A function f(x) is said to have a removable discontinuity at = a if: 1. f is either not defined or not continuous at r = a. 2. f(a) could either be defined or redefined so that the new function IS continuous at z = a. 2x2 + 3x - 5 Let f(x): x - 1 Show that f(x) has a removable discontinuity at x = 1 and determine what value for f(1) would make f(x) continuous at r = 1. Must define f(1) =

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 g (x) = f' (x) be a continuous function. If the derivative of the continuous function g (x)…

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Q: 2. Consider the function / with domain (-2, o0): 3|2 – 1| 2 + 27 - 4 if – 2 <z<1 f(z) = if r = 1…

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Q: Sketch the graph of a continuous function y = h(x) such that a. h(0) = 0, -2 < h(x) < 2 for all x,…

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Q: Consider the following example: if g: [a, b] → R is continuous and F is a function defined as F(x) =…

A: It is given that,  g : a, b → ℝ is continuous and F is a function defined as ;  F(x) = 1,x∈a,…

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A: When f'(x)&gt;0 then function increasing when f'(x)&lt;0 then function decreasing

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Q: Determine if the given function is continuous at x=a and if the function is differentiable at x=a y…

A: To determine: The function is continuous at x=a and if the function is differentiable at x=a. Given…

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A: Given: f(x)=1x2-x+1xx&lt;0-10≤x&lt;101≤x&lt;21x=2x-2x&gt;2 To determine: The given function is…

Q: a continuous function f such that f(4) = 4, f'(4) = 0, ƒ'"(x) 4 is:

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Q: If f(g(x)) is continuous at 0, then g(x) is continuous at 0  true or false

A: Given that If f(g(x)) is continuous at 0, then g(x) is continuous at 0

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A: In this question we will use basic of calculus i.e concept of continuity and differentability. We…

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: Consider the following example: if g: [a, b] → R is continuous and F is a function defined as F(x) =…

A: Please comment if you need any clarification. If you find my answer is useful please put thumbs up.…

Q: 1. Let f be defined on an open interval (a, b) and assume that f has a local maximum or a local…

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Q: If a function f(x) is not defined at x-c, then it is not continuous at a close interval [a, c). * O…

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Q: Suppose a function f is continuous on [0, 1], except at a = 0.25, and that f(0) = 1 and f(1) = 3. Is…

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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: Sketch the graph of a continuous function fon [0,4] satisfying the following properties. f'(x)= 0 at…

A: Given: f'(1)=f'(3)=0 f'(2) is undefined. f has an absolute maximum at x=2, f has neither maximum nor…

Q: Sketch the graph of a continuous function y = h(x) such that a. h(0) = 0,–2 < h(x) < 2 for all x,…

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Q: Suppose that the function f: [0, 1]  in R is continuous and thatf (x)&gt;= 2     if 0 &lt;= x &lt;…

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Q: Consider the following piecewise defined function: sin(ax) -1 < x < 0 4x f(x) = a2 –(b+1)x+b x²+x-2…

A: Given function is f(x)=sin(ax)4x,-1≤x&lt;0x2-(b+1)x+bx2+x-2,0≤x&lt;1x2-1+a ,1≤x≤2…

Q: 9. Consider the function f: R → R, defined by (x²sin(1/x) ifx # 0 f(x) = if x = 0 Then a. f is not…

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Q: Assume that ƒ is continuous on [0,1] and that f(0) = 2 and f(1) = 1. Show that the graph of y = f(x)…

A: given  f is continuous on [0,1] f0=2,f1=1y=x2+1

Q: 8. Suppose that f is a continuous function with f(x) > 0 for all real numbers x, and lim f(x) = 0 =…

A: Consider the provided question, Suppose that f is a continuous function with f (x)&gt;0 for all real…

Q: Prove that f(x) = other than the graphing method. x² – 1 is continuous at c = 0 by any method |

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Q: Consider the function xe* if x < 0 g(x) = x³ – 2x2 + x if 0 < x < c , %3D if x 2 c where c is a…

A: Given,gx = xex                            if x≤0x3 - 2x2 + x          if 0&lt;x&lt;c1x…

Q: If a function f(x) is not defined at x-a, then it is not continuous at x-a.

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Q: ... uavarasvo vr-vv, find the x-values (if any) at which f is not continuous. Which of the…

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Q: Use limits to determine if f(x) = is continuous at x = 1. z-2

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Q: Find c such that the function x ≤ c { is continuous everywhere. f(x) = x² - 3 X 6x 12 x > c -

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Q: 2. Consider the function f with domain (-2, 0): 3|22 – 1| if – 2<r<1 2.r2 + 2x – 4 f(x) = 3 if r = 1…

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Q: x²-1 for x# 1 - If flx) = show that flxx) is continuous at x = 1 x-1 2 for x = 1,

A: topic - limits and continuity

Q: A function ƒ is continuous for all x and has a local minimum at (2, –5). W statement below must be…

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Q: 13. Let g be defined by V7x +2 V6x + 4 | g(x) = if x 2 - and x 2 x – 2 k , if x = 2 For what value…

A: The given functiong(x)=7x+2-6x+4x-2,if x≥-27 and x≠2k,if x=2

Q: Suppose f '' is continuous on (−∞, ∞). (a)  If f '(−3) = 0 and f ''(−3) = 7,  what can you say about…

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Q: Find m so that f(x) is continuous at x = 2. x +4 if x 2 -

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Q: . Is f(x)= Vx + 1 continuous at x == -1? Yes, because all functions are continuous No, because the…

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Q: (2) Find an example of a function f : [0,1] → R such that f is not continuous, but that f satisfies…

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Q: 6. Determine the value of the constant a for which the function g(x) is continuous at x = 1 x* + 5x…

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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: h(x) = x+1 %3D at x = 1 x2-1

A: Function f(x) is continuous at a point x=a :Function should be defined at x=a, and  limx→a-f(x) =…

Q: Consider the piecewise-defined function Ax if x 0 h(x) е (a) Give values for A and B so that h(x)…

A: Given Data: Function: hx=Axif x≤0e-1/x+Bif x&gt;0 (a) The condition for the continuous function is,…

Q: 2. Consider the function f(x) = if x = {9 in lowest terms q > 0, p,q e Q; 0 if x e Q°,x = 0…

A: We use sequential approach of continuity to show it.

Q: (e) Every function f defined on (-0o, 0o) that satisfies the condition that lim f(x) = lim f(x) = ∞…

A: Critical points, continuity and differentiability