Find all points at which f(z) = (x)/(x2+y2) - i(y)/(x2+y2) is differentiable. At what points is f analytic? Explain.

Q: Use the Second Fundamental Theorem of Calculus to find F′(x).

A:

Q: Find the interval of x-values on which the curve is concave up and concave down , then sketch the…

A: Since you have asked multiple question, we will solve the first three subparts for you. If you want…

Q: b) Let f be a differentiable function of one variable, and let z = f(3x² – 5y²). Show that az əz…

A: Given  z = 3x2 - 5y2

Q: Show that f(z) = 3z2 + 2z + 5 is analytic function.

A:

Q: Define the function f(x, v) = 4x³-x³y-4y5 3x5-3y5 at the origin so that it becomes continuous there.

A: A function is said to be continuous at (a,b) if the the value of function at (a,b) is equal to…

Q: Check the differentiability of the function f(x, y) = √xy | at the point (0,0). Also check the…

A: As per the question we are give a bivariate function : f(x,y) = √|xy| And we have to check for its…

Q: Find all of the critical points of the function f(x, y) = x²y². Can the second derivatives test be…

A:

Q: Prove that y = x- 2 is differentiable and calculate y'.

A: Given: The function, y = x-2

Q: Find the linearization of the function F(x)=tan-1(2x)= arctan(2x) at x=0. Then use linearization to…

A: We know the linearization of the function f(x) at x=a    L(x) = f(a) + f'(x)*(x-a)   In the…

Q: · Use the definition of the derivative of complex function to show that f(z) is not dif- ferentiable…

A:

Q: use graphical approximation methods to find the point(s) of intersction of f(x)=e^x and g(x)=x^6 to…

A:

Q: Find f-(-1,1) of the function: f(x, y) = x + xy +2a°y?

A: Let's find.

Q: Let f(x) = x³ + 3x2 + x + 3. Determine the points f where the tangent line is horizontal on

A: to find the points where the tangent line is horizontal we have to first derivate the function and…

Q: Assume that y is a differentiable function of r such that y² = x² + 4x sec y. Find y' by implicit…

A: implicit differentiation

Q: (b) Test the continuity of the function f(x) = sgn(lxl) at x = 0. Is f(x) %3D differentiable at x 0?…

A: The function f(x) = (sgn|x|) To test the continuity of the function at x = 0  Also to determine…

Q: Integrate to find F as a function of x, and demonstrate the Second Fundamental Theorem of Calculus…

A: Integral is F(x)=∫4xt32dt

Q: What does it mean for f to be differentiable at a ?

A: we have to define that what we mean by the f is differentiable at a.

Q: Determine the points at which the function is not analytic: (iz^3 + 2z) / (z^2 + 1)

A:

Q: calculate the are between the curves f(x)=x^2 and g(x)=x^3 on the interval [-1,1]

A: Given,

Q: Determine if the function is continuous at point (0,0): F (x, y) _x³y°cos(x³+y³) (x²+y²)²

A:

Q: Show analytically that the function f is not differentiable at x = 0. Ax) = 2x+1 x>1

A:

Q: Consider a function f(x) = |x – 3|. a. Show that f (x) is not differentiable at 3. -

A: Given         f(x) =|x-3|

Q: Is the scalar valued function f(x)=(x^2-1)/(x+1) continuous?

A: This is a problem related to limit and continuity of the function. Please follow the procedure given…

Q: Find the imaginary part of an analytic function whose real part is e* (xcosy - ysiny).

A: it will be satisfy CR law equations

Q: Assuming y cos (3xz) = 5 defines z as a function of x and y. Differentiate

A: we have to derivative

Q: Determine the largest interval on which the function f(x) = (x + 1) %3D is concave upward.

A:

Q: Find the global maximum and global minimum of the function f(x)=sinx−x in the interval [−π,π].

A:

Q: Determine if f(x) is differentiable at x = 0 if

A: We will find out the required solution.

Q: Find the local maximum value of f using both the First and Second Derivative Tests. f(x) = x + V1 -…

A: First calculate critical point at which either local maxima or local minima will occur by putting…

Q: Find an analytic function whose real part is e-x (xsiny+ycosy)

A:

Q: Find an analytic function whose real part is e-x(x sin y-y cos y )

A:

Q: Determine the point at which the function is not analytic iz² – 2z ƒ(z) = 3z + 1 - i

A:

Q: Use the Cauchy-Riemann equations to show that the function f(z) - e² is not analytic anywhere.

A: The solution is given as

Q: Determine the set of points at which the function is continuous. F(x, y) - х-у 1 + x² + y2

A:

Q: How can you sometimes decide from examining ƒx and ƒy that a function ƒ(x, y) is differentiable?…

A:

Q: Use the Cauchy-Riemann equation to determine if the function f(2) = x³ – i(2 – y)³ is analytic or…

A:

Q: determine whether the piecewise-defined function is differentiable at x = 0.

A: Given f(x)=2x+tanx, x≥0           x2   , x<0

Q: Use the first derivatives test to find the local exterma of f(x) =x3-12x on R

A:

Q: Show that f(x)= |x| is not differentiable at x = 0.

A:

Q: ) Find an analytic function f(z) = u(xr, y) + iv(r, y) with real part -. -----) u(r, y) = x? – y? +…

A:

Q: Suppose that f: R² R is a function given by y³ x² + y² f(x, y) = 0 for x = y = 0. Show that f(x, y)…

A:

Q: Find the inflection point of the function f(x) = x°In(x). %3D (x, y) = (

A: The given function is fx=x5lnx

Q: (b) Show that the function defined by √₂²+y f(x, y) = 0 if (x, y) = (0,0) is not differentiable at…

A: On solving this we will get

Q: Is the function f(z) = (x2 - y2) + 2xyi entire? Why or why not?

A:

Q: At what points is the function f given by f(z) = x3 + i(1 + y) analytic? Explain.

A:

Q: Show that the function f(z) = z = is differentiable but not analytic at z = 0

A: Givenf(z)=zz