Suppose that f(x)=βx−3 if x≤2βx+2 if x>2 Find the value of β so that f(x) is continuous everywhere along the real line.

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Q: Find the values of a and b that make f continuous everywhere. x2 4 if x 3 a = b =

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Q: Find the values of m and n that make f(x) continuous over (-∞, ∞): x² 4 x -2 f(x) = { mx² 2 m = n =…

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Q: (-х+а, х < —1 If f(x) = {x² + 5, –1 < x < 2 is continuous then х — b, х 2 2 a + b =?

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Q: of f(x, y, tion of ve

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Q: Suppose that f(x, y) is continuous at (2, 3) and that f(2, y) = y3 for y ≠ 3. What is the value f(2,…

A: Given that f(x, y) is continuous at (2, 3) and that f(2, y) = y3 for y ≠ 3. We have to find the…

Q: Find (f - g)(x) if f(2) = 7x³ – 52² + 42x – 30 and g(z) = 7 O (f · g)(x) = 49zª + 269x² + 150 O (f·…

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Q: Classify the critical point (0,0) for for all - 0 <µ<0. 2 -

A: given system of matrix x'y'=022-μxy     for all -∞&lt;μ&lt;∞ claim- to classify the critical point…

Q: Let f(x, y) = 3x² – x – 3y + 5y2 – 10xy. - - - List the critical point:

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Q: Suppose that | f(z)dz = 2, | f(z)dz = 1, %3D [ 9(2)dz = - 5, | 9(2)dz - 2. Then, | (=) – g(2))dz =

A: Given: ∫25fxdx =2, ∫23fxdx =1, ∫25gxdx =-5, ∫23gxdx =-2 To evaluate:∫35fx-gxdx We know that…

Q: The function y = 1/x does not take on either a maximum or a minimum on the interval 0 &lt; x &lt; 1…

A: Extreme Value Theorem:If a function f(x) is continuous on a closed interval [a,b], then f(x) has…

Q: Find the linear approximation of the function at the given point. f(x y) = 4x²y3 at (-9,7) O A. L(x,…

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Q: Find positive numbers x and y, whose sum is 75, such that xy2 is maximized.

A: Positive numbers x and y,x+y=75xy2 is maximized

Q: 1. Show that the function f(x) = 3x + 2 is continuous at (-2, 3). Is it uniformly continuous?

A: As per our guidelines we are mandated to solve only one question at a time please repost the…

Q: 5. If c is a critical point of F(x), when the is a local maximum or minimum at c? Explain

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Q: Find the area of a triangle bounded by the yy axis, the line f(x)=4−67xf(x)=4-67x, and the line…

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Q: #! Find f'cx) if fex)= Čx²+SX+2)(X-)

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Q: The function passes through the points (0,3) (2,6) (4,4) and (6,1) x = 2 and x = 6 are critical…

A: Given data:     The given points are: (0.3), (2,6), (4,4), and (6,1). The first critical point is:…

Q: what are the critical points of f(x,y) = xye^(x+2y)  (show all steps please)

A: Critical points of a function of two variables f(x,y) occur when  fx=0 and fy=0. Now we have,…

Q: Suppose f is continuous on [1,5] and the only solutions ofthe equation  f(x)  = 6 are x = 1and x= 4…

A: Given: The function f is continuous on 1,5 and fx=6 has only two solution x=1, x=4 and f2=8, To…

Q: Let f be a continuous function with f'(x) = 3x² Of has no relative maxima. 0x=0 0x=2 0x=1 - 6x. At…

A: f be a continuous function with f'x=3x2-6x

Q: f(X)=X3+3x2-6 over closed interval (-2,5) what is the largest critical point?

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Q: Please show steps.

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Q: Find the value of k that makes function continuous at z = 4 | 2x + 8 x> 4 4x k x < 4 f(x) =

A: If the function is continuous at x=4 then the left and right-hand limit at x=4 should match. That…

Q: Find the higher-order deriv f"(x) =6Vx – 4 f(5)(x) =

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Q: Locate and classify all the critical points of the function. (If an answer does not exist, enter…

A: Points at which fx = fy = 0 are called critical points.

Q: . Determine the upper bound on the error in the approximation: x2sinx3 x. - if x|<0.8 6.

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Q: Suppose (0, 2) is a critical point of a function, with continuous second derivatives. In each case,…

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Q: Suppose (0, 2) is a critical point of a function with continuous second derivatives. In each case,…

A: The discriminant of a function, f at x,y is calculated using the formula: D=fxxfyy-fxy2 . If…

Q: Suppose that fis a continuous function and that1. f(x)dx=-1 and L(x)dx = 5, find the value of…

A: suppose that f is continuous function . We have to find the following

Q: Find the values of x, y and z that correspond to the critical point of the function 2 = f(x, y) =…

A: The given function fx,y=4x2+8x+7y+3y2 To find the critical points of the function

Q: Let f(x)=√x. By use of the little o notation justify that the linear approximation to f at x0…

A: Given,           f(x) =x

Q: What are the maximum and minimum values of the function y = | x | on the interval -1 ≤ x &lt; 1?…

A: Use the graphical approach to determine the maximum and minimum values of the function y = | x | on…

Q: Suppose that f(x, y) = yVx³ + 1 on the domain D = {(x, y) | 0 < y <x < 3]

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Q: If 7x-5,x < 1 h(x) 3x2 – x, 1 < x < 3 Is h(x) continuous at (x=1)?

A: Given: hx=7x-5,x&lt;13x2-x,1&lt;x≤3 We know that any given functiony=fx will be continuous at x=a…

Q: what are the nature of the critical points of f(x,y) = xye^(x+2y)  (show all steps please)

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Q: : Find the value of k that makes function continuous at x = 4 %3D 3x + 6 x > 4 f(x) = 6x – k x < 4 -

A: To find: The value of k

Q: let  f(x)=  x+2  if x1 Find the value of k that will make f continuous on (-∞,∞)

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Q: Find the value of K that makes 4-x2 f(x) = {2-x if x # 2 2K if x = 2 continuous at x = 2 ?

A: Find the value of k

Q: [1, 2). over Calculate M6 for f(x) = 3 · In(x³) M6

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Q: Classify all critical points for f (r, y) = 2x2 – y3 – 2ry.

A: Disclaimer: Since you have posted multiple question, we will be answering only first question for…

Q: *show work*

A: Given:A continuous function y = f (x) is known to be negative at x = 4 and positive at x = 9.

Q: Use the First Derivative Test to classify each critical point of f(x) = x^4 − 8x^2 + 3 as a local…

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Q: If F(X) is an antiderivative of *-2 + x-', then what is the value of F(1) - F(-1)?

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Q: Identify the removable discontinuity. f(x) =  x3 + 2x2  over  x + 2

A: Given query is to find identify the removable discontinuity.

Q: Suppose that a function f(x,y) has a critical point at (2,3). Given that fæx (2, 3) = -4, fæy(2,3) =…

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