Question

For functions f and g, where f(x) = 1 + x 2 , g(x) = x...

For functions f and g, where f(x) = 1 + x 2 , g(x) = x − 1 in C[0, 1] with the inner product defined by the integral: hf , gi = Z 1 0 f(x)g(x)dx, (a) find the norm of f and g. (b) find unit vectors in the directions of f and g. (c) find the cosine of the angle θ between f and g. (d) find the orthogonal projection of f along g

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
Let f and g be measurable unsigned functions on R^d . Assume f(x) ≤ g(x) for...
Let f and g be measurable unsigned functions on R^d . Assume f(x) ≤ g(x) for almost every x. Prove that the integral of f dx ≤ Integral of g dx.
Let V={f∈C1([−1,1])|f(1) =f(−1)}, then〈f, g〉=∫(f g+f'g′)dx (from -1 to 1) is an inner product on V...
Let V={f∈C1([−1,1])|f(1) =f(−1)}, then〈f, g〉=∫(f g+f'g′)dx (from -1 to 1) is an inner product on V (you do not have to verify this). Under this inner product, prove that: {x2}⊥={f∈V | ∫(x^2−2)f(x)dx= 0} (from -1 to 1)
1. V is a subspace of inner-product space R3, generated by vector u =[2 2 1]T...
1. V is a subspace of inner-product space R3, generated by vector u =[2 2 1]T and v =[ 3 2 2]T. (a) Find its orthogonal complement space V┴ ; (b) Find the dimension of space W = V+ V┴; (c) Find the angle θ between u and v and also the angle β between u and normalized x with respect to its 2-norm. (d) Considering v’ = av, a is a scaler, show the angle θ’ between u and...
a). Find dy/dx for the following integral. y=Integral from 0 to cosine(x) dt/√1+ t^2 , 0<x<pi  ...
a). Find dy/dx for the following integral. y=Integral from 0 to cosine(x) dt/√1+ t^2 , 0<x<pi   b). Find dy/dx for tthe following integral y=Integral from 0 to sine^-1 (x) cosine t dt
Prove that the family of trigonometric functions { 1, cos x, sin x, ..., cos nx,...
Prove that the family of trigonometric functions { 1, cos x, sin x, ..., cos nx, sin nx, ...} form an orthogonal system on [-pi,pi] prove that the following orthogonality relations hold integral from -pi to pi of sin nx dx = 0 and integral from -pi to pi of cos nx dx = 0
1. a True or False? If ∫ [ f ( x ) ⋅ g ( x...
1. a True or False? If ∫ [ f ( x ) ⋅ g ( x ) ] d x = [ ∫ f ( x ) d x ] ⋅ [ ∫ g ( x ) d x ]. Justify your answer. B. Find ∫ 0 π 4 sec 2 ⁡ θ tan 2 ⁡ θ + 1 d θ C. Show that ∫ 0 π 2 sin 2 ⁡ x d x = ∫ 0 π 2 cos...
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)
1a. Find the domain and range of the function. (Enter your answer using interval notation.) f(x)...
1a. Find the domain and range of the function. (Enter your answer using interval notation.) f(x) = −|x + 8|   domain= range= 1b.   Consider the following function. Find the composite functions f ∘ g and g ∘ f. Find the domain of each composite function. (Enter your domains using interval notation.) f(x) = x − 3 g(x) = x2 (f ∘ g)(x)= domain = (g ∘ f)(x) = domain are the two functions equal? y n 1c. Convert the radian...
Let f, g : X −→ C denote continuous functions from the open subset X of...
Let f, g : X −→ C denote continuous functions from the open subset X of C. Use the properties of limits given in section 16 to verify the following: (a) The sum f+g is a continuous function. (b) The product fg is a continuous function. (c) The quotient f/g is a continuous function, provided g(z) != 0 holds for all z ∈ X.
Prove that gradients of functions f(x, y) = 1/2 log(x^2+y^2) and g(x, y) = arctan(x) are...
Prove that gradients of functions f(x, y) = 1/2 log(x^2+y^2) and g(x, y) = arctan(x) are orthogonal and have the same magnitude at any point different from origin.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT