Define g(2) for the given function so that it is continuous at x = 2. 2x2 - 8 g(x) = 2х—4 Define g(2) as (Simplify your answer.)

Q: Find c such that the function x2 – 9 x с is continuous everywhere. - С —

A: f(x) will be continuous at x=c. when value of the function at c , left hand limit of f(x) at c  and…

Q: Determine if the following functions are continuous at the given value of x. 1. f(x) = 3x² + 2x + 1…

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

Q: Determine the domain of the function and prove that it is continuous on its domain using Theorems…

A: Given: f(x) = ln (9 - x 2) To determine: The domain of the function and prove that it is continuous…

Q: Find the value of the constant k so that f(x) is continuous for all real values of x where f(x) is…

A: Solution

Q: suppose f is a continuously differentiable function satisfying f(3)=6, and f'(3)=5. Find (f^-1)'(6)

A: Given f(3)=6, f'(3)=5  To find f-1'6 By the formula, f-1'x=1f'f-1x And we know that if f(a)=b then…

Q: The graph of the continuous function g, the derivative of the function f, is shown above. The…

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Q: 1) Find the value of C that make the function continuous at x-1? x 1 -

A: We have given piecewise function  Function is continuous at x=1 if  f1+=f1=f1- f(x) = C-x        if…

Q: Determine whether the following function is continuous at the given point 1 = 2x+11x f(z) = 2x 13

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Q: If f is continuous and ∫31 f (x) dx = 8 , show that f takes on the value 4 at least once on the…

A: Given that f is continuous and ∫31 f (x) dx = 8. We have to prove that, f takes on the value 4 at…

Q: Find c such that the function f(エ) 8x- 20 I > C is continuous everywhere.

A: NOTE: Refresh your page if you can't see any equations. . find the left-hand limit of the function…

Q: [2-x², x20 Given f(x) = , find the value c so that f(x) will be continuous at all values. x<0 x +C

A: Given that: f(x)=2-x2,    x≥0x+c,      x&lt;0   NOTE: As per our answering guidelines, we can only…

Q: Is the function a. EVEN h ODD f(x) 1, -π<x<0 1, 0≤x<T

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Q: Find the value of the constant a that makes the following function continuous on (−∞,∞).   f(x)=…

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Q: (a) Find the values of α and β such that the function f(x) = ( α cos x + 2 if x < 0 βe3x + αx2 if x…

A: Consider the given piecewise function

Q: For what value of b, f(x) is continuous at every x? (a²x-2a f(x) = (12 x2 2 x< 2

A: As f(x) has two parts and both parts are continuous in given x so make continuous only at point x= 2

Q: - Is the function given by G(x) = Why or why not? continuous at x = 0?

A: We know that function is continuous only if its left hand and right hand limit equal, That is ,…

Q: Find a value of a so that f is continuous at c = -3, or indicate this is impossible. x+3 x -3 f(x) =…

A: Given the function   f(x) = x+3-5x+3,  x≠-3a,                 x =-3   We need to find the value a…

Q: 8. Suppose that f is a continuous function such that f'(x) > 0 for all æ, f(0) = 0, and f(1) = 1. If…

A: f'(x)&gt;0 for all x, f(0)=0 and f(1)=1.To Find: If ∫01f(x)dx=13, find the value of ∫01f-1(x)dx.

Q: Find the constant a such that the function is continuous on the entire real line. S 8x², f(x) ax -…

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Q: A. Consider the function defined by [x² +1, if x<5 f (x)={ |6x– 4, if x25 a. Is f continuous at x =…

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Q: Determine the status of the function f(x) x² + 1'* € (-0, co0). strictly increasing O

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Let f(x)=x²+x. Compute f'(2) using the definition of the derivative, f(a+h)= f(a) f'(a)= lim h 0 h

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Q: 1. Determine whether the following functions are continuous at the given point. a) f(x) = 1 ; а — 3…

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Q: 12.x + 5x2 + 1 11. Determine the horizontal asymptotes of f(x): V16.x6 +6 1 12. Use the definition…

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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: If f is continuousand ∫31f(x) dx=8, show that f takes on the value 4 at least once on the interval…

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Q: Use the limit formula for the derivative of a function at a point to find f'(-3) for f(r) = 2r2 – r.

A: use limit definition to find the value of derivative.

Q: For all but two choices of a, the function (x) x if x a will be discontinuous at the point x = a.…

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Q: Let f(x)=4x^2-2x-2 find the following: 1) f(x+h)= 2) (f(x+h)-f(x))= 3) lim h→0 (f(x+h)−f(x))/h 4)…

A: We have to find 1) f(x+h)=2) (f(x+h)-f(x))=3) lim h→0 (f(x+h)−f(x))/h4) Find the equation of the…

Q: f(x) = Vx-3

A: Given function is fx=x-3.

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: Find the value of a such that the function S(«) = {** -1, x < 3 x 2 3 | f(x) = 2ах, is continuous at…

A: Given:      f(x) = x2 - 1  , x &lt; 3     f(x) = 2ax  ,   x ≥ 3

Q: 35. Given that f(z) is a continuous even function, then A 0 D

A: We will use the definition of an even function and properties of definite integrals to find the…

Q: Suppose f and g are differentiable functions on R such that, (x²+1)f (x) + 3xf(x) = e*2 + 7x and…

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Q: Use the definition of f'(x)=lim/(*+h)-J (x) to find the derivatives of h (а) h0 f(x)=x²-x+2.

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Q: The function f(x)=/25-x' is contionous on

A: It is continuous function.

Q: Suppose that f(x) is a differentiable function such that f(8)=5 and f(8)=0. If g(x)=sin(f(x)), then…

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Q: Find the values of a and b such that the following function a² cos(x − 2) — 26(³-x), if x 2, is…

A: Topic = Limits

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

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Q: Suppose that a continuous function g satisfies: | g(x)dx = 12 and g(2x)dx = 27. Find æg(3x²)dx.

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Q: Is the following statement correct? If the function f is continuous at x=1, then the constant a…

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Q: If a function f is continuous at 0, show that g(x) = xf(x) is differentiable at 0 and find the value…

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Q: Suppose that a continuous function g satisfies: g(x)dx = 42 and | g(2x)dx = 12. 2 | #g(3x²)dx. Find

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Q: 6. Determine the value of the constant a for which the function g(x) is continuous at x = 1 x* + 5x…

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Q: a) Find the values of α and β such that the function f(x) = ( α cos x + 2 if x < 0 βe3x + αx2 if x…

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Q: Consider the piecewise-defined function Ax if x 0 h(x) е (a) Give values for A and B so that h(x)…

A: Given Data: Function: hx=Axif x≤0e-1/x+Bif x&gt;0 (a) The condition for the continuous function is,…

Q: For what value of a is the function continuous at every x?

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