(c) Simplify the function f(x) = |x - 1|+ |x + 1|. Test the continuity of this function at x 1. At which points this function is nondifferentiable?

Q: Determine the domain of the function and prove that it is continuous on its domain using Theorems…

A: Given: f(x) = ln (9 - x 2) To determine: The domain of the function and prove that it is continuous…

Q: B) Test the functions continuity at the given poihts: (x²-x-6 1) f(x) 3D x * 3 ,at x 3, x 5 X-3 x =…

A: f(x)=x2-x-6x-3x≠35x=3

Q: Verify the Rolle's Theorem for the function (x2-1)(x-2) on [-1,2] find the point in the interval…

A: Given function is : fx=x2-1x-2 To verify the Rolle's Theorem and find the point in the interval…

Q: Determine the domain of the function and prove that it is continuous on its domain using Theorems…

A:

Q: Find the value of the constant (a , b, or c) that makes the function continuous.

A: If function is continuous  Then, it will be continuous on x=-1 and x=12 Therefore, limx→-1-1fx=f-1…

Q: Determine the domain of the function and prove that it is continuous on its domain using Theorems…

A:

Q: Find the constant a such that the function is continuous on the entire real line. [ 5x², x 2 1 x < 1…

A: The given function is: f(x)=5x2   ,   x≥1ax-3,  x&lt;1 To find constant 'a' such that the function…

Q: Discuss the continuity of the function h(x) = }" (x2 + 7х -5, x3 – 2x2 + 1, x < 3 x 2 3 on the…

A:

Q: 1. Test the continuity of the following functions at given points? x² -1 -1 <x<0 2x 0 <x<1 (a) fx)=…

A:

Q: Determine the whether the function is continuous at x=-2. Justify your answer 2x+7 if xS-2 using the…

A:

Q: Find the constant a such that the function is continuous on the entire real line. 4sin x if x < 0…

A:

Q: 9. Discuss the continuity of the function - a³, 0 a

A: We have to check continuity

Q: D. Discuss the continuity of the function g (x): 1 %3D on the interval [-1,2]. x2-4

A: Given, To discuss continuity of the function g(x)

Q: Discuss the continuity of the following function: 2* (1- x), x0 x < 0 x = 0

A:

Q: b. Test the continuity of the following function 1, V1-x,0sIs1, at x = 0,1 (x-2, x<0 x21

A:

Q: Determine the domain of the function and prove that it is continuous on its domain f(x) = x2 / (x +…

A: fx=x2x+x14 The domain is the set of all values of x for which denominator is non-zero. That is,…

Q: 2. Test continuity at x = 0 and x = 3 for the function (3 + 2x; - 3 3

A:

Q: 3. f(x) = v2x – 5 at x = 3 -

A: (3) Given function is fx=2x−5 We have check whether the function fx is continuous or not at x=3 For…

Q: Q3) Test the continuity of the function f(x): -15x <0 0S X< 2 F(x) = 2х— 1 x+ 3 X = 2

A:

Q: 1 Discuss the continuity of the function g(x) : on the interval [-1,2]. x2-4

A: Consider the given function and interval, f(x)=1x2-4 and [-1,2]   Now, check the value of the…

Q: Find the constant a such that the function is continuous on the entire real line. 8sin x if x < 0…

A: For continuity of f(x) LHL=RHL     so find lhl and rhl and equate both to get a.

Q: Consider a function f(x) = |x – 3|. a. Show that f (x) is not differentiable at 3. -

A: Given         f(x) =|x-3|

Q: Determine the domain of the function and prove that it is continuous on its domain f(x) = √(x2+9)

A: Solution:Given     f(x)=x2+9To find the domain of the function  and to prove f is continous on its…

Q: 4 If f(x) = x 2 - function for all real values of x, then f(8) is equal to

A:

Q: -x ifx1 function f. Where is f discontinuous? Justify your answer using the definition of…

A: We first make a table for the function x -4 -1 0 0.5 1 2 3 4 y 2 1 1 0.5 DNE 1 4 9 Then we…

Q: 1. Check the continuity and differentiability of the function f(x) rež x # 0 1+e* 0, at x = 0. x = 0

A:

Q: Find the continuity of the function Of(x)= tx²+3 と+ とく3 5x-3 at =t

A:

Q: 2. For the given function, f, determine if the function is discontinuous at a given point. State…

A: Function is f(x)=xx a=0 We have to check whether the function is continuous or discontinuous at…

Q: Consider the function (x)=x²+2x . Using the limit definition of the derivative, show that for any…

A:

Q: S(x) = 7x* – 1x* +2. | Use interval notation to indicate where f is continuous. Domain of…

A:

Q: Discuss the continuity of the function f(r) at a = 0.

A:

Q: (c) Consider the following graph of a function y = f(x): -2 -1 3 Test the continuity of f(x) at x =…

A:

Q: How can you sometimes decide from examining ƒx and ƒy that a function ƒ(x, y) is differentiable?…

A:

Q: ((4— х)2 х 1 continuity at the indicated test point. If it is discontinuous, specify the type of…

A:

Q: Discuss the continuity of the function f(x) = {x2 − 3x if x &lt; 2 2x + 4 if x ≥ 2…

A:

Q: Find the value of the constant ( a, b, or c) that makes the function continuous.

A: Given: fx=1x,x&lt;-1, x&gt;12ax+b,-1≤x≤12 if given function is continuous then limx→-1-fx=limx→-1+fx…

Q: Q4) Test the continuity of the function f(x): - 2 < x < 0 0< X <1 X = 1 F(x) = 3x - 2 2х + 1 3

A: Fx= 3x-2  -2≤x&lt;02x+1     0≤x&lt;13       x=1 We know that a polynomial function is always…

Q: x' - 27 x² -9 (c) at x = 3 and x = -3

A: First of all to find critical points put the denominator equal to zero. x2 - 9 = 0 x 2 = 9 x = 3, -3…

Q: Q2/B/ check the function continuity at x-0, for the fimction f(x)%= 1+ 4 2/3

A:

Q: 3. Apply the three conditions of continuity to determine if the function f(x) = 2x²+5x+2 x²-x-12 is…

A:

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

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Q: Discuss the continuity of the function. x2 – 4 f(x) X + 2 f is discontinuous at x =

A:

Q: let f be the function given by f(x)=kx/(x^2+1), where k is a constant.  For what values of k, if…

A:

Q: (-x3 – 4x + 20 ,x > 3 2 – 7x , x < 3 Determine whether the function f(x) = is continuous at x = 3.…

A: From the given problem: fx=-x3-4x+20 , x&gt;32-7x , x≤3 As we know that:  If limx→a+fx=limx→a-fx=fa…

Q: D. Discuss the continuity of the function on the closed interval. Function Interval 1. g(x) V49 [-7,…

A: Note: We are entitled to solve only one question at a time. Given: gx=49-x2 To Discuss: Continuity…

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.