Determine if the function f below is continuous at x = 1: [1– VI– x, x<1 In x, x < 1 f(x) = x > 1

Q: Q2. Let f: R → R be a function such that f(x) = x sin f is defined at xo, where the value of 8…

A: We have to find the value of delta(d) in terms of x0 and e while evaluating the limit at x := x0 for…

Q: Find all values of c such that f is continuous on (-0, o0). S1-x², {. f(r) %3D x, C = (smaller…

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Q: Q2. Let f:R- R be a function such that f(x) = x sin| f is defined at x, , where the value of d…

A: Topic- Limits

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,…

Q: compute f ' (a) using the limit definition and find an equation of the tangent line to the graph of…

A: Given f(x)=x2-x The limit definition for derivative of a function is given as: Using the above…

Q: Let xª sin , x + 0; f(x) ={ 0, x = 0, where a > 0 is a parameter. 1. For which values of a is f(x)…

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Q: Determine the interval(s) where f(x) = is continuous. 1- In(1/r)

A: It is given that, f(x)=11-ln1/x   A function is said to continuous in an interval in which it is…

Q: Let f be a function which is continuous on the interval [a, b]. The definite integral of f on [a, b]…

A: n is nothing but (b-a)/∆X mean,    n=(b-a)/∆X

Q: 3. Use the definition to show that the function f(x) = is continuous on the interval [c, o0), where…

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Q: c =

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Q: Let f be a continuous function such that 5 √ (f(x) — 2) dx? What is the value of f(x) dx = -2 and…

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Q: Suppose f" is continuous everywhere. For any constants a and b, show that xf" (x) dx = bf" (b) –…

A: Explained below

Q: Suppose f is a continuous function such that Si f(t)dt = e® In(x) for all x > 0. What is the value…

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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: If f : R+ → R is a function such that f(x + y) = f(x)f(y) for all x,y ∈ R+. Prove that f is…

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Q: Prove thait if y=f(x) f(x)=0 when x is a rotional number, then f(x)=0 for all x € R. is continuous…

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Q: Consider the function F(x) = | s(t) dt , where a is a constant and f is continuous everywhere. By…

A: Find we have to use definition of derivative.

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: 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: Discuss whether the following functions are continuous at the specified point(s). sin(x) (a) f(x) =…

A: To determine whether the following functions are continuous at the specified points or not. (a)…

Q: All the following functions have continuous extension at x = 0 EXCEPT. Select one: a. None of them…

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Q: Assume f(x) is continuous on [a, b]. Prove that if f(x) > 0 for all x € [a, b], then S. f(x) dx > 0.…

A: Extreme Value theorem states that if a real-valued function f is continuous on the closed inteval…

Q: Let f be a continuous function on R such that f(x+y)=f(x)+(y) ¥x, yER. Show that f(x)3cx for some…

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Q: Show that Jx² + 2, x 1 is continuous but not differentiable at x = 1. Sketch the graph of f.

A: fx=x2+2,x≤1x+2,x&gt;1

Q: Let f(x) = x?sin (-) for x + 0 and f(0) = 0. c) Show that f'is not continuous at x = 0.

A: Given function  f(x)=x2 sin1x      for x≠00                  for x=0 we have to show that f' is not…

Q: The function f(x)=³ in (x) is continuous everywhere except x (х-1) at x=0 and at x=1. When…

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Q: Determine whether the following functions are uniformly continuous on the given domain via € - 8. X…

A: Any absolutely continuous function (over a compact interval) is uniformly continuous. On the other…

Q: What value of c makes the following function continuous at (0, 0)? f(x) = с, x + y² + 5, (x, y) #…

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Q: Use the definition to show that the function f(x) = → is continuous on the interval [c, o), %3D…

A: The given function is f(x)=1x2 .we have to show that f(x) is continuous on the intervel [c,∞)…

Q: sketch the given function and determine whether it is piecewise continuous on[0,∞).

A: The given piecewise function is The graph of the function is as below:

Q: show that f,given by f(x) x +0 )is continuous on R-{0}

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Q: sketch the given function and determine whether it is piecewise continuous on[0,∞).

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Q: b) Show that the function f (x) = { * x² sin ! for x E (0, 1] for x = 0 is absolutely continuous on…

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Q: Is the following piecewise defined function f(x) continuous at x = = 0, [cos(x), x≤0 f(x) = x²+x+1,…

A: The given function is: fx=cos x,       x≤0x2+x+1,  x&gt;0 Check whether the function is continuous…

Q: x = 0 f(x) sin z x +0 а) х — 0. ? b) х — 4т. ?

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Q: Consider the function f defined on [0,∞) f(x) = xrsin(1/x), for x≠0 and f(x) = 0, for x=0 where r >…

A: Given: f(x)=xr sin1x,   x≠00         ;     x=0     a) f is continuous on [0,∞) f is continuous if…

Q: b) Show that the function sin for æ e (0, 1] { f (x) = for æ = 0 is absolutely continuous on [0, 1].

A: Function is called continuous function if the left and right hand limit values at each and every…

Q: Which of the following functions is continuous on the interval (-0, +)? …* f(x) = Vx² – 1 (A f(x) =…

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Q: Determine if the function f below is continuous at x = 1: ſ1– VT- x, x 1

A: According to question,given function,fx = 1-1-xx≤1ln xx&gt;1

Q: Find the value/s of a such that the function f is continuous everywhere.

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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: Is the given function f (x, y, z) = xª – 6xy? + 723 continuous at the origin? Yes No

A: If a function f and another function g is continuous at arbitrary point. Then there sum, difference…

Q: Show that f : (0,∞) → R defined by f(x) := 1/x is not Lipschitz continuous.

A: Definition:  Let S⊂ℝ and a  function f:S→ℝ is Lipschitz Continuous at x∈S if there is a constant C…

Q: Let f(x) be continuous on [0, oo) and twice differentiable on (0, co). If f'(x) > 0 and f"(x) 1,…

A: Let f(x) be a continuous function on [0,∞) and differentiable at 0,∞. The given double derivative…

Q: Determine the set of values of the continuous function defined by the formula: a) f(x)=cos sin

A: Given that fx=cosπ3sinxgx=π3sinxsinx is continuous in x∈-∞,∞gx is also continuous in  x∈-∞,∞.Range…

Q: Prove f (x) 1+ mx is continuous at x = 1, where m e R

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Q: 3. Let f(r) = r sin() if z #0, and f(0) = 0. Show that f is continuous at r= 0 by using e- d…

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Q: .For what values of a is Jaax - 2a, x z 2 f(x) 12, x < 2 continuous at every x?

A: Here given function  Since,  it is continuous for every x thus it Is also continuous for x=2