1. Consider the function 4.x + 8 { if x < 0 f(x) = x² 2.x – 8 x² – 2x if x > 0 Use the definition of continuity to determine all the points at which f(x) is discontinuous. Classify each discontinuity as removable or non-removable.

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

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Q: use the formal definition of limit to prove that the function is continuous at c. g(x) = 1/(2x), c =…

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Q: The following statement is false, explain why. The function g(x) = x^2 on the interval [-1,1] has…

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Q: Determine the intervals of continuity for the function: f(x) = over the interval of 0 < x < 2n…

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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: (5) Use the limit definition of derivative to prove the following: (a) For any a e R, (f(ax))' =…

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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) = V13 – x. Compute f'(4) using the limit definition f'(4) =| Find an equation of the…

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Q: Let the function f(x) be defined by: 2x – 6 x + 3 f(x) = {Vx – 1– V2 2 x = 3 Determine the…

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Q: 3. Define the function sin(2x – 2) x 3 3' - Determine if f is continuous at x = 1 and x = 3. If…

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Q: Let f(x) = V1– cos 2x a) f has a • discontinuity at 0. b) lim f(x) = c) lim f(x) =

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Q: 1- Discuss the continuity of the following functions at given points { V9r4+x² 5x2+3x+1 ,if a 0 (a)…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Show that g(x) = (x3-8) / (x-2) has a removable discontinuity at x = 2. How should g(2) be defined…

A: The left-hand limit of a function at a point is the value of the function at a point very close from…

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: x+1 x 0 6-х the indicated test point. If it is discontinuous, specify the type of discontinuity.

A: We have to solve

Q: Suppose that f (x) = x·g(x) for some function g that is continuous at 0. Prove that f is…

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

A: Given function is fx=xx. To find whether function is continuous at x=a, where a=0. Solution:   we…

Q: 1. X) = 3x -5x2 C = 2 2. f(x) = V3x - 1 C = 1 %3D f(x) 3. -3x+2 %3D x-1 C = 2 +4x-5 f(x) 4. %3D x+5…

A: NOTE: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

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: Suppose f : R → R is a continuous function with the property that f(x) = 0 for every x E Q. Prove…

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Q: (a) Let x2 if x is rational f (x) = 0 otherwise. Prove that f is differentiable at 0.

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Q: Why is the following function discontinuous at x = 1? (1+x² ifz 1 (a) f(1) does not exist. (b) lim…

A: We have to find out

Q: Suppose f(x,y) = sin-' (6 – 2x2 – y²) and g(x,y) = 4x2 – y2. Determine the continuity of the…

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Q: Use the definition of continuity to determine whether f is continuous at a.

A: Solution:Given     f(x)=x-4if x≤0x2+x-4if x&gt;0and a=0To find :f is continuous at 'a'Formula:limx→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: Consider the function f with domain (-2, ): 3|x2 – 1| 2x2 + 2x – 4 if – 2< x < 1 f (x) = 3 if x = 1…

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Q: (4) Find the values of a and b so that h(x) is continuous at = 4. Hint: Write down the limit…

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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: Now consider the equation for the function above: ex+2 + 4, Vx + 3 + 1, х 2 f(x) 2, 3x, Use the…

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Q: Let f(x) = /20 – x. Compute f'(4) using the limit definition f'(4) - - Find an equation of the…

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Q: Use the definition of continuity to determine whether the shown function is continuous at a = 0.

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Q: Consider the following. [2 x -1 if x 1 Is f differentiable at x=1 ? Yes, because f is continuous at…

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Q: 1 (a) What type of discontinuity does the function g(x)=- have at el/x – 1 x=0 ? Explain. (b) For…

A: This question is from limits and continuity.

Q: - Define the function f:R → R by ƒ (x) = x +1 if x 0 and f (0) = 4. Show that lim,-0 f (x) = 1 and f…

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Q: Q4: Discuss the Continuity of following Also find at x = 1 range. and x = 0. Sxx+1 3x+5 -2 -2x+1…

A: a Given function is fx=x+1,    −2≤x&lt;−1x,            −1≤x&lt;03x+5,      0≤x≤2 We have to check…

Q: 2x, ifx BDU G EDU y = 5, if x= 3 if x = 3 (x-5, if x 3

A: Given:   y=2xif x&lt;35if x=3x-5if x&gt;3 To prove whether y is continuous or not x=3. Solution: A…

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: x + 6|, if x - 1 x² – 3x

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Q: Use the definition of continuity to show that h(x) = x^2 + 5x/2x + 1 is continuous at the number a…

A: The given function,   h(x)=x2+5x2x+1

Q: ) For a, 3 ER and B > 0, let f(x) ={} x° sin(|x|-#), when x # 0 when x = 0 0, ange of a and B (and…

A: Continuity and differentiability

Q: Consider the function f with domain (-2, 0): 3|a2 – 1| if – 2 < x < 1 2x2 + 2x – 4 f(x) = 3 if x = 1…

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Q: f(x) = 3x - 5x² 1. c = 2

A: Given: fx=3x-5x2  ; c=2   The function will be continuous at x=c when, limx→c-fx=limx→c+fx=finite…

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

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Q: Use the definition of continuity to determine whether the given f is continuous at a =0.

A: the given f(x)=(x+3)2-9x        if x≠06                       if x=0 we have to use the definition…

Q: Now consider the equation for the function above: 2x + 3, x 4 - x-3 ’ 2, x = 4 Use the equation and…

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Q: Use the definition of continuity to determine whether f(x) is continuous at a= 0.

A: Given function, We have to use the definition of continuity to determine whether f(x) is continuous…