Suppose that the vector field, , is continuously differentiable and satisfies in the interior of the domain , open and bounded, whose boundary is a smooth surface (at least class) , steerable. Show that cannot be tangent to in every point of the surface
Suppose that the vector field, , is continuously differentiable and satisfies in the interior of the...
Give an example of a continuously differentiable function from to , which has an isolated local maximum at (0,0) and in (-17,9) and (0,3) an isolated local minimum in each case. Justify your answer. R2 We were unable to transcribe this image
Suppose that is a bounded function with following Lower and Upper Integrals: and a) Prove that for every , there exists a partition of such that the difference between the upper and lower sums satisfies . b) Furthermore, does there have to be a subdivision such that . Either prove it or find a counterexample and show to the contrary. We were unable to transcribe this imageWe were unable to transcribe this image2014 We were unable to transcribe this...
Partial Differential Equations: Calculate the eigenvalues and eigenfunctions for the eigenvalue problem associated with the vibrating string problem with homogeneous boundary conditions. i.e., , We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Let C be a curve of length L in space and a vector field of constant norm and tangent to C at each point of the curve. What is the work done by along C? Justify your answer. We were unable to transcribe this imageWe were unable to transcribe this image
8. Constantly Differentiable continuation Determine a function f: R->R that apply to the following properties - For all applies f(x) = sin(x) - For all ,applies f(x) = - f is continuously differentiable r e-oo, 0 OC e1, o0) We were unable to transcribe this image
Can you find a differentiable function f(x) defined on the interval [0, 3] such that , and for all x ∈ [0, 3]? Justify your answer (do not write only Yes or No, but explain your answer). We were unable to transcribe this imageWe were unable to transcribe this imagef'(x) <1
8. Constantly Differentiable continuation Determine a function f: R->R that apply to the following properties - For all applies f(x) = sin(x) - For all ,applies f(x) = - f is continuously differentiable r e-oo, 0 OC e1, o0) We were unable to transcribe this image r e-oo, 0 OC e1, o0)
a) The following vector field State whether the divergence of at point A is positive, negative or zero. b) Say if the rotational of at point B is a null vector, which points in the direction of the z-axis or points in the negative direction of z. We were unable to transcribe this image履 2 0 2 4 We were unable to transcribe this imageWe were unable to transcribe this image 履 2 0 2 4
Let two times differentiable in the point . The first and second order differentiable equation of in , imply that the functions and , given by: satisfies and . Prove that if with then it satisfy f: RR a ER f We were unable to transcribe this imageተ ፖ : R Ꭱ : ] . r(h) = f(a+h)-f(a) – f'ah R(t) = f'(a +t) - f'(a) - f"(a)t r(h) lim h 0 h -0 lim R(t) h 0 u:R u(w)...
Let S be the surface reproduced below and parameterized by b) Calculate Vector Field Flow through S, if the surface is oriented at point (2, 0, 0) by the normal vector ⃗n = ⃗k.u, u) = (2-u We were unable to transcribe this image