Let f:R→Rbe a continuous function such that f) = f(x° ) for all x eR. Consider the following statements. I.f is an odd function. II. f is an even function. III. f is differentiable everywhere.

Q: (x³ +y³) cos(x5 + y5) 3 f(x, y) = y) = { (2²³. if if (x, y) = (0,0) (x, y) = (0,0)

A: Note the following result:  If one function F has limit zero at a point 'c' and another function G…

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A:

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A: f(x)=210 is continous interval on.. a. all real numbers

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A: This is differentiability problem

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A: Question - Determine the set of points at which the function is continuous.

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Q: H.W Is f (x) = x. |x| differentiable function? %3D

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A: Order of the function

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.

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Q: Consider a function f : N x N -→N given by f(x, y) = 3*7. For what natural n, 21 · 5" 3 is in the…

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Q: 11. Let f(x, y) = x² - y, g(t) = (Int) In(1-t), and h(x, y) = g(f(x, y)). Find the set on which h is…

A: Given that  f (x, y) = x² - y g(t) = (In t) In(1 - t) We have to find the Composite Function h(x, y)…

Q: (H.W): Is this function

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A: fx=x2-2x S=(1, 3) fs=f1=12-21=1-2=-1 fs=f3=32-23=9-6=3   Given f(x) is a ceiling function  According…

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A: By using conditions of continuous function.

Q: Let F(x, y) =. Evaluate (31) F dr (1,0,0) O a. 9 + 3e3 8+ 3e3 С. 8— Зе3 O d. 10 – 3e3

A: We will use basic knowledge of vector calculus and integral calculus to answer this question.

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

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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.