1. Evaluate the following limits. L'Hopital's rule is NOT allowed. 4. lim x-∞ 8118 5. lim 1-x+ 2x + 7 √9x² +5-3x (x - 1) tan(x³ - x) x-1(x + 1) sin²(2x - 2)

Q: If 8 cos (3x) < g(x) < 8 + 2x for all x. Find lim g(x)

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Q: 5. Let r(x) be a nonzero rational function. Evaluate r(x+1) lim X00 r(x)

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Q: 1. Evaluate the limits below. If they do not exist, explain why. Show your work (you can use any…

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Q: (x² + 2x – 3 if x > 2 The value of lim f(x) if f(x) = {6-x if x < 2 A. 5 В. 2 С. 3.5 D. does not…

A: The objective of the question is determine the limit of the given function.

Q: Use L'Hospital's rule to find the limit. (a) lim x-1 x²-3x + 2 x² - 1 sin (2x) 2-0 sin (7x) (b) lim

A: L'Hospital's rule a.

Q: tan(3x) lim x→0 2x2 + 4x

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Q: 2. Find limits numerically. Use at least 3 relevant x-values for each. sin(4x) sin(4x) (a) lim x→0-…

A: Explained below

Q: 3. (a) Differentiate the function f(x) = x2 from first principles.

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Q: 52. Let X if x 2 (a) Evaluate each of the following, if it exists. (i) lim g(x) (ii) lim g(x) x→1…

A: Limit exist at x = a If left hand limit = right hand limit lim x→a- g(x) = lim x→a+ g(x)

Q: The function f is continuous for all real numbers. If lim f(x) = 0, then what is lim xe-2x)? x-2 x-1

A: The function f is continuous for all real numbers  If limx→2f(x)=0then if we put x=2t then…

Q: If lim f(x)=-2 and lim g(x) = 2, what is the value of lim [f (x)+2g(x)]?

A: Given, limx→afx=-2  and  limx→agx=2

Q: Your friend from Calc 2 says that the following statement is not true: x2-x-2/x-2 = (x+1) She is…

A: We have to answer the given questions.

Q: 1. (10 pts) Use the following graph of y = f(a) to answer each part: 1 -2.1 Y a (a) Determine the…

A: Answer of every question is given below.Explanation:Step 1: Step 2: Step 3: Step 4:

Q: Prove directly from definition that if f(x) and lim √(x) = ∞0 tim X-> 1 + then also lim f(x) = a ∞o…

A: A limit is said to be the value that a function approaches the output for the given input. The limit…

Q: 1 2 Determine the following limits: X-9 .1.1 lim x+3 X-3 .1.2 lim X-0 3.2.1 using factorization.…

A: Please find attachment

Q: Lim x tends to pi/4- (LHL) √(1-√sin2x)/(pi - 4x)

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Q: Q2/ A. Find the following limits. Answer four only. x+3 i. lim x-3x²+4x+3 X+) √2+1! x-1 lim x-1…

A: Since you have posted multipart questions i can do first three subparts as per our company…

Q: B. Prove the following: NO Differentiation 16-x 4. lim 1x16√x-4 = -8 sin 5x 1 x→0 sin 10x 2 5. lim…

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Q: Find lim x→-3 sin(−4 π x)   lim x→-3 sin(−4 π x)

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Q: If 6 – 4x <g(x)<6 cos x for all x, find lim g(x).

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Q: f (x) =  x^2 +2         x3         1. At what value is this function discontinuous, if any?…

A: Given function, f(x)=x2+2,     x&lt;310     ,      x=3-3+4x,   x&gt;3

Q: The given function is: VIXI The given function can be written as: y = y = √x, x ≥ 0 S-√√x, x 0…

A: The function is given as , y=x3