Let f(x) = −2/x and g be the function defined b)Is f . g continuous at x = 3? If not, does f ◦ g have a removable discontinuity, a jump discontinuity and/or an infinite discontinuity at x=3?

Q: If f is continuous at a number, x, then f is differentiable at x. True

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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: b) Suppose that f(x) 1 if x is negative. Can ƒ be continuous at x = 0?

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Q: If f is continuous at a number, x, then f is differentiable at x. True False

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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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A: Given that  f(x)= 1(x+2)2 is continuous at x = -2

Q: What is the definition of f(x) is continuous at x = a? ||

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Q: Let 4 – x² if x > 1 f(r) if x < 1 Determine whether or not f (x) is continuous at r = 1.

A: If left hand limit and right hand limit same, then f(x) is continuous at x=1.

Q: Suppose that f (x) &lt; 0 if x is positive and f (x) &gt; 1 if x is negative. Can f be continuous at…

A: f(x) will be continuous at x = 0 if LHL = f(0) = RHL

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Q: Suppose that f is a continuous function such that | f(x) dz = -12. Find | () dr.

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Q: ずx 1

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Q: B) If f is differentiable at x, then prove that f is continuous at x Is the converse true? Why

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Q: define the function at 5 so that it becomes continuous at 5.

A: First, we rationalize the function, so that it becomes continuous at 5 which is shown on the board

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A: Since the f(x) is continuous function in [0, π], therefore the value of function at x = 0 must equal…

Q: Suppose that f is a continuous function such that | f(x) dz = -12. Find (*") dr.

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Q: Use limits to determine if f(x) = 1 is continuous at x = 0. (z+2)?

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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: suppose that f is a function satisfy |f(x)|&lt;=|x| for all x. Show that f is continuous at f = 0.…

A: Suppose that there is a function f that satisfies

Q: Show that the following function is not continuous at (0,0). { 3 x2+y6, 0, , if (x, y) # (0,0); if…

A: To prove that given function is continuous. gx,y=xy3x2+y6,   if x,y≠0,00,              if x,y=0,0

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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: 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: 2. Determine whether f is continuous or discontinuous at 1. (x – 1 if x > 1 f(x) -x² if x <1 O f is…

A: Given query is to find function is continuous or not at x = 1.

Q: Consider f(x) = #3/5. Is f(x) differentiable at x=0? Is f(x) continuous at x=0?

A: The given function is,

Q: Let f be a function of multiplicity 5 at P. Then at P, µ(x) f(x) has multiplicity: f(x)'

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Q: Determine whether the statement is true or false. If a functionf is continuous on [a, b]andf has no…

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Q: Show that f(x) has a removable discontinuity at x = 0 and determine what value for f(0) wou make…

A: Given that ,  fx=9x+-8x+9xx-1if x≠0 and x≠13if x=0 We know that, A function fx is said to have…

Q: Is f(x) = √x continuous at x = 0?

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Q: Prove that the function f(x)=sinπ|x| is continuous at x = 0 but not differntiable at the same point.

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Q: Give a formula of a continuous function that is differentiable except at 0.

A: Consider the provided question, For a function to be continuous at a point x=a, we say that the same…

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Q: 1. Explain what it intuitively means for function f(x,y) to be continuous in some domain D.

A: To explain the meaning of the given statement.

Q: Use the definition of continuity to determine whether the shown function is continuous at a = 1.

A: Given:              fx=2-xIf x&lt;11If x=1x2If x&gt;1

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: what condition when present are sufficient to conclude that a function f(x) is continuous at x=a

A: To show a sufficient condition to conclude that a function f(x) is continuous at x=a.

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Q: Determine whether f is continuous on its domain. If it is not continuous on its domain, say why. 4F…

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Q: Find the value of fa) which makes f(x) continuous at x = a (if exists) where X - x f(x) a =

A: Given function is fx=x-xx Find the value of fa=0.