9z 21. Answer the following questions given the function f below. xy if (x.y) # (0,0) f(x,y) = x+y? if (x.y) = (0,0) a. Is f continuous at (0,0)? b. Is f differentiable at (0,0)? c. If possible, evaluate f, (0,0) and f, (0,0). d. Determine whether f, and fy are continuous at (0,0). a. f(x.y) (1) - continuous at (0,0).

Q: QUESTION 5 Given function f(x,y)= A. 2 B. 3 C. D. 0 ANSWER: 6 2 63xy of Evaluate at point (0, 1). ox

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

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Q: Given the following function: R? →R: f(x, y) = x*y² + x²y³ Calculate: (1,2) 3

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Q: Suppose f is a differentiable function of x and y, and g(r, s) = f(2rs, s² - 6r). Use the table of…

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Q: Prove that the following function is differentiable for every point of R?: f(x, y) = x + y

A: This is differentiability problem

Q: For each of the following functions, find ∂z/∂x and ∂z/∂y. (b) z = x/y2 - y/x2

A: To find ∂z/∂x and ∂z/∂y. (b) z = xy2-yx2

Q: X+4x+x-6 P+x-2 x+1,-2 Where is the function f(x)= x=-2 discontinuous? Oa. 1 Ob. -2 Oc. 1, -2 Od. The…

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Q: Answer the following questions given the function f below. ху if (x,y) # (0,0) f(x,y) = X +y if…

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Q: Find the value of a,b,c for the fact that makes the differentiation equal to zero for the…

A: we have to find the value of a,b,c.

Q: Determine and sketch the contour plot for the function f (x, y) at three level curves.

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Q: Given a function f: A → B and subsets X,Y C B, prove that f"(XNY) = f(X)nf-(Y).

A: He we will prove the given result.

Q: Describe the x-values at which f is differentiable. f(x) = (x − 3)2/5

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Q: Find the values of a and b that makes the following function differentiable. S(2) – {3e¬3 la(6 – 2)²…

A: Given fx=3ex-3      if x<3a6-x2+b   if x≥3

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Q: For which of the following functions f(x, y) does one have = 0? Select one: O A. f(x, y) = sec x ·…

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Q: Question 1 A. The multivariable function f (x, y) = 3x² + 2xy – 7y² + 13x 6y + 4, find: i. f(x, y)…

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Q: Suppose f is a differentiable function of x and y, and g(r, s) = f(4r-s, s2 - 9r). Use the table of…

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Q: Determine which of the following functions are one-to-one. OA. f: R² → R² defined by f(x, y) = (x +…

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Q: Use the chain rule to find the indicated partial derivatives. z = x² + x²y₁ x = s + 2t - u, y = stu²…

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Q: 6. For the following functions, show whether they are concave/convex/neither and then show whether…

A: Given function is fx,y=xy First, let us find the stationary points of the given function.…

Q: Let f(x) = x3 - 4 for all real numbers x. The for all x # 0 define a new function g by g(x (2x)1…

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A: is differentiable. Therefore, we have, RHD=LHD=f(x) Now,

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Q: Use the definition of differentiability to prove that the following functionns are differentiable at…

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Q: 7.4. For each of the following functions, determine the set of points at which it is (i)…

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Q: 8. If f and g are differentiable at xo such that f(x) = g(xo). prove that each of the functions h =…

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Q: H.W: Determine which the following functions are differentiable. a) f(z) ix ze.e 6) f(Z) =

A: Let us consider the complex function f(z)=u+iv then the function is differentiable if and only if…

Q: 2. Check the following function f(z) = iz – 37 is analytic or not (Use C.R equations).

A:

Q: Suppose f is a differentiable function of x and y and g(u, v) = f(2u – v, v² – 4u). Use the table of…

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.