(a) Suppose that a function f(x) is defined for all z in [-1, 1]. Can anything be said about the existence of lim f(x)? Give reasons for your answer. (b) Find the limit of the function 21 + 7 f(x) = 13 – x² + x + 7 as r + 00 and r + -0.

Q: (b) Assume that lim,6 f(r) = 9 and that lim,6 g(r) = 3. Compute lim f(r)g(r) - f (x)f(x) + g(x)g(x)

A: To Determine: The given expression:

Q: 1. Let f(x)= x²+x-6 |x2| 7 x b 2 x + a 3 2 if x 2

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Q: 5. Evaluate each expression using the given graph of f(x). lim f(x) a) x-1- 2- 1- b) lim f(x) -2 -1…

A: Given graph, The objective is to find,  a) limx→1-f(x)  b) limx→1+f(x)  c) limx→1f(x) d) f1 e)…

Q: Evaluate the derivative of  the image  if a = 90 and b = 0.5 at x = 4 using CDA  with Δx =0.11.…

A: For the given values of a, b and c, f(x) is given by f(x)=90cos0.5xx2

Q: 4. Evaluate the limit. (a) limx-1 √x+2 x+1 (b) lim, ²

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Q: 2. Question: Prove that the limit does not exist x² + 7x + 9 lim X→-5 x2 - 25

A: Given: limx→-5x2+7x+9x2-25 for evaluating given limit, we put x=-5 in given limit

Q: Use the graph of f(x) below to answer the following questions: -1₁ --2 y=f(x) 3₁ 4₁ I 5 I I X

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Q: Find lim f(x) if, for all x > 1, x- 00 6ex - 15 < f(x) < 3ex Vx - 1 х —

A: 6ex-153ex&lt;f(x)&lt;2xx-1

Q: (2) Use the definition of limit of a function to find lim x³-3x-2 x+2x2 - 3x+2

A: To find the limit of the function x3−3x−2x2−3x+2 as x approaches 2, it can apply the definition of…

Q: Give the two-step method for evaluating a limit of the form lim f(x)8(x).

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Q: Find the lim f(x) if, for all x > 11, 7x-1 < f(x) < 7x + 5x x2

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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: Find the limit of the following functions (some are indeterminate forms). x2+x-12 1. lim- x-3…

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Q: 6. a) State why the limit of f(x) = √5x - 1 does not exist for x

A: Please refer to the image below

Q: Verify that L’Hôpital’s Rule applies and evaluate the limit.

A: Consider a function fx. The limit of a function at x=a is given by: limx→a fx=fa

Q: Let 16x-5 1x² +5 Enter the exact value of the one-sided limit lim f(x) 3-2 f(x) = if x ≤ 2 if x > 2

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Q: If 2x < g(x) < x* – x² + 2 for all x, find lim g(x). x-1

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Q: Find lim f(x) if x →∞ 4x - 1 X f(x) 5.

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Q: Given the function f(x) = Which f the following is/are true? (x- 1)(x + 1) 1. lim f(x) = +00 2-1+ 2.…

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Q: I.B. Sketch the graph of a function f satisfying ALL the given conditions. • The domain of f is…

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Q: Find the limits lim (Vr + x - V – x) X00

A: Given: Let y=limx→∞x2+x-x2-x To Find: To evaluate the given limit.

Q: 5. Let a, b, and c be real numbers with a < c< b and let f : (a, b) → R be a monotone function. If c…

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Q: Calculate (a) so that the function is a real number

A: Approach to solving the question:For solving this question to find the value of 'a', we use the…