((4— х)2 х<1 Given the function f(x) = { (x + 4)² x = 1, at x = 1, determine its (х — 4)2 х> 1 continuity at the indicated test point. If it is discontinuous, specify the type of discontinuity.

Q: 1. Consider the function f(x) = x6 - x³. a. Determine the absolute extremum using the First…

A: The given function is fx=x6-x3. a. Find the absolute extremum using the first derivative test. b.…

Q: 11. Find the absolute extremum of f (x) = 4- x3, where -2 < x< 1

A: Given: The function is  f(x)=4-x3,  -2≤x≤1   To determine: The absolute extremum of the function…

Q: ´28 – e14z x 0 Determine whether the function f(x) = 14x – 1

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Q: Time left 2:32n 2+1 x+3 Given the function f(x) = {x + 1) x= 0, atx 0, determine its continuity at…

A: We have to solve

Q: x²-1 If f(x) = for x +1 and f(x)=2 when x 1, show that the function x-1 is continous at x=1?

A: Show that f is continuous at x=1

Q: 1) Find the absolute extremum values of f(x) = x² – 4x + 16 over the interval [1, 4].

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Q: 2. Given the function: f(x) 3 x -3 x≤2 2 x² + 1 x > 2 Is f(x) continuous and differentiable at x=2?

A: Here is the solution:

Q: let                    x^2+1   if x is less than 1 f(x)=                   x+1        if x is…

A: Consider the given function fx=x2+1  if x&lt;1x+1   if x≥1. The point is x = 1. Obtain the left hand…

Q: 10- Continuity of the function f(x){*-5 -1<x<2 x² -1 2< x< 3 at x=2?

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 1. Given that x +1 2x2-1 g(x) Show that the g(x) function is continuous at a = 4.

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Q: Suppose the nonzero function f(x) is infinitely differentiable and that f'(x) = -3f(x) for all a…

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Q: Is there an unbounded function f:[0,1] →R where it is discontinuous only at a single point in [0,1…

A: f: [0, 1] →R Domain: [0, 1] The function is discontinuous at a single point of the domain.   Let's…

Q: Find value a  such that f(x)={x^2+2x-1 if x not equal to 1…

A: given,f(x)=x2+2x-1  if  x≠1a                if x=1left hand limit at x=1limx→1- f(x)=limx→1-…

Q: 1. Consider finding the root of f(x) =x´ – 5 use secant method, ɛ = 0, and start with the a interval…

A: given , f(x) =x2 - 5  we have to find roots of f(x) in interval by using secant method

Q: 18. Solve for A and B so that f(x) has a limit at both x = 2 and x = 4. 3x + 4, x> 4 f(x) Ах + B,…

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Q: 5. Prove f(x) = e* + x has a root on the interval (-1,0) using the Intermediate Value Theorem.

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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: 1) Find the absolute extremum values of f(x) = x² [1, 2]. – 2x + 12 over the interval

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Q: 2. f(x) = is a continuous function but it is discontinuous at x = 3. Explain why X - 3 this is not a…

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Q: 3. Find the constant k that will make f continuous on (-0o, 00). Sx – 4 , (kx2 – 24x + 46, x > 5 x<5…

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Q: 2. Test continuity at x = 0 and x = 3 for the function (3 + 2x; - 3 3

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Q: x2 – 4x + 3 - f(æ) = 5. Let x - 3 How could we define f(3) x = 3? so that J is continuous at

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Q: If f(x)= (x^4) + 3x + 1 and there are two roots x=a and x=b in the interval [-3,-1] with a &lt;b.…

A: The given function is,

Q: 3. f(x) = v2x – 5 at x = 3 -

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Q: 4. Consider the function f(x) = (2x - 3)5. Discuss the continuity and %3D differentiability at x =…

A: 4.f(x) = (2x-3)15 from the graph, f(x) is not differentiable at x=32 , since slope changes at x=32…

Q: 1. Employ the following methods to find the maximum of f(x) = 4x – 1.8x² + 1.2x – 0.3x* (a)…

A: Given f(x)=4x-1.8x2+1.2x3-0.3x4. To find: (a) find the maximum using golden search method.…

Q: x2-x-1 , if x 1 is 1 if x= 1 continuous at x=1 since the right and the left limits are equal at x =…

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Q: 6- if f(x) is a continuous function at x = 0, then a = 1- cos 4x x0 V16+ Vx -4 3.

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Q: The interval on which f(x) = VI-x is decreasing where x€ [-1.1] is

A: Given function f(x)=1−x2   on  [−1,1]

Q: 1) Find the absolute extremum values of f(x) = x2 – 4x + 18 over the interval [1, 4]. [2 marks]

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Q: The distance between the x-intercept of the tangent line to the curve y = and the x-coordinate of…

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Q: A particular finite difference formula for the first derivative of a funtion is: f '(xi) =…

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Q: 12. Suppose we know that f (x) is continuous and differentiable on the interval [1,9], that f (9) =…

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Q: S x2 – 3 |kV5+x _if x > –1 if x < -1 - 2. Determine the constant k such that the function f(x) : is…

A: As per our guidelines, I can answer one question and maximum three subparts of a question. Since you…

Q: On the interval 0 < x < 3, the function f (x) = x² – 8x + 16, which one it is  a) is concave down…

A: Given:      y=x2-8x+16 , 0 &lt; x &lt; 3

Q: (a) Discuss the continuity of piecewise function, x-7x+12 x 3 at x= 3 using the continuity test. (b)…

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Q: Q.4 A/ Prove the function continuous at x = -2, (x2 + 5 13-3x where %3D if x<-2 if x 2-2 f(x) = %3D

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Q: 2. Find the (exact) values of a and b so that f is continuous at a = 2. 8r2 + 20x + 28 if x 2

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Q: 9. Discuss the continuity of the function x 2 x2,

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Q: 5. Discuss the continuity of the function x'- 1 f (x) = { 2, **- 1 at x = -1. x+2 2, x=- 1

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Q: 1 Discuss the continuity of the function f(x) on the interval (0,2] and [-1,3] x2 -4

A: A function f(x) is said to be continuous in the closed interval [a,b] if→ f is continuous on (a,b).→…

Q: Q. 1: Determine the func- tion is continuous or dis- continuous at x = -1 and x = 1.

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Q: 3. Consider the function f(x) = r - 1+x 1- a. Explain why, when evaluated in a floating point…

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Q: 1) Find the absolute extremum values of f(x) = x² – 4x + 8 over the interval [1, 4].

A: f(x) = x2 – 4x + 8

Q: There is an infinite discontinuity at x = 0 and f(0)=-2

A: