21. Discuss the continuity of: for for 0sx<1 for 1sx<2 f(x)=- for x= 2 for *> 2

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

A: Given that,

Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. x² + 2x…

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Q: Suppose f(x) = - 2x - cosr. (a) Show that f is strictly decreasing on R. (b) Hence, justify that 2x…

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Q: -x²+5 < f (x) < x+1 2

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Q: Suppose the inequality (x² – 4x + 3) < f (x) < cos ( TX *) holds for all values of x. 2 Find lim f(…

A:

Q: Use limits to determine if f(x) = is continuous at z = -2. (z+2)²

A: Given that  f(x)= 1(x+2)2 is continuous at x = -2

Q: Determine the whether the function is continuous at x=-2. Justify your answer 2x+7 if xS-2 using the…

A:

Q: The limit as x approaches infinty of (x+3^x)/(x^2-3^x) Evaulate using L'Hospital's Rule providing a…

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Q: II. Determine if Vx2 – 3x – 4, if x 1. is continuous or not at x = -1 and at x = 1. In the case of…

A:

Q: Express the limit as a definite integral. 4 lim non + (i/n)- (i/n)9

A:

Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

A:

Q: Suppose f is continuous on [1,5] and the only solutions ofthe equation  f(x)  = 6 are x = 1and x= 4…

A: Given: The function f is continuous on 1,5 and fx=6 has only two solution x=1, x=4 and f2=8, To…

Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

A: Given the functionfx=x2+2xx≤14-x1&lt;x&lt;3x-3x≥3we discuss about the discontinuity of the…

Q: (x2 + 3x f(x) = 3 – 6x if x -2 Check the continuity of the function f(x) at x = -2

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Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

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Q: x+4 Which will prove that f(x) = %3D x2+16 is continuous at C= -4? 1. f(-4)=0 II. lim f(x)=0 III.…

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Q: 2. Test continuity at x = 0 and x = 3 for the function (3 + 2x; - 3 3

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Q: Compute the limit as x goes to 0 of [tan(x) - sin(3x)] / (x^2)

A: limx→0[tan(x)-sin(3x)]x2=[tan(0)-sin(3(0))]02=00

Q: If Зх — 2,х <3 -{ - h(x) х4 — 74, х 2 3 Is h(x) continuous at (x=3)? 1 Add file

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Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

A: To check for the continuity of the function fx=x2+2xx≤14-x1&lt;x&lt;3x-3x≥3

Q: How many continuous functions f are there which satisfy (f(x))² = x² for all x?

A:

Q: Use the definition of continuity and the properties of limits to show that the function is…

A: A function is continuous in an interval if is continuous on every point of the interval. Now, a…

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: I'm having trouble understanding the continuity questions, please see the attached screen shot.

A: We find left and right hand limit at x=0.Left hand limit = 1

Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

A:

Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

A: Given the function,fx=x2+2xx≤14-x1&lt;x&lt;3x-3x≥3

Q: 3x if x S -2 3. If f(x) x* - 1 if -2<x<2 = 3 if x 2 2 Discuss continuity at x = 2 and x = -2

A: We have to find the continuity of the given function at x = 2 and x = -2. So, for that, we have to…

Q: 15. Suppose that the functionf:R Ris differentiable at xg. Prove that xf (xo)- xof (x) lim = f(xo) -…

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Q: Check the continuity of the function f(x) at x = -2 f(x) = - 6r + 3x l-6x if xs-2 if x>-2

A: Given,         The function fx at x=-2.           fx=x2+3xif x≤-2x3-6xif x&gt;-2

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

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Q: 29- For uhat values of a and b is ax+2b x+3a-b くXS2 3X-5 Continuous at every X

A: Dear,as per company guidelines we can answer only one question at a time, kindly post other question…

Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x²+2x x≤1…

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Q: Use the definition of continuity and the properties oflimits to show that the function…

A: Consider the given function as fx=x16-x2

Q: Suppose that f(1) = -3, f(4) = -4, f'(1) = -3, f'(4) = -5, and f" is continuous. Find the value of…

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Q: Comment on the continuity of f(x) at x = -2, x = 0 and x = 3 If discontinuous, what is the type of…

A: At x=-2, L.H.L.=limx→-2-fx=2R.H.L.=limx→-2+fx=-1f-2=2 Since L.H.L.≠R.H.L., therefore the limit does…

Q: Define limit of a function g(x) at x = a. 3+2x for -sx<0 for 0sx< |-3-2x for x 2 Given, f(x) = 3-2x…

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Q: 21. Discuss the continuity of : 1 x+ - for x 2 (ans.: discontinuous at x-0,2 ; continuous at x-1)

A: We have to check for the end points.

Q: Find the limit as x approaches zero of f(x)=tan(x)/x

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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: 4. a) Explain using theorems from Section 2.5 why the function is continuous at every number in its…

A: We have to solve given questions.

Q: If 5х + 3,х <2 { h(x) = 2x2 + 5,2 < x < 4 Is h(x) continuous at (x=2)?

A: We use definition of contunity

Q: 9. Discuss the continuity of the function x 2 x2,

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Q: 5. Discuss the continuity of the function x'- 1 f (x) = { 2, **- 1 at x = -1. x+2 2, x=- 1

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Q: 29 - For uhat values of a and b is ax+2b x+3a- b くXS2 3X-5 Continuous at every X ?

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Q: Discuss the continuity of : Q1 x+ for *く0 for osr 2 Q2 1-x lim

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Q: Q4) Show that f(x)=|x x<2 3x -2 x2 2 is continuous at x=2 %3D

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Q: Q. 1: Determine the func- tion is continuous or dis- continuous at x = -1 and x = 1.

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Q: Determine the continuity of the function at the given points. forx =-1 %3D f(x = - 2, for x -1 at x…

A: If function f is continuous at x=a then limx→af(x)= f(a)

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

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.