4. Let fcx) bc a cor [o, 0) 6iven th f'(x)LO far x> the following is greater than B aj Să f(t) dE b) f(o)+ Si fo c) f(i)+ S fC d) Së f(t) dE elflo) tf(1)

Q: Exercise 2. Prove that dim(null T") = dim(null T) + dim W – dim V and dim(range T") = dim(range T),…

A: We prove dim null T*=dim null T + dim W-dim V and dim range T *=dim range T for every T L(V·W).

Q: 1. Evaluate: 1 1+x 2. Find Fa) given f'a)=3Sinx-4e*, FET)=4e"

A:

Q: 2. In the following cases, express the f(t) as a single sinusoid: a. f(t) = cos wat - √3 sin wat b.…

A:

Q: 1. Let r(t) = (Vt,t + 2t2, e'). Describe the domain of r. 2. Let r(t) = ((t + 2)-1, sin(t), In(1 –…

A:

Q: 7) Use Theorem 7.1.1 (Table) to find L{f(1}} for the following: S)-(e*-e*)}° a.

A: The given function is f(t)=(e-3t-e5t)2. Expand the function implies, f(t)=e-6t+e10t-2e2t The Laplace…

Q: c) calculate the matrix representing T with respect to the standard basis e1=(1,0)T, e2=(1,0)T of R2…

A:

Q: 4. Find f"(2). (a) f(u) = 2u²5 – u).

A:

Q: If f(x)= x, find f'(0).

A:

Q: f ▼ is defined by V= d/dx i + d/dy j + d/dz k and A& functions then show that V.(A+B)= V…

A: ∇=ddxi+ddyj+ddzkA and B are differentiable function then ∇.A+B=∇.A+∇.B