Directions: Using the definition of continuity, identify the intervals where in the function the following function is continuous. 1. f(x) = Vx2 – 4 (x² –9) 2. f(x) = x+3 x+8 3. f(x) = - х2+x-2

Q: III. Directions: Find the derivative of the given functions with respect to x using the limit…

A: i) f(x)=3x2+5x-7ii) fx=12x2-9x

Q: (a) Find all possible points of discontinuity. (b) Discuss the continuity of ƒ at the points…

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Q: cos( (b) Test the continuity of the function f(x) = x-2 at the point x = 2. x = 2 4'

A: A function f is said to be continuous at x=a if both left hand limit and right limit exist at x→a…

Q: Consider the function y = g(x) = -x² + 3x + 6. (a) Use the limit definition to compute a formula for…

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Q: 2x - 5 when x 3 a. Use interval notation to express the interval(s) over which f is continuous. b.…

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Q: ek - 8 2x - 1 if x-1 se the definition of continuity to determine if f(x) = %3D

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Q: Duestion:- For what of value the constant "<' is on (-o, 00 ? the function continuous f(x)={ -" if…

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Q: to be continuous al x- 2) Find the value of c thent makes the function f= Continuou, everywhere. Use…

A: As there are multiple question as per bartleby policy i can answer 1st question only. Kindly ask…

Q: Choose the correct option. The function f(x)=xk is continuous at x = k when - (a)k≠0 (b)k<0…

A: The function f(x)=xk is continuous at x = k when

Q: a² - 5x + 10 Consider the function f(x) over the interval [3, 6]. Show that the function I - 2…

A: To Verify Rolle's theorem.

Q: x -3 2x+1

A: For the continuity of the piecewise function  Both side value are same at x- and x+  So here let's…

Q: x+2 Find all x values at which f (x) = is not continuous. Identify the removable %3D x² -3x-10…

A: Removable discontinuity is a point at which a graph is not connected but can be made connected by…

Q: Determine the intervals of continuity for the following function. Choose the correct answer below. O…

A: Given query is to find the the interval where function is continuos.

Q: (x? + 3x f(x) = - 6x if xs-2 if x>-2 A) Check the continuity of the function f(x) at x = -2 %3D

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Q: Determine whether the function is continuous or discontinuous at the given x-value. Examine the…

A: To find that the function is continuous or discontinuous

Q: Determine where f(x) is discontinuous. Use the definition of continuity discussed in this chapter to…

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Q: B. Directions: Determine whether the following functions are continuous on the given interval. x-5…

A: 1).f(x)=x-5x2-x-6f(x)=x-5(x-3)(x+2)⇒Function is discontinuous at x=3 and -2And 3∈(-1,3)Therefore…

Q: True/False; f (x) =; 1 is continuous on 2х —1 A) False B) True If f(-3)=6, f(2)= and f is continuous…

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Q: using the definition of continuity and the properties of limits to show that the function is…

A: We have to test the continuity

Q: S-2x f(x) = x2 Discuss the continuity of the given function at x=0. If discontinuous, is f(- x>0…

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Q: [4] Let k and c be real numbers. Let f(x) be a piecewise function defined by x + 3 if x 2 Using the…

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Q: 2 - x 0< x < 1 1 < x < 2 X = 2 2 < x <3/ 2 Test continuity for the following function f(x) = 3 2x -…

A: For a function f(a) to be continuous at x=a :

Q: 4. Given the function, g(x) 3 x 2 a. Determine the possible points of discontinuity. b. Discuss the…

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Q: x²– y² )² Consider the function f (x.y) =| x²+y², Which ONE of the following statements is TRUE? O…

A: We will find limit at (0,0).

Q: f(x) = -2x2-2x+4 is %3D x-1

A: Follow the procedure given below.

Q: 1. Given 2+1 if r1 4 - r (a) Find all possible points of discontinuity. (b) Discuss the continuity…

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Q: Find the value of constants c and d that make the function below continuous at x = 7. Sx² - 3x x 7…

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Q: R Determine the intervals wherein the function is continuous and the values of x wherem there is…

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Q: Consider the function y = g(x) = -x² + 7x + 3. (a) Use the limit definition to compute a formula for…

A: Recall:     g'(x)=limh→0g(x+h)-g(x)h Slope, m=lim∆x→0g(x+∆x)-g(x)∆x Point- slope form is…

Q: 4. f(-5) = 5. Is the function continuous at x = -5? If not, what type of discontinuity occurs? 6.…

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Q: x+6 At what points is the function y = continuous? %3D x- 9x + 18 Describe the set of x-values where…

A: We can find the required answer as below.

Q: 2. If not, indicate Given the function below, determine if the function is continuous at the point I…

A: We need to check continuity of given function.

Q: Q.1 Find all values of x, at which f is continuous and discontinuous. x²-9 f(x) = x-3

A: 1. Given function is, f(x)=x2-9x-3=(x+3)(x-3)(x-3)=x+3 As, the function is a polynomial function and…

Q: x 2) Discuss the continuity of the graph of f(x) given below on the closed interval [-4, 2] D(-4,6)…

A: This question is related to continuity of functions, we will solve it using given information.

Q: (рx* + x — q, 2х + q, x< 2 2 < x < 5 i: x 2 5 For what values of p and q the function f (x) %3D 2рх…

A: function is continuous at every xlimx→2-f(x) = limx→2+f(x)p(2)2+(2)-q = 2(2)+q4p+2-q = 4+q⇒4p-2q-2=0…

Q: f(x) = -x² +9 d the x-values at which f is not continuous. Which of the discontinuities are…

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Q: Determine whether the function is continuous or discontinuous at the given x-value. Examine the…

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Q: Q) Test the continuity of the function f(x): 3 - x X + 1 2Sx <3 3S X< 4 F(x) = 2х —1 X = 4

A: Use limit method

Q: 7. Find all constants a, b that make f continuous at x = 2. (Use limits and definition of…

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Q: f (x): [ 1, if X is rational         [ 0, if X is irrational the function is given.Accordingly the…

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Q: - Consider the graph of the function f below. At each value of z listed below, determine if f is…

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Q: (c) Simplify the function f(x) = |x – 1| + |x + 1|. Test the continuity of this function at x = 1.…

A: From the given information. The function f(x) is as follows.

Q: Consider the function y = g(x) = -x² + 7x + 3. (a) Use the limit definition to compute a formula for…

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Q: fa). 2-メ,/ X<ー1 %3D X4リ -12x <1 fat x =ー1 メ+T メフ-1

A: Given: - The function is, f(x)=2-x, x&lt;-1x2+1, -1≤x≤1x+1, x&gt;-1at x=-1 To discus: - The…

Q: x2 – 9 f(x) %3D x2 – 9x + 18 Determine where f(x) is continuous, algebraically. Enter your answer in…

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Q: Given 2+x if r1 4 – z (a) Find all possible points of discontinuity. (b) Discuss the contimuity of f…

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Q: Determine the continuity of the following functions. Determine continuity, if applicable. the kind 9…

A: To check the continuity of the given functions.

Q: Which of the following is TRUE for all? All functions are continuous at all points in its domain.…

A: Given :   Continous and differentiable functions

Q: -x when x 1 a. Use interval notation to express the interval(s) over which f is continuous. b. Is f…

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Q: re) { V1- x /1 — х х2 — 2 for x 1 а. f (x) : b. f(x) = 2x 3-х

A: Discuss the continuity of the given functions