Determine whether the function of f(x) is continuous at x = -1 x2 -1 f(x) ={ x +1 X + -1 -2 X = -1

Q: Determine whether function is continuous and/or differentiable at x = 1. f (x) = 1/x

A: Consider the given function fx=1x

Q: Determine the value of x of the continuous function: * (x – 1 x 3 f(x) = {3x – 3 Зх — (-4x + 3

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Q: Find the local maximum and local minimum values of f using both the first and Second derivative…

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Q: Differentiate the function.      f(x)  =        ______1______                            In x

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Q: Find the critical point for f and then use the second derivative test to decide whether the critical…

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Q: Find the constant a such that the function is continuous on the entire real line. [ 5x², x 2 1 x < 1…

A: The given function is: f(x)=5x2   ,   x≥1ax-3,  x&lt;1 To find constant 'a' such that the function…

Q: Let f(x) = 2x2 + x. Determine f'(1) using the definition of the derivative as a limit.

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Q: Discuss the continuity of the function on the closed interval.

A: Given: f(x)=x2-1x+1 The function is continuous at a point if the function returns a unique value…

Q: Determine the values of a and b such that the function (x -a ,x 1 Is continuous of all values of x.

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Q: Find the value of the constant (a, b, or c) that makes the function continuous.

A: A function fx is continuous at x=a if its left-hand limit, right-hand limit, and fa are equal and…

Q: Consider the piecewise function: |x- 1| x² – 1' x <1 f(x) = (Ax² + 6, x 2 1 For what real number A…

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Q: Determine the values of the constants a and b which make the function f(x) below continuous at x =…

A: A function f(x) is continous at x = a when:

Q: Determine the open intervals where the function f(x)= xe^x is increasing and where it is decreasing.

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Q: Determine if the function is continuous at the given point. Sx³ x 2) f(x) = at x = 2.

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Q: Determine the domain of the function and prove that it is continuous on its domain f(x) = x2 / (x +…

A: fx=x2x+x14 The domain is the set of all values of x for which denominator is non-zero. That is,…

Q: Determine the domain of the function and prove that it is continuous on its domain f(x) = e - x 2

A: Consider the given function. fx=e-x2 The function is define for every real value of x. Hence,…

Q: Is the function f(x)= x+|x|-1 differentiable at x=0.

A: Consider the given function:

Q: f(x): at x = 3 X-3 f(x) = at x = 0 f(x)%3D%x6 at x - 0

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Q: Is the function continuous  f(x) = e^x / 1 - e^x

A: We need to check the continuity of the function

Q: Is the function given by g(x) = x²-3x continuous at x = 4? Why or why not?

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Q: 3. f(x) = v2x – 5 at x = 3 -

A: (3) Given function is fx=2x−5 We have check whether the function fx is continuous or not at x=3 For…

Q: Consider a function f(x) = |x – 3|. a. Show that f (x) is not differentiable at 3. -

A: Given         f(x) =|x-3|

Q: Determine the domain of the function and prove that it is continuous on its domain f(x) = √(x2+9)

A: Solution:Given     f(x)=x2+9To find the domain of the function  and to prove f is continous on its…

Q: f(x) = Vx-3

A: Given function is fx=x-3.

Q: The interval over which the function f(x) = becomes continuous is %3D x+8 (-3, 0) (-3, 3) (-00,…

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Q: Let a be a real valued constant. Find f' (x) = limħ→0 f(x+h)-f(æ) for f (x) = Vax h

A: Given, α be a real valued constant.  fx =αx  We have to find f'x = limh→0fx+h-fxh

Q: Let f(x) be a polynomial and g(x) = f '(x) be its derivative. If the degree of (f(x) + f(-x)) is 10,…

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Q: Is the function given by f(x)=x^2+3x/2x-1 continuous over its domain?

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Q: Determine if the given function is continuous at a given value of x. 2. f(x) = x² - 4x – 2 at x = 1…

A: Since you have posted multiple questions i can do first three subparts as per our company guidelines…

Q: Determine where the function F(x)=8x/x2+4 is continuous. The function is continuous on ?

A: Suppose   are continuous function at then rational function is continuous at   if .

Q: x +1 x 2

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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: Let 'f be a continuously differentiable real valued function defined bx+a x<1 by f(x) = 5x² Then the…

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Q: Examine whether or not the function (4-x² f (x) =- [4+x if x0 Is continuous at x = 0

A: Check whether limx→0f(x) = limx→0(4-x2) and limx→0(4+x), if both sides are equal then it is…

Q: Determine whether the function f(x) = (2x + 1)/(2x2 - x - 1) is continuous: a) at 2; b) at 1.

A: It is given that, fx=2x+12x2-x-1We have to find that the function is continuous at   a 2 and b 1

Q: Determine the value of x of the continuous function: * х — 1 f(x) = {3x – 3 (-4x + 3 x 3

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Q: Show that f(x)= |x| is not differentiable at x = 0.

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Q: Determine if the function is continuous or discontinuous at x=2. h(x) = x - 1, if x 22 2x- 1, if x<2…

A: if Left hand limit and right hand limit are equal then function is…

Q: Find the intervals on which the function is continuous. f (x) = { %3D 3, x = 2

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Q: Let f(x) х — In (x +x |1. Find f'(x). x2 = x sec-1

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Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests.…

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Q: Show that the function f(x) = 1 – I - x² is continuous on the interval [-1, 1].

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Q: determine whether the piecewise-defined function is differentiable at x = 0.

A: to determine if the function is differentiable we have to check if it's differentiation is equal…

Q: Redefine the function f to make it continuous at x = 0. -8x + 36 + x (х — 4) ; x + 0,4 f(x) = 4; x =…

A: Consider the condition for continuity.

Q: Find the constant a such that the function is continuous on the entire real line. (9x², Flx) = {9x?,…

A: Given function is : fx=9x2    ,      x≥1ax-6   ,    x&lt;1 Here given that function is continuous…

Q: Explain why f(x)=3x^2+1 is continuous at x=-2

A: Consider the function  f(x)=3x2+1

Q: Find the constant a such that the function is continuous on the entire real line. 5x², ах — 7, f(x)…

A: For a function to be continuous, the value of the left and right limits at critical point needs to…

Q: Determine if the function is continuous at the given point. 1 f(x) = {* - (x2 – 2 x 0 at x = 0.

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Q: Find the value of a which makes the function below continuous on (-∞, ∞). f(t) = [a(x²/2) x < 1…

A: We will use the definition of continuity to solve this question.