Use the definition of continuity and the properties of lim- its to show that the function is continuous at the given number a. f(x) = (x + 2x*)*, a= -1

Q: Use the Squeeze Theorem to evaluate the limit lim x→4 f(x)  if 8x − 16 ≤ f(x) ≤ x^2   on[2,6].

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Q: If f' is continuous ,f(8)=0, and f′(8)=14 evaluate limx→0 f(8+3x)+f(8+5x) / x

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Q: 1 lim In(1+x)/

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Q: Let f(x)={5x+1  x≠4               {1       x=4. What is f(4)? If f(4) does not exist, type: 99999…

A: The given function is

Q: Explain why the following limits of (a) and (b) do not exist. (a) lim - x→1x-1 sin x (b) lim x→1…

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Q: Use the Squeeze Theorem to find limx→c f(x).

A: Given that 4-x2≤f(x)≤4+x2 To find the limit of the function using the Squeeze theorem when x→c=0.

Q: Use the Squeeze Theorem to prove that if lim f(x) = 0, then lim f(x) = 0.

A: Given: The limit limx→cfx=0, To prove: limx→cfx=0 using squeeze theorem. Squeeze Theorem: If f, g, h…

Q: 2 Use the definition of continuity to show f (x) = is x+3 continuous at x=1. Whenever you find a…

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Q: Let Зх — 2. if x + 2, f (x) = 5, if x = 2. (a) Find lim→2 f(x) (b) Prove your answer to Part (a)…

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Q: given the attached function, find the following limit limh-->0 (f(-1-h)-f(-1))/h -6 -3 -3/2 -3/4

A: Explanation: Given that,  Now find the f(-1-h) put x = -1-h                           Now find the…

Q: Let f(x) = 3x + 2. Use the € – d definition to prove that lim 3x +2 1. x→1 Definition. E-d proof.

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Q: 3. Use continuity to evaluate the limit. (5 – x2 lim In x+1 1+ x

A: We have to find limit

Q: lim f(x) given that |f(x)/x² + 1|< 1 x→+∞

A: Recall: Squeeze Theorem for limits:              Assume that functions f,g and h satisfy…

Q: Use continuity to evaluate the limit. lim 9 sin(x + sin(x))

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Q: If f is an odd function and if lim f(x) exists Prove that this limit must be zero.

A: if limit is exist then right hand limit and left hand limit must be equal

Q: Suppose that f(x) and g(x) are polynomials in x and that lim, (f(x)/g(x)) = 2. Can you conclude…

A: f(x)/g(x) is a rational function, where f(x) and g(x) both are polynomials.    Since the    is a…

Q: Use the Squeeze Theorem to find lim f (x), given that 2 - |- 8| < f(1) < 2+ |r – 8|.

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Q: . The function f (x) is defined by the rule 2-36 if x + 6 f (x) x-6 25 if x = 6 (a) Calculate lim f…

A: Continuity criteria :  f ( x ) is continuous at x = a when following properties are satisfied :  1)…

Q: Use the definition of continuity and the properties of lim- its to show that the function is…

A: It is given that f(x)=3x4-5x+x2+43 so, when a=2, then we can say that lima→2f(x)=lima→23x4-5x+x2+43…

Q: Sketch the graph of any function f such that as lim attached, Is the function continuous at x = 3?…

A: limx→3+fx=1  &amp;  limx→3-fx=0 Let us consider a function, fx=x-3    if  x&lt;3x-2    if  x≥3 Now,…

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

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Q: Suppose that a function f(x) is defined for all real values of x except at r = c. Does it imply the…

A: Here we have to check whether the limit exists or not.

Q: 3. If f is a continuous function, what can you say about lim f(x)?

A: Given thatf is continuous To determinelimx→1f(x)

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

A: This question can be solved using the concept of continuity of a function at a given point.

Q: Find lim f(x), lim f(x), lim f(x), and f(a), if they exist. Xa

A: Consider a function f(x) which has a hole at x=c. Then the right, as well as the left limit of this…

Q: If f(x) = Vx² + x – x, find lim f (x), where f(x) is defined at X → 0.

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Q: When lim f(x) exists, it always equals f(a). State whether this statement is true or false. Xa

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Q: Evaluate the limits by previous methods or by L'Hospital's Rule, if applicable: a) lim- X- sin x -X…

A: We have to find the limits of the given following conditions

Q: 11. ((x) – (x + 2r'), a--1

A: To find the limit.

Q: use the definition of differentiability f'(x) = lim- h-0 f(x+h)-f(x) h to For f(x) = %3D 6. (x-1)…

A: fx=x2x-1 Now,…

Q: Suppose that f(x) = 1 if x 0. Does lim,→0 f(x) exist? (Draw a picture.) O No, because the limits…

A: Given, limx→0-=1limx→0+=2 Hence, limx→0fx does not exist  since both the limits are not the same.…

Q: Suppose that ƒ(x) and g(x) are polynomials in x

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Q: Consider the piecewise function x² +2x- 1, if x < -2 -x +1, if - 2 < x < 1 x² + 1, if x 21 f(x) =…

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Q: Find the indicated limit, if it exists. x+4 x<-5 lim f(x), f(x) = X-5 4 - x x2-5

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Q: Find the indicated limit, if it exists. 9- x? x0 lim f(x), f(x) = X-0

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Q: Determine the value for c so that lim f(x) exists. x-3 f(x) = 5**, *+c, for x 3

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Q: For all x > 0, 4x – 9< f(x) < x² – 4x + 7. Find lim f(x). x→4'

A: As per the policy, we are solving first question only, please  repost and specify which question is…

Q: Use continuity to evaluate the limit. lim In(2 + V1 + x)

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Q: Use the Squeeze Theorem to find limx→8f(x), given that  2−|x−8|≤f(x)≤2+|x−8|.   limx→8f(x)=

A: To use the Squeeze Theorem to find limx→8f(x), given that  2−|x−8|≤f(x)≤2+|x−8|.

Q: The function f is defined by x – b f(x) = x² – a² (a) Evaluate lim,za f(x) supposing a + b. Again,…

A: fx=x-bx2-a2 a). limx→afx=limx→ax-bx2-a2=a-ba2-a2=a-b0=∞             ∵a≠b⇒a-b≠0

Q: Suppose that f (x) is a function such that lim f(r) and lim f (r) both exist. Does this mean lim…

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Q: Suppose f(x) = x2 if x ̸= 2 and is undefined at x = 2. The domain is (−∞,2)∪(2,∞). Find lim f (x).…

A: The limit exists at x tends to 2 for f(x). First of all, consider the condition for the limit to…

Q: Use the Squeeze Theorem to evaluate the limit lim f(x), if x-5 10x – 25 < f(x) <x? on [3, 7].

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Q: Use the Squeeze Theorem to find lim f (x), given that 8 – |x – 3| < f (x) < 8+ |¤ – 3|. lim f (x) =…

A: Given  8-x-3 ≤ f(x) ≤ 8+x-3

Q: Given f(x)= 5x+1,Find lim (x +h)- f(x) h when x>--? h0

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Q: What is the lim f(x) where f(x) = {x" + 10x+24, if x -3 %3D X-3 A. 0 В. 3 С. 12 D. DNE

A: Given: fx=x2+10x+24, x≤-3-x, x&gt;-3   As we know that; The limit limx→afx exists when the left-hand…

Q: Let f(x) = x^2 − 10x. If you construct an ϵ-δ proof to show that limx→5 f(x) = −25, what is the…

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Q: Let f(x) be the function defined by x²+ 4x (xs3) 2x - 1 (x>3) the rule f(x) Find the one-sided limit…

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