Consider the set U = {(x, sin(1/x)) : 0 < x} C R². a) Show that every point on the vertical line segment given by {(0, y) : –1

Q: b) Let f :R R , then prove that the following three statements are equivalent. (i) f is continuous…

A:

Q: . Let f (x) be a continuous function on [a, b], where a, b ∈ R and a &lt; b. Suppose that there are…

A: To prove thatlimn→∞​yn​−xn​f(yn​)−f(xn​)​=f′(c)given that  f(x)  is differentiable at  c , we follow…

Q: be coutinious at x Q3) Find the values of k and m that will make the following function continuous…

A:

Q: Suppose f(x) is continuous on [3, 8] and -5 < f'(x) < 3 for all x in (3, 8). Use the Mean Value…

A:

Q: O Find the limit function of th Ca)» (1- )*

A:

Q: Q3: A- Find the limit for the following functions: - tan2x 4х-3 Зx3-9х2 +х-3 1- lim x→0 sin4x 2- lim…

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

Q: Find the limit as t-➜0 of r(t)=

A:

Q: 3-√I lim I-9 T-9

A:

Q: What does is mean for two functions f(x) and g(x) to be orthogonal

A:

Q: 8n Show that fn (x) = x2" – x" is unfiormly converges or not by using uniform norm

A: The given function is  fn(x)=x2n-x8n We show that the function is uniformly converges or not by…

Q: ss the continuit 1 x+- for

A:

Q: 15) Prove that if ffx) is continuous at x=0 then so is V f(x) provided that fix) zo for all x in the…

A: Step 1: Step 2: Step 3: Step 4:

Q: a)Find the average of the function f(x)= x² +1 on the interval [-1,2] Answer:

A:

Q: Let h be a differentiable function. Also he [a, b]. Prove that there is a sequence {x} = (a, b)such…

A:

Q: Q2) Discuss the continuity at x=2. When: x> 2 x = 2 3x + 1 f(x) : x² + 3 %3D 2x + 1 x< 2

A: The given functionf(x)=3x+1x&gt;2x2+3x=22x+1x&lt;2to check continuity at x=2

Q: Give an example of a sequence of continuous functions: fn: [0, 1] R that is pointwise convergent but…

A: Consider the function fx=0, x is irrational in 0,1mn, x is rational in 0,1. This function is called…

Q: Find the value of ſ (2x – x³) dx by evaluating it as the limit of sums.

A:

Q: f(x) = 3x - 2sınx +7 %3D aluse the intermediate Value Theore m to show that flx) has at least one…

A:

Q: Use the e-6 definition of continuity to prove that the following functions are continuous at the…

A:

Q: 3) √³/₂2 5 - dx -2 2x-1

A:

Q: Suppose fis a real valued function defined on an open interval I and differentiable at every x eI.…

A:

Q: -2 x<-1 Q1)a) For what values of a and b is g(x) = |ax - b - 1<x< 1, 3 x21 Continuous at x=1

A: From  the given problem:   gx=-2x≤-1ax-b-1≤x&lt;13x≥1     As we know that a function f(x) is…

Q: Q2) Discuss the continuity at x=2. When: x> 2 X = 2 x< 2 Зх + 1 f(x) = } x? + 3 %3D 2х + 1

A: Our objective is to discuss the continuity at x=2.

Q: b) Discuss the continuity conditions of the function- f(x) which shown in figure at x= 0,x = 1,x= 2…

A:

Angles

In mathematics, angles constitute a very important part. Just like the concept of lines, an angle is a necessary figure that is used for measurement. How do you define its formation? It is formed when two or more lines meet at a point. The point at which two or more lines meet is known as the vertex. When the lines get inclined at this point, they do form various angles. Angles are measured from the vertex in terms of degrees.