Let f be given by x² – 4 if x < 2 2 f (x) = ax² – bx + 3 if 2 < x < 3 if x > 3 - 2х — а +b Determine the values of a and b that make ƒ continuous everywhere.

Q: Find c such that the function 10 г c - || 26 х > с is continuous everywhere. c =

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Q: B) Test the functions continuity at the given poihts: (x²-x-6 1) f(x) 3D x * 3 ,at x 3, x 5 X-3 x =…

A: f(x)=x2-x-6x-3x≠35x=3

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: Let f(x)= x2 − 6. Prove that the root of this function is equal to √6 {correct to 2 dp}, and lays…

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Q: Find conditions on a and b that ensure f (x) = x3 + ax + b is increasing on (−∞,∞).

A: Consider the given function as fx=x3+ax+b

Q: Suppose that f(x) = βx2 − 3     if x ≤ 2                                βx + 2       if x &gt; 2…

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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 the constant a such that the function is continuous on the entire real line. Ssin x g(x) = if x…

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Q: 1) Find the values of a and b that make f continuous everywhere. x' - if x<2 х—2 f (x) = { ax? –…

A: NOTE: Refresh your page if you can't see any equations. . the function is continuous everywhere  so…

Q: Which is the correct conclusion about the function h(x) ={V4- x2 if x - 3 if h has a removable…

A: Given function is: hx=-x-2    ;  if x&lt;-24-x2     ;  if -2≤x&lt;2x-3  ;  if x&gt;2 We have to…

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: 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: Find the constant a such that the function is continuous on the entire real line. 4sin x if x < 0…

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Q: Consider the following function: - 4 if x 3 Find the values of a and b that make f continuous…

A: The function is continuous every where, if it is continuous at each point in the domain. The…

Q: c. Consider the compound function: 2|x| for h(x) V(5 +x) - V5 for 0<x<5 %3D (Vx -5)2-25 (x2 - 25)…

A: Given,  h(x)=2|x|                             for  x≤05+x-5(x-5)2-25         for     0 &lt;x…

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: Find the values of k that make the function continuous. k2 – 22x, x > 11 - f (æ) = kæ, x < 11

A: to find the values of k the function is to be continuous for x=11 value of k is 22 or -11.

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: Let f (x) = 2x3 – 0.0064x? – 1.5x + la (a) Indicate that f(x) = 0 has a root in the interval [-3, 0]…

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Q: Suppose that the function f: [0, 1]  in R is continuous and thatf (x)&gt;= 2     if 0 &lt;= x &lt;…

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Q: , for x 1 Let f(x) be a function de fined by f(x)3= Discuss the contuniuty of f andf".

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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: S(x) = 7x* – 1x* +2. | Use interval notation to indicate where f is continuous. Domain of…

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Q: Let f(x) = { if x - 4 m= mx 6 - If f(x) is a function which is continuous everywhere, then we must…

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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 x23

A: we have to find the value of k where f(x) is continuous everywhere  Also find the domain in the next…

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: Find the values of a and b that make f(x) continuous for all real numbers. (x+2, f(x) = { ax³, (x² +…

A: Given that f is a continuous function, then it is continuous at all the point. So, the function is…

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

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Q: Let f be the function (8x-1 for x х Find the values of a and b that make the function continuous.

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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: Q2/B/ check the function continuity at x-0, for the fimction f(x)%= 1+ 4 2/3

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Q: 3. Apply the three conditions of continuity to determine if the function f(x) = 2x²+5x+2 x²-x-12 is…

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Q: Find the values of a and b that make f(x) continuous for all real numbers. (x+ 2, f(x) = { ax³, (x²…

A: f(x)=x+2,x≤-1ax3,-1&lt;x≤1x2+bx,x&gt;1

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: 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: Let f(x)= {x^2-8x+16, if x≤3/ax+b if x>3 Find a and b such that the function f(x) is differentiable…

A: Given fx=x2-8x+16x≤3ax+bx&gt;3 is differentiable everywhere so it is also continuous.

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

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Q: Find the values of a and b such that the following function f(x) = 2a cos(x + 1) - b.5x+2, if x -1,

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Q: Find the constant a, such that the function is continuous on the entire real line. ( 2x², f(x) = if…

A: Given the function is f(x) = 2x2,if  x≥1ax-1,if  x&lt;1

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

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Q: Consider the function f with domain (-2, 0): 3|a2 – 1| if – 2 < x < 1 2x2 + 2x – 4 f(x) = 3 if x = 1…

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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: (-x3 – 4x + 20 ,x > 3 2 – 7x , x < 3 Determine whether the function f(x) = is continuous at x = 3.…

A: From the given problem: fx=-x3-4x+20 , x&gt;32-7x , x≤3 As we know that:  If limx→a+fx=limx→a-fx=fa…

Q: , for x 1 Let f(x) be a function defined by f(x)=- Discuss the contuniuty of f and f'.

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Q: Find the values of a and b that make f continuous everywhere. x2 - 4 if x < 2 X - 2 f(x) if 2 s x <…

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Q: Let f(x)={4x−4 if x≤6               {−5x+b if x>6 If f(x) is a function which is continuous…

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Q: Find c such that the function x c is continuous everywhere. x² – 8 f(x) = {

A: ANSWER : c = 5

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.