(b) Suppose that f(x) : УBx2 — 3 (Bx +2 if if x< 2 x > 2 Find the value of ß so that f(x) is continuous everywhere along the real line.

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Given: fx=2x−1x2+3x2+1, and gx=x2+872−3x25 To check whether: f'x=4x2x2−1+2xx2+3−2xx2+12x2−1x2+3x2+1,…

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A: We have to find the linearization L(x) of the function at a.  We have, f(x)=9x and a = 3

Q: 5) f(x) = x³ – x² + 1 B) Removable discontinuity at: x =-1 Essential discontinuity at: x = 1 A)…

A: As per our guideline we are allowed to answer only one question. Kindly repost the other question as…

Q: For the continuous function f(x), if f’(-4) does not exist, then x=-4 is a critical point.

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Q: Show that the function f(x) = e¯*/2 has inflection points x = f1. at

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Q: For what value(s) of x is the function f(x) = } 2x + 4 (x² +x +1 if – 2 sxs1 if x>1 NOT continuous?

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Q: is continuous or discontinuous at x = -4 using the three step continuit x + 6 x -4

A: We have to check continuity  of function

Q: 2. Find all values k that make this function continuous at x = 3. Зх — 9 - if x > 3 f(x) = x² – 3x…

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Q: The f(x) 6x2 -5x-4 2x2 +x is discontinuous %3D at x = -1/2. By redefine = w , then f will be…

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Q: Show that g(x) = x|x| has an inflection point at x = 0, but gʻ"(0)

A: given function g(x) = xx

Q: on f(x, y) = 3x + 9y subject to th %3D

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Q: If y = f(x) is an odd differentiable function defined on (-o, 0) such that %3D f'(3) = -2 then…

A: A function f(x) is said to be even if f(-x) = f(x) And odd if f(-x) = -f(x)

Q: Find the value a that will make f(x)={2x^2-7x+3/x-3  if x is not equal to 3…

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Q: Is f(x) = -3 A. Yes B. Does Not Exist continuous at x = 3? C. No D. Cannot be determined

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Q: The function f(x)=(x)/(x-1) is discontinous at x=1 because

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Q: Find the linearization L(x)  of the function f(x) = x^4 -2x^2+3  at  x =0.

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

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Q: (b) Suppose that f(x) = SBx? – 3 if if xS2 (Bx+ 2 %3D Find the value of ß so that f(x) is continuous…

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Q: Find c such that the function Sx2 – 4 - 4 x c is continuous everywhere. c =

A: Here, the given function is: f(x)=x2-4, if x≤c10x-29, if x&gt;c To find the value of c such that the…

Q: Suppose that f and g are discontinuous at x = c. Does it follow that f + g is discontinuous at x =…

A: Let us define that Then both f and g are discontinuous at x=2

Q: -Q3/As the function f(x,y) = at (-1,2) xy 1 + x² + y² is Continuous

A: Here we have to check the continuity of the function at the given point.

Q: 2) Consider the piecewise function: |x – 1| x² – 1' x 1 For what real number A is the function…

A: A function f(x) is continuous at x=a if the left-hand limit and the right-hand limit of the function…

Q: Show that f(x) = 2a + 3b is continuous, where a and b are constants

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Q: Let f(x)=(7+3x)4   f(x) has one critical value at A =

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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 =…

A: f(x)=x2-x-1if x&lt;13x3-4if x&gt;11if x=1

Q: For what value of a is x² -1, x< 3 f(x) 2ax, x2 3 continuous at every x?

A: Given function is Since, f(x) is continuous at every x, so f(x) is continuous at x=3.

Q: Find the constant c that makes g continuous on (-0;0) x-2x-8 g(x) = a+1 if x+2 if X=-2

A: Continuity of a function at a point x=c : If function is defined at x=c and limx→c fx=fc then we can…

Q: Consider the function xe* if x < 0 g(x) = x³ – 2x2 + x if 0 < x < c , %3D if x 2 c where c is a…

A: Given,gx = xex                            if x≤0x3 - 2x2 + x          if 0&lt;x&lt;c1x…

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: 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: for the funciton f(x) = x^3 - 75x Its local maximum  is____, which occurs at _____> Its local…

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Q: Suppose that ƒ(x) = x2 and g(x) = | x | . Then thecompositions( ƒ ∘ g)(x) = | x | 2 = x2 and (g ∘…

A: Given: The composite of the two functions are given as,

Q: Determine f such that f′′(x) = 12x − 1 and 1 is both a critical number and a y- intercept of f

A: Given:  and 1 is both critical number and y-intercept.

Q: B. Determine whether f(x) (x - 3) (2x + 1) (x + 4) is continuous at x= 3.

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Q: 4x-8 i- -2 x +3a

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Q: Investigate the continuity of the function at x=3. S-2x +4 if x23 f(x)x-1 fx<3 At x3

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Q: x² -2, x#-2 2. f(x)= 4,x=-2 a. Removable discontinuity at x = 1; Essential discontinuity at x = 1 b.…

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Q: Use the linearization of f(x) 1 at x = 4 to approximate f(4.3) . - f(x) =

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Q: Find a value of the constant k, if possible, that will make the function continuous everywhere. (kx…

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Q: The function f(x, y) -{¹. - x² - y², 0, if if x² + y² 1 , is continuous

A: Given function is fx,y=1−x2−y2, if x2+y2≤10,             if x2+y2&gt;1. We have to check whether the…

Q: Which values of C makes r(x) (a) left-continuous, (b) right-continuous (c) continuous x2 +3 for x 2

A: If the function r(x) is left-continuous, then use limx→-1-rx=limx→-1+rx, to determine the value of…

Q: Find m so that f(x) is continuous at x = 2. x +4 if x 2 -

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Q: For every continuous f:[0,+0) →R _function , if a>0 2fx'f(x*)dx =[ xf(x)dx Demonstrate that this…

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Q: Examine whether or not the function fx' - 2r +1 ifxs 2 S (x)= x'-2r +1 [3x-2 if x>2 Is continuous at…

A: Given function, fx=x3-2x+1,     if x≤23x-2,            if x&gt;2 To find the continuity of the…

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Using the product rule of natural logarithm, it can be written that ln(ab)=ln(a)+ln(b) . Using the…

Q: (b) FIND the value of c, so that f(x) = {cx – 1, x< 0 lx² – 1. x 2 0 is continuous everywhere.

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Q: .For what values of a is Jaax - 2a, x z 2 f(x) 12, x < 2 continuous at every x?

A: Here given function  Since,  it is continuous for every x thus it Is also continuous for x=2