(a). Find the values of a and b that make ƒ continuous everywhere. if x<2 x-2 S(x)={ar - bx +3 if 25x<3. |2x-a+b if x23

Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A: If f(x) is symmetric about the origin then f(x) is an odd function.

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: 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: For what value of b, f(x) is continuous at every x? (a²x-2a f(x) = (12 x2 2 x< 2

A: As f(x) has two parts and both parts are continuous in given x so make continuous only at point x= 2

Q: Find numbers a and b, or k, so that f is continuous at every point. x2, ifx s5 f(x) = kx, ifx>5

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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: If f(x) is an even, continuous function for which = 4 and dx = 4, then f (x) dx 3 2

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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: (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: Suppose that f(1) = 1, f(4) = 6, f (1) = 7, f '(4) = 5, and f " is continuous. Find the value of xf…

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Q: If f is continuous on [a, b], then the horizontal line y = k for every k between f (a) and f (b)…

A: If function 'f'  is continuous on closed interval [a, b], and if f(a)≠ f(b), then for any number k…

Q: 4 Suppose that f(1) = 9, f(4) = -7, f'(1) = 6, f'(4) = -1, and f" is continuous. Find the value of…

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

A: Continuity of function at a Point : Suppose a function f:A→B where A,B⊆ℝ .Then f is continuous at…

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: 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: 35. Given that f(z) is a continuous even function, then A 0 B D

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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: x² – 16 f (x) = x( x 2(х — 1)°(х — 2) : о 1)8 (x – 2) : 0 - -

A: If the given function is equal at LHL and RHL at x=3 then the given function is continuous at x

Q: Sßx² – 3 (Вх + 2 if (b) Suppose that f(x) if Find the value of ß so that f(x) is continuous…

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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: 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: 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: 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: 4ex +x-k if x 0 be continuous everywhere?

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Q: Find number k, so that f is continuous at every point. tan kx f(x) = x 4x+3 k2, x 20 O O and= Cannot…

A: The function is given by fx = tankxx ,x&lt;04x+3k2 ,x≥0 To evaluate : The value of k so that f is…

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

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Q: 2. Find the values of the constants a and b for whichf is continuous everywhere if ax + b, f(x) =…

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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…

A:

Q: Graph h and describe the discontinuity: for x 0 Is h left- or right-continuous?

A:

Q: A continuous function y f(x) is known to be negative at x = 2 and positive at x=7. Why does the…

A: Given that f(x) is a continuous function.

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: - 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: 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: 2x, ifx BDU G EDU y = 5, if x= 3 if x = 3 (x-5, if x 3

A: Given:   y=2xif x&lt;35if x=3x-5if x&gt;3 To prove whether y is continuous or not x=3. Solution: A…

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: Suppose that  f(1) = 4, f(4) = 5, f '(1) = 6, f '(4) = 5, and f ''  is continuous. Find the value of…

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Q: Suppose that a continuous function g satisfies: | g(x)dx = 12 and g(2x)dx = 27. Find æg(3x²)dx.

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Q: 1. If f:(0, 3) → R is continuous, must its range be an open (possibly infinite) interval?

A: Given statement is : If f:(0, 3) → R is continuous, must its range be an open (possibly infinite)…

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

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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: Suppose that a continuous function g satisfies: g(x)dx = 42 and | g(2x)dx = 12. 2 | #g(3x²)dx. Find

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Q: 2. Find the (exact) values of a and b so that f is continuous at a = 2. 8r2 + 20x + 28 if x 2

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Q: EDU 2x, ifx 3

A: A function, f(x) is continuous at x=c if limx→cf(x)=limx→c-f(x)=limx→c+f(x).  The limit of y at x=3…

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: There is an infinite discontinuity at x = 0 and f(0)=-2

A:

Q: Find values ofa and b that make B(x) both continuous and differentiable at x = 2: ax? B(x) ={ 6x + b…

A:

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.