If f(z) is continuous at z then it must be differenttiable at z, 0.

Q: Suppose that F(x, y, z) = 0 defines z as a function of x and y and F is differentiable. Prove that…

A: Solution is given below:

Q: g (x) = In tdt %3D 1 Is this function is continuous everywhere. If not than where it's not…

A: see below the answer

Q: Sx, ifx 1 f(x) = Show that f is R- integrable.

A: R- integrable function

Q: Is the function f(x, y) = ||x| - |y|| - |x| - |y| differentiable at (0,0)?

A:

Q: Show that the function f (x, y)=(2 + x-y) / [1+ 2x ^ 2)+(3y ^ 2)] ∈R has a limit at (0,0).

A: I have provided a solution in step2.

Q: Show that the function f(x, y) x4 + y? has no limit as (x, y) approaches (0,0).

A: Note: Since we can solve at most one problem at a time, we have solved the first one. Kindly…

Q: Use the definition of differentiability to show that f(x, y) = y² – xy+5x is differentiable…

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Q: Differentiate f(x) with respect to g(x) of yx=xsiny

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Q: Find the derivatie: F (+2 %3D (-t*+*z+)た =人

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Q: The function f is a composite of two continuous functions: y = cos x and y = x 2, so f is continuous…

A: The function fx is a composition of functions y=cosx and y=x2and it is a continuous function.

Q: Use Theorem 9.2.1 to show that T is not continuous at 0, no matter what value is chosen for b.

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Q: Explain why f (x) = sin (x² + 3r + 1) is a continuous function for all c € R. %3D

A: Let us assume that: g(x)=sin(x)and h(x)=(x2+3x+1)So,…

Q: Define f(0,0) in a way that extends f to be continuous at the origin. 2.2 11x - xy + 11y 2 f(x,y) =…

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Q: Assume that f : (0, 1) → R is a differentiable function with the derivative f' increasing on (0,…

A: Given f:0,1→R is a differentiable function and derivative of f is increasing in 0,1 that is f'x>0…

Q: Show by definition that f(x) = |x| : R → R is continuous on R. 2.

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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: If f is continuous everywhere except at x = 2, then f(x +1) dx is not integrable. True False

A: To check whether the given statement is True or False."If f is continuous everywhere except at x=2,…

Q: Clarify that f f :(0,1) →R defined by f(x): not uniformly continuous. =-

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Q: Suppose f is continuous on [0, 1]. What is lim n→ ∞ 1 S fo 0 f(x) dx?

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Q: define the function at 5 so that it becomes continuous at 5.

A: First, we rationalize the function, so that it becomes continuous at 5 which is shown on the board

Q: Use a linear approximation to estimate f(0,1), given that y=f(X) is a differentiable  with f(0)=1…

A: Consider the given information

Q: Let h(x) = f(g(x)), where f and g are differentiable on theirdomains. If g(1) = 3 and g′(1) = 5,…

A: Given: Let h(x) = f(g(x)), where f and g are differentiable on theirdomains. If g(1) = 3 and g′(1) =…

Q: (2) Are all entire functions differentiable on D?

A: Here we check whether given statement is true or false. Are all entire functions differentiable in…

Q: If f(x,y,z) = z In(x²ycosz): then fz is

A: Here, the given function is: f(x,y,z)=z ln(x2ycos z) Using the properties of the natural logarithm:…

Q: Prove that if f : V → W is differentiable at a point a ∈ V it must be continuous there.

A: I have proved limiting value is equal to functional value

Q: Show that the function f defined by (r, y) = (1, –1) (r, y) # (1, –1) f(r, y) = 1² + y is not…

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Q: Determine if f is continuous at (0, 0) where: 3.x?y x4 + 2y2' (x, y) # (0,0) f (x, y) = (x, y) =…

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Q: Show that the limit of the function f(x,y) = at (0,0) does not exist. (x+y)² x² + y²

A: Limit of a Function: Like a single-variable function, a multi-variable function can also have limit.…

Q: What value of c makes the following function continuous at (0, 0)? f(x) = с, x + y² + 5, (x, y) #…

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Q: Let esinx SoN f(t) dt and f is a continuous function, determine the value of f ()

A: If we have F(x)=∫0xf(t)dx then we have F'(x)=f(x). This is called the fundamental theorem of…

Q: Find the limit of f(x) as x approaches 2, where

A: fx=1,  x≠20,  x=2

Q: Let f(r, y) be a continuous

A: Introduction: A global extremum, also known as an absolute extremum, is the lowest or highest point…

Q: Where is f(a) not continuous?

A: Given:

Q: Prove that f(x, y) = x sin y is differentiable everywhere.

A: Answer

Q: Show that the function f(x) = csc(x) is not uniformly continuous on (0, pi/2]

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Q: continuous at (C

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Q: Determine f(5) if f is a continuous function that satisfies t 4x+sin(rz) f(t)dt = x for all z. %3D

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Q: Let f(x, y) = x2y4 sin(1/ (sqrt(x2+y2)) where (x, y) cannot be (0, 0) and f(0, 0) = 0 Is f…

A: Answer

Q: Q: Which c.d.f. F is of X is continuous at x=0?

A: If F(0) = F(0-) then F(x) is said to be continuous at x = 0

Q: Suppose that f: R2R is a function given by S x²+y² f(x, y) 0 for xy = 0. Show that f(x, y) is…

A: We have to show the given function  f(x, y) is continuous  at ( 0,0)

Q: Show that f (x, y) = has no limit as (x, y)→(0,0) Vx2+y2

A: The objective is to show that f(x,y) has no limit as (x,y) approaches to (0,0).

Q: Show that f(x) := x/3, x e R, is not differentiable at x 0.

A:

Q: The limit of f (x, y) : as (x,y) approaches (0,0): %3D O Infinity O Doesn't exist Exists and equal…

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Q: Suppose F(z) = e dt. Use the Fundamental Theorem of Calculus to evaluate the derivative. F'(z) = dt…

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Q: Show that the function f(z)=sin x cosh y+i cosx sinh y is continious as well as analytic every…

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Q: Find the values of a and b such that f is differentiable at x = 3

A: Given,            The function is fx=ax+bx≤32x1-1x>3To find : Find the values of a and b such…

Q: Consider function f(x, y) = x cos(TxYy) + x³y. .3,

A:

Q: Suppose that F(x, y, z) = 0 defines z as a function of x and y and F is differentiable. Prove that…

A: This is a problem of the chain rule and Implicit function theorem.

Q: Show that the function f(z)=sin x coshy+I cosx sinh y  is continuous as well as analytic every where

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