For what values of a and b will f(x) be continuous on everywhere at x = 2 if the function is x2 -4 x< 2 x - 2 ax? - bx +3 f(x) = 25x<3 2x - a + b x 2 3

Q: For what value of the constant c is the function f continuous on (−∞, ∞)? f(x) =    cx2 + 6x…

A: fx=cx2+6x     if x&lt;3x3-cx       if x≥3 fx is continuous for all x&lt;3 &amp; x&gt;3, because it…

Q: For what values of a and b will f(x) be continuous on everywhere at x = 2 if the function is x2 – 4…

A: Given f(x) = x2-4x-2x&lt;2ax2-bx+32≤x&lt;32x-a+bx≥3 It is continuous if and only if limx→2-f(x) =…

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: For what values of a and b will f(x) be continuous on everywhere at x = 2 if the function is x² – 4…

A: f(x)=x2-4x-2x&lt;2ax2-bx+32≤x&lt;32x-a+bx≥3

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: For what values of a and b is -2, f(x) = { ax – b, -1 <x< 1 3, continuous at every x?

A: Given: fx=-2,    x≤-1ax-b,    -1&lt;x&lt;13,   x≥1

Q: For what values of a and b is ax + 2b, g(x) = {x + 3a - b, 0 2 continuous at every x?

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Q: Find c so that f is continuous at every point f(x) = 5x+12c, if x < -5 f(x) = (cx^2)+1, if x ≥ -5

A: Given- fx=5x+12c if x&lt;-5cx2+1   if x≥-5 To find- The value of c that  the above function is…

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: 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: Find the value of k so that the function ( 5x +3 if x<3 f(x) = | kx² is continuous everywhere? if x…

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Q: if x3 is continuous at x = 3

A: Given query is to find the value of c so that function is continuous at x = 3.

Q: Given f(x) is a continuous function. If f( – 5) = 1 and f'(x) > 4 for – 5 <x < 2, what is the…

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Q: For all but two choices of a, the function (x) = x if xS a and x' ifx > a will be discontinuous at…

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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: The value of k that makes x2 – kx + 2x – 2k f(x) x # -2 x + 2 4, continuous at x = -2 is x = -2 O 2…

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Q: 7. For what value of the constants A and B is the function f continuous on (-0o, 0)E AV-x+6-1 for x…

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Q: Find a value of the constant k, if possible, at which ( kx² f(x) = 3 -2x +k x> -2 x<-2 is continuous…

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Q: 2. Supposethat f(x)=?βx? −3 if βx + 2 ifx≤2 x &gt; 2Find the value of β so that f(x) is continuous…

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Q: For what values of a and b is -2, xS-1 f(x) = ax - b, -1 <x<1 3, continuous at every x?

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Q: For what value of the constant c is the function f continuous on (-, o)? cx2 + 8x if x 3 C =

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Q: find constants a and b such that f(2) +3 = f(0) and f is continuouspiecewise f(x) = ax + b , if…

A: We have been given a piecewise function and a condition f(2)+3=f(0) and the fact that f(x) is…

Q: -2 x< -1 Q1)a) For what values of a and b is g(x) = ах — b -1<x<1, x21 Continuous at x= -1

A: The suitable formula for continious       LEFT HAND LIMIT = RIGHT HAND LIMIT

Q: For what values of a and b is ах + 2b, x² + 3a – b, Зх — 5, 0 2 |continuous at every x?

A: Given:

Q: 4 If f(x) = x 2 - function for all real values of x, then f(8) is equal to

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Q: if x3. then h(x)is continuous at if x = 3 (b) (0,4) x-3 - Let h(x) =32x + 1 (a) 3 (c) (-0, 3) (d)…

A: As we know that a function is said to be continuous at a point x=a when…

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: 3x if x 2

A: Given that a function of f(x) and we find value of k. We know that if a function is continuous at x=…

Q: the following function is a continuous function at x=2 امرفق x² +x-6 x+ 2 x) = x2 - 4 x = 2

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Q: Suppose that f(x) = SBx? – 3 if if (Bx+2 x> 2 Find the value of B so that f(x) is continuous…

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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: Find values of the constants k and m, if possible, that will make the function f continuous…

A: If f is continuous at x=a then limx→a-fx=limx→a+fx=fa . Assume , f is continuous every where to find…

Q: For what values of a and b is the following function continuous at every x - 3 XS - 1 f(x) = { ax -…

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

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

Q: For what value of the constant c is the function f(x) continuous at x = 1 Seter-2, | In (x) + 6, if…

A: We will use concept of left hand limit and right hand limit in this problem.

Q: if x1 O No, since g(x) is undefined at x=1. O Yes, and g'(1)=3. O Yes, and g'(1)=8. O No, since g(x)…

A: Given

Q: -2 x<-1 Q1)a) For what values of a and b is g(x) = |ax - b - 1<x< 1, 3 x21 Continuous at x=1

A: From  the given problem:   gx=-2x≤-1ax-b-1≤x&lt;13x≥1     As we know that a function f(x) is…

Q: 1+ cx, if x 2 Given the function: f(x) = C - x, What should be the value of c so thatf is…

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Q: If f(x) = a #0 and f is continuous, the value of k is 2x k x = 0 o 1 o 1 2 1/2

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Q: (b) Suppose that f(x) = ൜βx2 − 3    if x ≤ 2βx + 2      if x &gt; 2 Find the value of β so that f(x)…

A: For continuity, left hand limit=right hand limit=f(x)

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 a value of the constant k, if possible, at which kx2 f(x) = x+k x> -7 is continuous everywhere.…

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Q: Then the value of k for which f(x) is continuous for all real values of r is

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Q: a) Suppose that f(x) = 4x if x<-1 = cx + d if – 1<x< 2 = -5x if x 2 2 Find values of c and d such…

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Q: (b) Suppose that f(x) =  βx2 − 3            if x ≤ 2 βx + 2             if x > 2 Find the value of β…

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Q: ⎪ ⎨ ⎪ ⎧x^2 − 1 , − 1 ≤ x < 0 2x , 0 < x < 1 1 , x = 1 −2x + 4 , 1 < x < 2 0 , 2 < x < 3 a) Is f…

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Q: For what values of h and k is h+2x , 15 x52 -2 < x<-1 2< * 2 - Continuous at every x ? 2x2 - 2x-4,…

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Q: Where is the function f(x) below discontinuous? if z 2 Choose all answers that apply. f(x) is…

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

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.