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7. Suppose We have three functions f(x), g(x), and h(x), such that f(-2) = 7, 9(-2)...
Let H=F(x,y) and x=g(s,t), y=k(s,t) be differentiable functions. Now suppose that g(1,0)=8, k(1,0)=4, gs(1,0)=8, gt(1,0)=2, ks(1,0)=1, kt(1,0)=5, F(1,0)=9, F(8,4)=3, Fx(1,0)=13, Fy(1,0)=7, Fx(8,4)=9, Fy(8,4)=2. Find Hs(1,0), that is, the partial derivative of H with respect to s, evaluated at s=1 and t=0.
2. We say that two curves intersect orthogonally if they intersect and their tangent lines are orthogonal at each point in the intersection. For example, the curve y = 0 intersects the curve x2 + y2-1 orthogonally at (-1,0) and (1,0). Let H be the set of curves y2b with b ER. (a) Prove that the tangent line of each curve in H at a point (r, y) with y / 0 has slope (b) Let y -f(x) be a...
2. We say that two curves intersect orthogonally if they intersect and their tangent lines are orthogonal at each point in the intersection. For example, the curve y = 0 intersects the curve x2 + y2-1 orthogonally at (-1,0) and (1,0). Let H be the set of curves y2-2.2-b with b є R. (a) Prove that the tangent line of each curve in H at a point (x, y) with y 0 has slope - (b) Let y-f(x) be a...
At least one of the answers above is NOT correct. (1 point) Suppose f(x, t) = e 3t sin(x + 2t). (a) At any point (x, t), the differential is df = e^(-3t)cos(x+2t)dx+(e^(-3t))(2cos(x+2t)-2sin(x+2t))dt (b) At the point (-1,0), the differential is df = cos(-1)dx+(2cos(-1))+3sin(-1)dt (c) At the point (-1,0) with dx = -0.5 and dt = 0.3, the differential is df = 0.97344 Note. You can earn partial credit on this nrohlem (1 point) Consider the surface xyz = 20....
9. Suppose that we are given the following information about the functions f,g and their deriva- tives and integrals; =4 f(0) = 0 • f(1) = • f'(1) = 2 g(0) = 5 g(1) = 4 • g'(1) =-2 So f(x)dx = 8 5* |(x)dx = 5 Sa f(x)dx = 11 S3 f (x)dx = 6 (d) (5 points) Evaluate Si f(x)dx. (e) (6 points) Evaluate ( f (.5.1 + 4)d.. (f) (6 points) Evaluate, (ثم) (g) (6 points) Evaluate,...
7. [5 marks] Suppose that f(x), g(x), and h(x) are functions such that f(x) is O(g(x)) and g(a) is O(h(x)). Prove that f(x) is O(h(x)) 7. [5 marks] Suppose that f(x), g(x), and h(x) are functions such that f(x) is O(g(x)) and g(a) is O(h(x)). Prove that f(x) is O(h(x))
1.Z=f(x,y)=6x+7y where i) x=g(x)=x^2 y=h(x)=x^4 and ii )x=g(x)=x and y=h(x)=x^3. Please calculate Total derivative by applying this formula dZ=Zx dx/dx +Zy dy/dx
Differentiate. Let f and g be functions that satisfy: f(4)-1, g(4)--3, f'(4)--2,and g'(4)-3. Finod h(4) for h(x)-f(x)g(x)-2/(x)+'7 O-5 -13 13 Differentiate. Let f and g be functions that satisfy: f(4)-1, g(4)--3, f'(4)--2,and g'(4)-3. Finod h(4) for h(x)-f(x)g(x)-2/(x)+'7 O-5 -13 13
12. Let g(x), h(y) and p(z) be functions and define f(x, y, z) = g(x)h(y)p(2). Let R= = {(x, y, z) E R3: a < x <b,c sy <d, eszsf} where a, b, c, d, e and f are constants. Prove the following result SS1, 5100,2)AV = L*()dx ["Mwdy ['Plzdz.
d2y d2y dy +6 da2 (h) +13y 2sin x +9y = 18x -+3 +6 dx da d2y (i) d2y (j d2 18x3 4y = 2 sin x dæ2 d2y ,dy .dy 9y 9x2 +21x - 10 dc (k) (1)2 7 + - 4y = e-4x +6 'da2 da2 d2y dy dy (m) 2 dæ2 (n) 4 7y= e 6 cos x 9y = 4e-3r dr2 dr dx d2y d2y (p*) dy + da2 dy (o* 2a COS I 2y 2...