Show that Jx² + 2, x < 1 [x+2, f(x) = x > 1 is continuous but not differentiable at x = 1. Sketch the graph of f.

Q: Show that f (x) = 1 is not uni form continuous on (0,3) I-3

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Define g : R →R x sin (1/x), g(x) = 10, x # 0 x = 0. Explain why g is continuous at 0; in…

A:

Q: Define the function f(x, v) = 4x³-x³y-4y5 3x5-3y5 at the origin so that it becomes continuous there.

A: A function is said to be continuous at (a,b) if the the value of function at (a,b) is equal to…

Q: 2. f(x) = Vx – 1 at x = 5

A: Function is continuous and differentiable both at x= 5.....for detail...go through the solution

Q: Let f be the function defined by: sin x, x <0 x2, 0 <x < 1 2 - x, 1<x < 2 x-3, x22 f(x) = %3D For…

A:

Q: Does the MVT apply to f(x) = - on the interval [1, 4]?

A:

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) =…

A:

Q: Determine the domain of the function and prove that it is continuous on its domain f(x) = cosx2 /…

A: f(x)=cosx2x2-1

Q: ずx 1

A:

Q: Show that the function given by f(x,y)= x² + 3xy is differentiable at every poin using the…

A: Introduction: Distinctiveness (differentiability) implies continuity. If a function is…

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: Show that the function is continuous on  (∞ , -∞).

A:

Q: Let f : R → R with f(x) = 3x² + 2. Prove that f is differentiable at the point –1 %3D

A: f(x) =3x2+2 f'(x) =limh→0f(-1+h) -f(-1)h        =limh→03(-1+h)2+2-3-2h        =limh→03+3h2-6h -3h…

Q: Suppose that fx) is continuous on [0, 9] and F(x) is an anti-derivative of f. If F(0)=9 and F(9)=7,…

A: Given that:                           f(x) is continuous in [0, 9].…

Q: Determine if the function is continuous at point (0,0): F (x, y) _x³y°cos(x³+y³) (x²+y²)²

A:

Q: Use the prové thát 1 x| < ]x| fór áll * # 0. onclü X| S x| för åll x € R. Hint. Apply MVT to f(x) =…

A:

Q: Explain why the function ƒ(x) = sin (1/x) has no continuous extension to x = 0

A: Then we can extend the definition of the function at that point to make it continuous there.

Q: YDiscuss the integrabilty of the function f(x) = on [0,7).

A: We need to find the integrability of the function and find the integral of it.

Q: Is the scalar valued function f(x)=(x^2-1)/(x+1) continuous?

A: This is a problem related to limit and continuity of the function. Please follow the procedure given…

Q: Determine the set of points at which the function F(x, y) = arctan ( 3x +7/y – 7 ) is continuous.

A:

Q: Show that f(z) =xy+iy is everywhere continuous but is not analytic

A: Answer

Q: 11. Prove from the definition that the following functions are differentiable. ()- (b) f =xy?

A: By the definition, the function f(x,y)=xy^2 is differentiable if fx(x,y) and fy(x,y) both exist.

Q: Define f(0,0) in a way that extends f to be continuous at the origin. 6x² -x²y² + 6y² x² +y? f(x,y)…

A:

Q: that makes y continuous but not differentiable by writing the required procedures to that If: X≥0…

A:

Q: show that f,given by f(x) x +0 )is continuous on R-{0}

A:

Q: Is the following piecewise defined function f(x) continuous at x = = 0, [cos(x), x≤0 f(x) = x²+x+1,…

A: The given function is: fx=cos x,       x≤0x2+x+1,  x&gt;0 Check whether the function is continuous…

Q: Determine the set of points at which the function is continuous. F(x, y) - х-у 1 + x² + y2

A:

Q: if x = 0 f (x) = %3D x* sin(-) otherwise

A: In the given question, concept of continuity is applicable. Continuity Continuity for a graph y=fx…

Q: Let f (x) = In(x + 2). Use the definition of the derivative and your now expanded knowledge of…

A:

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

A:

Q: show me the follewing funct continuousornot at X-o tion f(x): Ix1 130

A:

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: Suppose that f hits every value between y = 0 and y = 1 on the interval [0, 1]. Must f be continuous…

A:

Q: Prove that the function f(x)=sinπ|x| is continuous at x = 0 but not differntiable at the same point.

A:

Q: Give a formula of a continuous function that is differentiable except at 0.

A: Consider the provided question, For a function to be continuous at a point x=a, we say that the same…

Q: Give a 8, e proof that f(x) = x² + 3x is continuous at x = a, where a is any real %3D number.

A:

Q: Decide whether or not the real function In (cos 2x) 2x2 x + 0, f(x) = -1, = 0, x = is continuous at…

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

Q: Show that the function f(z) = z = is differentiable but not analytic at z = 0

A: Givenf(z)=zz

Q: The function f (x) ,x € [-27, 2n] is continuous on: 1-cos x

A:

Q: what condition when present are sufficient to conclude that a function f(x) is continuous at x=a

A: To show a sufficient condition to conclude that a function f(x) is continuous at x=a.

Q: (i) Consider the function such that f(x) = 2x if 0SxS1 and f(x) = x-1 if x> 1. Is f continuous over…

A:

Q: 5. Is the function given by g(x) = 4x³. 6x continuous on R?

A: