(b). Analyze general properties of continuity and discuss the continuity of the following. (i). f(x) = Vx² – 9 (i). f(x) =- (x+1)(x-2)

Q: Consider the function if g(x) = if 2. if x>0. And study its continuity at x=0

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Q: Let f(x)=3−2x+7x^2 Use the limit definition of derivative to find f′(x)

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Q: f(x) = V3x–1 c = 1

A: As we know that; If the function fx is continuous at x=c then, limx→c-fx=limx→c+fx=finite…

Q: 2. Let f (x) = x² + 3x – 5. а. Use the formal limit definition of the derivative to compute f'(x).

A: Given,          fx=x2+3x-5

Q: Let f (x) = xex . Use the limit definition to compute f'(0), and find the equation of the tangent…

A: Given: fx=xex We know that f'x=limh→0fx+h-fxh…

Q: Let f(x) = 2x² + 1. Use the limit definition of the derivative to find f'(x).

A:

Q: Suppose that a function ƒ satisfies the following conditions for all real values of x and y: i) ƒ(x…

A: The given conditions are,

Q: Discuss the continuity of the function. f(x, y, z) = 1/(√x2 + y2 + z2)

A: Given rational function is

Q: Let f(x) = 2x2 - 3x - 5. Show that the secant line through (2, f(2)) and (2 + h, f (2 + h)) has…

A: Definition used -                   The slope of secant line -…

Q: 1. For what value of k is the function h(x) continuous on the whole real line? HINT: Use definition…

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

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

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Q: Let f(x) = 1/x-2. Find f'(x) using the limit definition of the derivative

A: We find f(x+h) first.

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: Find the limit of f(x) = v9 – x² as x approaches -3 from the right.

A: follow next step

Q: Let f(x) = V17 – x. Compute f'(8) using the limit - definition f'(8) = | 8 Find an equation of the…

A: To find the derivative of f(x)=(17-x)1/2 using limit definition and also obtain the equation of…

Q: Use the limit definition of the derivative function to find 4 x2]. dz Which of the following sets up…

A: The objective is to use the definition of limit to find the derivative.

Q: (a) Let f (x) = Vx – 1. Use the limit definition of the derivative to find f' (x).

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Q: Let f(x) be a continuous differentiable function that f(x)- 4 satisfies lim =D5 %3D x3 x-3 Which…

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Q: Let f(r) = 1-5r2. Use the limit definition of the derivative to show that f'(z) = -10r. %3D

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Q: Find the limit and discuss the continuity of the function.

A: Evaluate lim(x,y)→(2,4)x+yx2+1

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

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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: Let f(x) = V9 – 2x. Find f'(x) using the limit definition of the derivative.

A: To find f'(x) by definition f(x)=√(9-2x)

Q: Use the limit definition to compute f '(a) and find an equation of the tangent line. f (x) = 2x2 +…

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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: Determine the points of continuity of the function f (x) [x] for all x E R.

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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: Let f(x) = 3√(x + 1) − 4 = (x + 1)1/3 − 4. Use the limit definition of the derivative to show that f…

A: Consider the given function: fx=x+13-4=x+113-4 Vertical tangent at point indicates that at that…

Q: Given f(x) = |2x – 2|. 1) At which points is f not differentiable? Prove your claim using the limit…

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Q: Let f (x) = 2x² + 1. Use the limit definition of the derivative to find f'(x) %3D

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

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Q: Discuss the continuity of f(x) = {Vx, x > 1 1, x<1 at x = 1.

A: A function f is said to be continuous at some point a if the value of the function at that point is…

Q: Given f(x)= x² and  g(x)= 4x+1 if x>2          = x²+5 if x≤2 a)use the limit definition of…

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

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

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Q: Find the limit of the function f(x) = x²esin(1/x) as x approaches to zero.

A: To find limit of function f(x)=x2esin(1/x) as x approaches to 0. (Using Squeeze theorem)

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

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Q: Let f(x) = V5x + 2. Find the derivative f'(x) using the limit definition.

A: We have to find derivative

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

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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: Determine the limit as x approaches the given x-coordinate and the continuity of the function at…

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Q: Q1) check the continuity of fX) at X--1, 0,1.2,3 -1<x<1 f(x) = 2x-1, 3x-2 2SxS3 2, 1=3

A: As per the answering guidelines we need to answer only first question so please repost the other…

Q: Analyze continuity of the function.

A: Before going to the continuity, we will be finding the domain of the given function. Note that the…

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

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Q: Let f(x) = 2x2 +1. Use the limit definition of the derivative to find f'(x).

A: We can find f'(x) Using following formula

Q: Let f(x)=√18 x. Compute f'(2) using the limit definition f'(2) = Find an equation of the tangent…

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Q: Discuss the continuity in R3 of the function f(x, y, z) %3D x2+ y2+z2 -1

A: Given: f(x,y,z)=1x2+y2+z2-1.

Q: 6. Discuss the continuity for the following functions x+y a) f(x,y) = 4x2-y2-4 x+y b) f(x, y) = %3D…

A: The objective is to discuss the continuity of the functions.