* 0 ☆ T 7.3. Show that (a). f(z) = x - iy² is differentiable only at y = -1/2 and f'(z) = 1, (c). f(z) = yx + iy2 is differentiable only at x = y = 0 and f'(z) = 0,

Let h be a differentiable function with a tangent line at x = TT. The equation of the tangent line is y=-0.2x + 0.5. What must be true about h and h' at x = πT? I. h(TT) = -0.1283 II. h'(TT) = 0.3 III. h(0) = 0.5 OI and II O II and III OI only O III only

Let H(x) = f(xg(x)), where f and g are differentiable functions such that g(2) = 3, g' (2) = 5, and f'(6) = -2. Find H'(2). Show your work.

1. . Let f be a function that is defined and differentiable on all of R. Here is some information about f and its derivative f': 12 3 4 -3 v2 0 -1 8 7 3 f'(x) -2 17| 4 f(x) -6 2 (a) Suppose h(x) = (² – 4r- + 5) · f(2). Find h' (2). f(x) 3- 5z (b) Suppose R(r) Find R'(-1).

b) Consider the second-order truncation error (0 (Ax)²) with the step size (-Ax) and then, obtain a finite difference approximation for the first-order derivative of U(x, t) respect x (Ux(x, t)).

1. Determine whether the given functions are differentiable (anywhere). If the function is differentiable then find its' derivative. i) f(2)=-2(xy + x)+i(x²-2y-y²) ii) 8(z)-2+z iii) f(z)-e² (cos(²-x)+sin(x²-x²)) 2. Find the square root of -5+5 3. f(2)=2³ +42-6 in the polar coordinate form u(r,0) +iv(r,8).

An equation for the line tangent to the graph of the differentiable function f at x = 3 is y = 4x + 6. Which of the following statements must be true? 1. f (0) = 6 II. f(3) = 18 III. f' (3) = 4 B None I and II only II and III only I, II, and III

If y 1 = f(x), then ƒ'(x), y', dy, and dx [Select] f(x) all represent the of f at x.

A function H is differentiable at x = 2. An equation for the line tangent to the graph of H at x = 2 is 3x + 3y = 3. Find H(2) and H' (2). H(2) = H' (2) = 0 O Dointsl DETAUS

Assume that F= (e^x−y)i+ (2y−x)j, C1 is curve from (0,1) to (2,5) along the graph of y=x^2+ 1, and C2 is the line segment from (0,1) to (2,5).(a) Parameterize C2and compute ∫C2F·dr. Must it be the case that the value you obtained for∫C2F·dr is equaled to that of ∫C1F·dr? Explain. b) Use the Fundamental Theorem of Line Integrals to compute ∫C1F·dr or explain why this can not be done.