This question will get you to prove that f(x) = x¹ is continuous at x = 1. (a) Assuming 0 0, find a 6> 0 such that |x-1|< d implies |2³ - 1| < £. (Hint: you can assume d < 1, to derive a simpler estimate)

Q: - Let 3x² + 1 13 10x - 7 ermine if f(x) is continuous at x = 2 by computing limit: f(x) = x 2

A: Given query is to find function is continuous or not on x = 2.

Q: s] B1(a): Find the value of k that makes function continuous at x = 4 x > 4 6x – k x < 4 3x + 6 f(x)…

A: The given function is fx=3x+6if x&gt;46x-kif x≤4. Assume that the above function is continuous at…

Q: (2x+1 x² +2 x> h) Xsh Q3) If the function f(x) %3D having limit at x h. Find the value of h.

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Q: 5.) Ms. Cyrus has 64 songs on her phone. Two- fifths of the songs are R&B songs. The rest are jazz.…

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Q: (12|+ 3, if xs-3 Let f(x) ={ -2r, if -3 <x < 3 6r +2, if x2 3. Show that f(x) is continuous at x =…

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Q: 9. Find the value of a so that the function g(x) is continuous at x = 0 where g(x) = { = 1 2xe3x 1…

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Q: . For which x value(s) is f(x) = 1 + x x² + 2 continuous? Explain why.

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Q: 2. Find all values k that make this function continuous at x = 3. Зх — 9 - if x > 3 f(x) = x² – 3x…

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Q: 4. Find the value of the constant b for which f is continuous at a = - -1 and determine f(-1). 5 x <…

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Q: 2 2. Is f(x) = { = { x²-1 x+1 if x = -1 if x −1 continuous at x = −1? (Show your work using limits.)

A: See this solution in below.

Q: 7. Is the function given by G(x) at x = 2? Why or why not? 1 x² - 6x + 8 continuous

A: Theory : If A function f(x) is continuous at some point a, then it must satisfy All of these…

Q: Find x and y for which the following equation is satisfied: x+2 = - 5+i i-5

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Q: x+2, The function f(x) = 2x², Select one: Ⓒ True False x≤1 1<x<3 is continuous from the right at x =…

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Q: Let 1, if-3 <x s2 f(x) = %3D 4-x, if 2 < x<4 Without graphing, is f(x) continuous at x 2? Clearly…

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Q: 3. Find a value of b so that the function x 1 f(x) = is continuous on (-0, 0).

A: A function is said to be continuous if Left Hand limit = Right Hand limit = f(a) In this question,…

Q: 2. f(x) = is a continuous function but it is discontinuous at x = 3. Explain why X - 3 this is not a…

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Q: 2. If function f(x) = 3²-12 is continuous at x=2, find f(x). x-2

A: We need to find f(x).

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: 1. Function f is continuous on (-00,00). Find constant k. f(x) [kx² + 2x x-kx if x ≥ 2 if x < 2

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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: 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: (2x² - 2x 4 B) For what values of k and h is y={ k + 2x 2 + hx2 - 2 < x<-1 - 1<x< 2 2 <x<4…

A: B) Given, y=2x2-2x-4, -2≤x&lt;-1k+2x, -1≤x≤22+hx2, 2&lt;x≤4 and also continuous at x=-1, 2.  We have…

Q: Find the value of the constant c that makes the following function continuous on (-∞, ∞). x² { x = 1…

A: The given function is If function continuous at

Q: 7. Find all constants a, b that make f continuous at x = 2. (Use limits and definition of…

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

A: Given: hx=7x-5,x&lt;13x2-x,1&lt;x≤3 We know that any given functiony=fx will be continuous at x=a…

Q: F:[- 2,2]– R, F(x) = L((- 3(² + 1) dt

A: We have F(x)=∫-2x2(t-3)(t2+1)dt       Apply Liebnitz's rule for differentiation under integration…

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A: (A)Calculation of critical point of g(x):we can find derivative We can see that f(x) is positive and…

Q: I'm stuck on this question and I don't know how I should be approaching this. What should I do?

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Q: the answer quickl

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