(7) Compute the derivatives of order 4 ands of the following functions at the point Xo=0:1...
*9. For each of the following pairs of functions, determine the highest order of contact between the two functions at the indicated point xo: (e) f,g : R-R given by f(x)and g(x) 1+2r ro0 (f) f, g : (0, oo) → R given by f(r) = In(2) and g(z) = (z-1)3 + In(z): zo = 1. (g) f.g: (0, oo) -R given by f(x)-In(x) and g(x)-(x 1)200 +ln(x); ro 1 x-1)200 *9. For each of the following pairs of functions,...
Problem 5. (1 point) Find all the first and second order partial derivatives of f(x,y) 7 sin(2x + y) + 9 cos(x - y). A. = fx(x,y) = B. = fy(x, y) = af C. ar2 = fcz(x, y) = af D. ay2 = fyy(x,y) = E. af деду fyz(x, y) = af F. მყმz = fxy(x, y) = Note: You can earn partial credit on this problem.
9 and 11 please 2-11 CAUCHY-RIEMANN EQUATIONS Are the following functions analytic? Use (1) or (7). 2. f(z) = izz 3. f(z) = e -2,0 (cos 2y – i sin 2y) 4. f(x) = e« (cos y – i sin y) 5. f(z) = Re (z?) – i Im (32) 6. f(x) = 1/(z – 25) 7. f(x) = i/28 8. f(z) = Arg 2TZ 9. f(z) = 3772/(23 + 4722) 10. f(x) = ln [z] + i Arg z...
10. Use the limit definition of the derivative to calculate the derivatives of the following functions. a. f(x) = 2x2 – 3x + 4 b. g(x) = = x2 +1 1 x2 +1 c. h(x) = 3x - 2 a. 11. Find the derivative with respect to x. x² - 4x f(x)= b. y = sec v c. 5x2 – 2xy + 7y2 = 0 1+cos x 1-cosx cos(Inu) e. S(x) = du 1+1 + + f. y =sin(x+y) g....
I need to answer a, c, and d 1. Find the limit at xo if it exists. (a) f(x, y) = xy/(x2 + y2), Xo = el + e2 (b) f(x, y) = xy/(x2 + y2), Xo = (0,0). (c) f(x) = (1-cos x)/x2, X,-0. [Hint: limx-o (sin x)/x = 1 .] (d) f(x)-|x-2le, + lx + 2le_, xo = 3. (e) f(x, y) = ye, + (xy)리[(xy)2 + (x-y)2je2, Xo = (0,0). At which points is each of these...
2. (each 1 mark) Find the derivative of the following functions: 9x + 7 (a) y = 92 - 1 (b)r = (02 9016 /09 - 9 ( 9 ) (c) y=rºcot x + 9x2 cos x – 14x sin x 9t sint (d) s = cost + +9 (e) h(x) = cº sin (vą) + 240 sec (1) ) 10 (f) f(0) = (_sin 98 (1+cos 90 ) (g) g(x) = (1 + csc(+10) + In (922 – 8)...
2. Consider the following function: Compute each of the following: Hint: There is probably a better way to compute these than to just mindlessly compute all ot partial derivatives in the order given 3. Is there a function f(x, y) with partial derivatives f, (z, y) = 2r + 5e" + 4y and f,(x, y) = 2y + 5e" + 2x? If so, give an example of a function with these partial derivatives. If not, say why not 2. Consider...
Find the first-order partial derivatives (fr. f,) and second-order partial derivatives (fxxıfyy, fxy, fyx) of the following functions. a. f(x,y)=x’y+x’y? +x+y? b. f(x, y) = (x + y)? Find the critical points at which the following function may be optimized and determine whether at these points the function is maximized, minimized or at a saddle point. z = 5x2 – 3y2 – 30x + 7y + 4xy
+20 Problem 7. Let f :D + R, xo be an accumulation point of D and assume lim f(x) = L. Use the e-8 definition of the limit (not theorems or results from class or the text) to prove the following: (a) The function f is “bounded near xo”: there is an M ER and a 8 >0 such that for x E D, 0 < l< – xo<8 = \f(x) < M. Hint: compare with the proof that a...
5. Find the derivatives of the following functions: (a) f(x) = 3" sin?(5x)