10 if x < c If f(x) is continuous 10x 35 if x > c - everywhere then: С —

Q: 7. A function f (x) is continuous on the closed interval [2,5] withf (2) = 17 and f(5) = 17. Which…

A: Rolle's theorem

Q: Sx² 1 if if > 2 x f(x) = 5 3 if x < 2 af is differentiable at x = = 2 bf is continuous at x = 2 cf…

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Q: 10 If f is a continuous function and F'(x)=f(x) for all x € R, then x)dx=?

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Q: 3x2 – 1 if x1 Determine c and d so that f is continuous everywhere as indicated in the figure)

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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: 2. Given the function: f(x) 3 x -3 x≤2 2 x² + 1 x > 2 Is f(x) continuous and differentiable at x=2?

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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: Find a constant c such that x² – c2 if x 4 g(x) ={ is continuous everywhere.

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Q: Suppose f' (x) = g (x) (x + 1) (x – 2)´, where g (s) is a continuous function which is always…

A: When f'(x)&gt;0 then function increasing when f'(x)&lt;0 then function decreasing

Q: x< x3 B- If f(x) = Ax? is continuous at x = ; Find A? HIN IN

A: We are given : f(x)=x3       , x&lt;12Ax2     ,x≥12 is continuous at x=12 Condition for f(x) to be…

Q: 9. If f is continuous and 1| f(x)dx = 8, show that f takes on the value 4 at least once on the…

A: We need to show f takes value 4.

Q: 46. Find the values of a and b that make ƒ continuous everywhere. 4 - if x < 2 f(x) = ax? if 2 <x <…

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Q: (-) = { kx + 5 for x 2

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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: Зx2 — 1 Q7- Let f(x){ cx + d Vx + 8 if x 1 Determine e and d so that f is continuous everywhere (as…

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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: (x² + 8, if x4) Consider the function f(x) = Find the value of B such that f (x) is continuous at x…

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Q: If G(x,y) is differentiable with respect to x and y then it is always possible to find the number…

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Q: x2 – 4x + 3 - f(æ) = 5. Let x - 3 How could we define f(3) x = 3? so that J is continuous at

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Q: 3x2 – 1 if x 1 Determine c and d so that f is continuous everywhere

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Q: Зx2 — 1 if x 1 Determine c and d so that f is continuous everywhere

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Q: At what value(s) of x is the function below discontinuous? x+4, if x1 O x=1, only O x=-1, only At…

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Q: (x²-x for x +0 If f(x) : and if fis continuous at x = 0, then k= 2x f(0) = k -1/2 O 1/2 O 1

A: f(x) = (x2 - x)/2x limx→0 x2-x2xlimx→0 x(x-1)2xlimx→0 x-12= -12

Q: 3. Find the value of k that will make f continuous on (-o, 00). NORS x + 19 if x 1

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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: V4+x-2 If f(x) = ,x*0 be continuous at x = 0, then f(0) = 1/2 1/4 3/2

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Q: 4. At what value(s) of x is the function x + 2 x2 for x 1 f(x) = 3- x discontinuous?

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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: If f(2) is a continuous function at a point z, , then f(z) is differentiable at z, . But the…

A: Authoring guidelines:…

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: 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: H.W Ex 2: Determine if the f(x) is continuous at x 3 ? at x-3 f(x) =- x²+2 at x 3

A: Given query is to find f(x) is continuous or not at x = 3.

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: 1(a): Find the value of k that makes function continuous at x = 4 4x +8 > 4 4x – k a <4 f(x) =

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Q: - 35) Prove that if y=flx)is continuoUS and flx1= 0 when x is a rational number, then f Lx)=0 for…

A: The objective is to show f(x) =0 for all x belongs to R.

Q: 2 If f is continuous on [0, 2] and f(x) dx = 5, find the value of | f(æ – 2) dæ.

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Q: S x2 – 3 |kV5+x _if x > –1 if x < -1 - 2. Determine the constant k such that the function f(x) : is…

A: As per our guidelines, I can answer one question and maximum three subparts of a question. Since you…

Q: . Is the function continuous on the interval (4, 10)? (x + 1 if x > 8 f(x) = E) + 7 if x < 8 A.…

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Q: If f is a continuous function and F'(x)=f(x) for all x € R, then - x)dx=?

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Q: (e) If f(x) is continuous at x = 0, then what is the value of n: if 20 if x=0 f(x)=\ 38

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Q: x3 B- If f(x) = ;, Find A? is continuous at x = %3D (Ax² x 2 1/N IN V

A: Given: f(x)=x3x&lt;12Ax2x≥12 Since f(x) is continuous at x=12. limx→12-f(x)=limx→12+f(x)

Q: 4. `s.] Find the number a and b at which f is continuous everywhere? x² -1 if x 2

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Q: 3x? – 1 if x 1 Determine c and d so that f is continuous everywhere (as indicated in the figure) -1

A: Given  f(x)=3x2-1if x&lt;0cx+dif 0≤x1x+8if x&gt;1

Q: D etermine if continuous f(x) = X-2 x² -14 %3D at x=2

A: Here we will check that given function is continuous at x=2 ,

Q: 3. What value of k would make f (x) continuous at x = 3 ? 3.

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Q: Q.4 A/ Prove the function continuous at x = -2, (x2 + 5 13-3x where %3D if x<-2 if x 2-2 f(x) = %3D

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Q: 1 if z 0. Is F(x) is continuous at I = 0? Justify your answer.

A: Given that for x&lt;=0, F(x) = (x - 1)/4 Then as x tends to zero from the negative side of zero, we…

Q: If ƒ(x) is continuous [-00,b]then on ſf(x)dx= lim [ ƒ (x)dx а. a a

A: Explanation of the solution is given below...

Q: Find a constant b such that h is continuous at x = 2, where h(x) = {x + 1 for lxl &lt; 2 b - x 2 for…

A: Given, hx=x+1x&lt;22b-x2x&gt;2