Consider the function f(z) = (a+ 1) x²y² + i(3 + 1)x²y?. Determine at which points the function f(z) is differentiable. Determine at which points the function f(2) is analytic.

Q: В. B. Show that the function f (z) = -i z2 is analytic.

A: The solution is given as

Q: Find the constant a such that the function is continuous on the entire real line. [ sx², ax - 5,…

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Q: Find an analytic function whose real part is u(x, y) = x³y - y³x 7²+1

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Show that the function f(x) = e¯*/2 has inflection points x = f1. at

A: We have the given function as fx=e-x22              ⋯⋯1 As we know that, a point of inflection of…

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Q: Given the function f(x) = (x² – 1)(x² + 1), the number of horizontal tangents %3D of ƒ is

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Q: Consider the function f(x)=5x+6x^2 over the interval [0,1].

A: Given that :-         f(x) = 5x+6x2 over [0,1] (a)  By deviding the interval into n sub intervals of…

Q: Show that g(x) = x|x| has an inflection point at x = 0, but gʻ"(0)

A: given function g(x) = xx

Q: 1. Find and sketch the domain of f(x, y) = (x – 3y)t.

A: For the solution of the problem follow the next step.

Q: Locate and classify the local extremum of the function f (x, y) x² + y? – 8x – 2y + 6. | -

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Q: The function f(z) is analytic if

A: analytic functions are functions which are locally given by the convergent power series. i.e any…

Q: sketch f(x)=sec x over the half-open interval -r,27). 2 1 3/% 27t 52

A: Given query is to find sketch the graph of sec(x) .

Q: Find the linearization L(x)  of the function f(x) = x^4 -2x^2+3  at  x =0.

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Q: Find the constant a such that the function is continuous on the entire real line. S 8x², f(x) ax -…

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Q: Let f be a differentiable function such that f(4) = 3 and f'(x) = -3x + 3. What is the approximation…

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Q: Let f be a differentiable function such that f (1) = 8 and f' (x) = V2x – 1. What is the value of f…

A: Given data is : f'x=2x-1

Q: Find the extremum points of the function f(x,y) = y² +x*y +x² - 2y and determine the nature of the…

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Q: For the function f(x.y.z)= 3+5xy"-2z*, find f,, f, and f. -口 fx = 5-口 fy=

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Q: Find the constant a such that the function is continuous on the entire real line. (5x2, ах — 3, x 2…

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Q: Find values of a, b, and c such that the graph of f(x) = ax³ + bx² + cx_has a horizontal tangent at…

A: The graph passes through (1,1). So at x=1, f(x)=1

Q: Show that f(x) = 2a + 3b is continuous, where a and b are constants

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Q: Let f be a function defined on the real line R and suppose that it satisfies the condition If(x) –…

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Q: Find a function f such that f′(x)=2x^3 and the line x+y=0 is tangent to the graph of f.

A: Solved below

Q: Find and sketch the domain of the function f(x,y)= exy/ x-y2

A: See the attachment

Q: Find the interval in which the function is positive. f(x) = x2 - 7x + 10 %3D I. (- , 2) II. (2, 5)…

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Q: 1. Why is f not a function from R to R if a) f(x) = 1/x? b) f(x) = VT? c) f(x) = ±/(x² + 1)?

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Q: 1. Decide if there is an analytic function f (x + iy) whose real part satisfies Re(f) = xe".|

A: Given problem: To decide analytic function fx+iy whose real part satisfies Ref=xey.

Q: Specify the domain of f and sketch its gr f(x, y) = Vx2 + y² – 16

A: Given,        f(x, y)=x2+y2-16

Q: Consider the cubic functionf (x) = ax3 + bx2 + cx + d, where a  0. Show that f canhave zero, one,…

A: We have fx=ax3+bx2+cx+d This implies  f'x=3ax2+2bx+c Set f'x=0 i.e 3ax2+2bx+c=0 and solve it using…

Q: Find the best quadratic approximation to f on the interval [ -1, 1].                     f(x) = lxl

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Q: Find the analytic function whose imaginary part is v =2xy

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Q: Find a function f such that f'(x) = x4 and the line 2x - y = 3 is tangent to the graph of f.

A: Given that

Q: The function f(x)=/25-x' is contionous on

A: It is continuous function.

Q: Find the interval(s) where f(x)= x²- 2x+3 is continuous.

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Q: Find and sketch the domain of the function f (x, y) = In(9 – x² – 9y²).

A: The given function,  f(x,y)=ln9-x2-9y2

Q: Show that the function g(x) =x |x | has an inflection point at (0,0) but  g " (0)  does not exist.

A: Given function:                                 g(x)=x|x|   To find out the Inflection point=?…

Q: Find the values of k in f(x)=x^2-kx such that the line y=5x-4 is tangent to the function.

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Q: 2. Use the First Fundamental Theorem of Calculus to differentiate the function -5x f(1) = | V1+ tª…

A: To differentiate the function by using first fundamental theorem of calculus f(x)=integration (x to…

Q: Find the linearization L(x)of the function at a .

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Q: Show that the function f(2) = xy| is not analytic at the origin, even though C.R. equations are…

A: It is given that the function fz=xy. To check the function f is differentiable at z=0.…

Q: f(x) = 2x2 + 10, g(x) = 4x + 16

A: Sketch the curve f(x) and g(x) in same phase

Q: Find the constant a such that the function is continuous on the entire real line. 5x², ах — 7, f(x)…

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Q: Show the function f(z) = 1+2i+2Re(z) is differentiable or not differentiable at any points.

A: Solution

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

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Q: Q1// Find and sketch the Domain of f(x,y) In (x' y)

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Q: Let f(x, y) = -e2"-y + In(3x – y). Find the domain of this function.

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Q: Consider the function f(x, y) = 4x² – 8y² subject to the condition x + y = 25.

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