Problem 2.62. Let CCR be a convex set and f: C → Rn be continuously differentiable. Furthermore, suppose 0 € C and f(0) = 0. Show that af = [² of (or)rdo, f(x) = x = C. (2.255)

Q: 4 For which values of a e R is the function f(x + iy) = (a²x – axy)+ i ax? + ay an entire function?

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Q: f'(x) = V= and f(1) = 3- I|

A: Explanation of the answer is as follows

Q: 2. Check the following function f(z) = iz – 3z is analytic or not (Use C.R equations).

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Q: Given f(x, y) = 50x + 70y − 5x² − 3y² – xy, and evaluate ƒ(10, 7). f(10, 7) =

A: To evaluate f(10,7)

Q: 1 2.if [(fT))=, find [ f(4t) S

A: Laplace transform of the function

Q: 5. (S.10). By using the second divided difference find f [1, 1.2, 1.4] for f (x) = e-a*; 6. (S.15).…

A: Since you have asked multiple question, we will solve the first question (5) for you. If you want…

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A: Given X have a p.d.f and Y=

Q: 3. 1 Let f(x, y) = ₁-x²-y² (a) Find a value of c for which there is no level set at f = c. (b) Find…

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Q: For the function f(x.y) = e 4xy, find f, and f,. f, =

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Q: 4. The function h satisfies the following equation: Vr E R, h(rh(x)) = [h(x)]*. In addition, we…

A: Consider the given information. hxhx=hx3 Find the derivative of the above equation.…

Q: 1.4 For which values of a ER is the function f(x+ iy) = (a²x – axy) + i ax? + ay an entire function?

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Q: Let f(z) = 3z +2²-9 Determine the value(s) of z, if any, for which f has a horizontal tangent line.…

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Q: Let f(x)= 4x-1, h(x)= -x+4. Find (fo h)(-2). (foh)(-2) =

A:

Q: Suppose f is a differentiable function. If f(5) = 3.1 and f'(5) = 5.4, then estimate the value of…

A: given  f(5)=3.1f'(5)=5.4using linear approximation f(x)=f(a)+f'(a)(x-a)

Q: Provide concise explanations for the answers to the following: c.) Which is greater, f (2) or f…

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Q: Suppose f is a function of two variables with the property that f(−x, y) = − f (x, y) for all values…

A: Given Information: is a function of two variables such that  for all values of x and y.To find: The…

Q: QUESTION 7 Consider a function f: R2 R, where f(xy) = x2 +y3. (a) Determine f(1,1) from definition.…

A: solve the following

Q: 1. Find the interval(s) wheref(x) = xe6* is concave down, if such an interval exists.

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Q: Given the equation y In (x? + y² + 4) = 4, evaluate dy Assume that the equation implicitly defines y…

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Q: f ▼ is defined by V= d/dx i + d/dy j + d/dz k and A& functions then show that V.(A+B)= V…

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Q: If ƒ(t) = (t² + 2t + 2) (3t² + 5), find: f’(t) = ƒ'(5) =

A: given,  f(t)=(t2+2t+2)(3t2+5)

Q: 2. Use the following graphs to insert between the quantities in the boxes to form true statements.…

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Q: 1 4 Show that are eventually fixed point for the function: 8 '5' 4x 0<x< 1 2 – 4x f (x) = %3D 1 3 4х…

A: Given the function f(x), we need to prove that 18 and 45 are the fixed points. In order to prove…

Q: 8. The function f is given by the equation f(x) = (ar²+bx+c) e", where a, b and c are real…

A: fx=ax2+bx+cex The point 0,0 is on the graph f and is an inflection point of the graph with y=x as…