suppose u and v are functions of x that are differentiable at x=2 and that u(2) =3, u'(2) = -4, v(2) = 1, and v'(2) find values of derivatives at x = 2 (d/dx)(uv) =
1. For differentiable vector functions u and v, prove: u'(t) X v(t)+ u(t) X v'(t) lu(t) X v(t)] 2. For the differentiable vector function u and real-valued function f, prove: lu(f(t)))= f(t)u' (f (t)) 1. For differentiable vector functions u and v, prove: u'(t) X v(t)+ u(t) X v'(t) lu(t) X v(t)] 2. For the differentiable vector function u and real-valued function f, prove: lu(f(t)))= f(t)u' (f (t))
Use integration by parts to derive the following formula. ſxIn \/ dx=x** 12+Cnt=1 (n+1) If u and v are differentiable functions, then udv=uv - vdu. Let udv = x. In|x dx. Determine the best expressions for u and dv. Select the correct answer below and fill in the answer boxes to complete your answer. O A. u= O B. u= dx, dv= dv= dx Find du du= dx Integrate dv to find v. The constant of integration is not introduced...
3. Below you are given the graphs of the functions f and g. Suppose that: u(x)-f(g(x)), v(x)-f(x) g(x), and w(x)-g(f(x)) Use the graphs to find the indicated derivatives. If the indicated derivative does not exist, write "D.N.E." in the space provided. Be sure to include work that shows how you arrived at your answer. 20 a) u'3) b) v-4) c) wl) 3. Below you are given the graphs of the functions f and g. Suppose that: u(x)-f(g(x)), v(x)-f(x) g(x), and...
3. Find the derivative using the quotient rule. 2e* f(x) = x-1 4. Let u and y be differentiable functions of x. Find the value of the indicated derivative using the given information. Pay careful attention to notation. du Find dx v at x =1 if u(1) = 3, u'(1)=-5, v(1)=7, v'(1)=-3
Question 2 (20 points): Consider the functions f(x, y)-xe y sin y and g(x, y)-ys 1. Show f is differentiable in its domain 2. Compute the partial derivatives of g at (0,0) 3. Show that g is not differentiable at (0,0) 4. You are told that there is a function F : R2 → R with partial derivatives F(x,y) = x2 +4y and Fy(x, y 3x - y. Should you believe it? Explain why. (Hint: use Clairaut's theorem) Question 2...
3 Ltuts.),)wher F.,and v are differentiable. Suppose also that (-2-)1 (-2-3)--101, u (-2-3)-4, x (-2-3)--5 F (L-7)-3, F(-2-3)-3, F(I.-7)-2, and F.(-2-3)-0. Find W (-2-3 Circle your answer below o w(-2-3)-2 (e) W(-2-3)-12 ( W(-2-3)-14 (g) W(-2-3)-35 (h) W (-2,-3)-199 W(-2,-3)-202 M x2 + xy + y2 + 3y the local maximum and minimum values of the function f(x,y) 4. Find . Circle your answer below. (a) Relative minimum f(1.-2)--3, and no relative maximum. (b) No relative minimum, and relative maximum...
Find the results of next functions 2.-Find the values of a and b such that fis differentiable at x 1 ax+b si 1s. Sol, a- 2, b-1. f(x)=1si x<1 x-7 si 0<x Sb| f(x) =16/x si x< 3 If ... a) decide a value of b far which f is continuous b)fis differentiable in the value of b that ycu find in part a)? 4.- In the following functions determine what is requested sen(x) si x < mx+b si x...
2. Sketch the graph of the following functions and find the values of x for which lim f(x) does not exist. b)/(x) = 1, x = 0 f(x)- 5, x=3 c) x2 x>1 2x, x> 3 d) f(x)-v e) (x)- [2x 1- sin x Discuss the continuity of the functions given in problem #2 above. Also, determine (using the limit concept) if the discontinuities of these functions are removable or nonremovable 3. Find the value of the constant k (using...
a. Find the Jacobian of the transformation x = u, y = 4uv and sketch the region G: 1 s u s 2.4 s4uvs 8, in the uv-plane. b. Then usef(x.y) dx dy-f(g(u.v),h(u.v)|J(u,v)l du dv to transform the integral dy dx into an integral over G, and evaluate both integrals a. Find the Jacobian of the transformation x = u, y = 4uv and sketch the region G: 1 s u s 2.4 s4uvs 8, in the uv-plane. b. Then...