynomial for g centered at 0. Let Pfg be the second order Taylor polynomial for fg centered at 0. Is Pfg = PfPg? If not, is there a relationship between Pfg and PfPg ?

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Consider the function f : R → R defined by f(x) = ( 5 + sin...
Consider the function f : R → R defined by f(x) = ( 5 + sin x if x < 0, x + cos x + 4 if x ≥ 0. Show that the function f is differentiable for all x ∈ R. Compute the derivative f' . Show that f ' is continuous at x = 0. Show that f ' is not differentiable at x = 0. (In this question you may assume that all polynomial and trigonometric...
Let f: R -> R and g: R -> R be differentiable, with g(x) ≠ 0...
Let f: R -> R and g: R -> R be differentiable, with g(x) ≠ 0 for all x. Assume that g(x) f'(x) = f(x) g'(x) for all x. Show that there is a real number c such that f(x) = cg(x) for all x. (Hint: Look at f/g.) Let g: [0, ∞) -> R, with g(x) = x2 for all x ≥ 0. Let L be the line tangent to the graph of g that passes through the point...
suppose and are functions that are differentiable at x=0 and that f(1)=2, f'(1)=-1, g(1)=-2, and g'(1)=3....
suppose and are functions that are differentiable at x=0 and that f(1)=2, f'(1)=-1, g(1)=-2, and g'(1)=3. Find the value of h'(1). 1) h(x)=f(x) g(x) 2) h(x)=xf(x) / x+g(x)
The functions f and g are defined as ?f(x)=10x+33 and ?g(x)=11?55x. ?a) Find the domain of?...
The functions f and g are defined as ?f(x)=10x+33 and ?g(x)=11?55x. ?a) Find the domain of? f, g, fplus+?g, f??g, ?fg, ff, f/ g, and g/f. ?b) Find ?(f+?g)(x), (f??g)(x), ?(fg)(x), (ff)(x),(f/g)(x), and (g/f)(x).
Let f, g : Z → Z be defined as follows: ? f(x) = {x +...
Let f, g : Z → Z be defined as follows: ? f(x) = {x + 1 if x is odd; x - 1 if x is even}, g(x) = {x - 1 if x is odd; x + 1 if x is even}. Describe the functions fg and gf. Then compute the orders of f, g, fg, and gf.
Suppose g : (a,b) ? R^n is a differentiable parametrized curve with the property that at...
Suppose g : (a,b) ? R^n is a differentiable parametrized curve with the property that at each t, the position and velocity vectors are orthogonal. Prove that g lies on a sphere centered at the origin.
1) For each of the following state whether it is true or false. If true give...
1) For each of the following state whether it is true or false. If true give one sentence exolanation. If false, give counterexample. a)If f is differentiable on (0,1) and f is increasing on (0,1) then f' > 0 on (0,1) b)Suppose that f is thrice differentiable function defined on (-1,1). Suppose that the second order Taylor polynomial of f at 0 is 1-x^2. Then f has a local extremum at 0.
a) Let f : [a, b] −→ R and g : [a, b] −→ R be...
a) Let f : [a, b] −→ R and g : [a, b] −→ R be differentiable. Then f and g differ by a constant if and only if f ' (x) = g ' (x) for all x ∈ [a, b]. b) For c > 0, prove that the following equation does not have two solutions. x3− 3x + c = 0, 0 < x < 1 c) Let f : [a, b] → R be a differentiable function...
Let f : R → R be differentiable with derivative f'. Prove that f(x + h)...
Let f : R → R be differentiable with derivative f'. Prove that f(x + h) = f(x) + f'(x)h + o(h), as h → 0.
4a). Let g be continuous at x = 0. Show that f(x) = xg(x) is differentiable...
4a). Let g be continuous at x = 0. Show that f(x) = xg(x) is differentiable at x = 0 and f'(0) = g(0). 4b). Let f : (a,b) to R and p in (a,b). You may assume that f is differentiable on (a,b) and f ' is continuous at p. Show that f'(p) > 0 then there is delta > 0, such that f is strictly increasing on D(p,delta). Conclude that on D(p,delta) the function f has a differentiable...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT