For the following function, factor the numerator and denominator into linear terms and find the limit as x goes to -1 and 2. g(x)=(x4+6x3+3x2-26x-24)/(x4-8x3+17x2+2x-24)

Q: Evaluate the limit of the given functions. 3x² - 17x+ 20 25x + 36 1. 2. lim x+44x² t³-1 1 lim t-1…

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Q: Evaluate the limit A. ƒ(x) = 5x + 2 at x = 3 x²-9 B. f(x) at x = 3 x-3

A: A. f(x)=5x+2B. f(x)=x2-9x-3

Q: Find lim f(x) for the given piecewise function. x→4 2x + 3 if x 4

A: The given function is:

Q: Consider the following function T² -7x-18 if x -2 Find lim [f(x)]*. I-2-

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Q: O Find the limit as x >t 8. 5. géx) = x³+7x2_2 XメーX +」

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Q: Evaluate the limit of x approches 0 on the function (2e^(9x)-2)/(7x)

A: The given limit of the function to be evaluated is,

Q: lim (6x2 + 8x – 13) x--3

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Q: If f(x)=√3+5x, find f′(3) using the definition of derivative. a.) f′(3) is the limit as x->     of…

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Q: find the limit of rational function (a) as x→00 and (b) as x→ -o. 3x7 + 5x? – 1 f(x) 6x3 7x + 3 -

A: (a) Given f(x)=3x7+5x2-16x3-7x+3 For x→∞…

Q: 2x2-х+3 3) lim x→-1 3x² + 5x+ 2

A: To Find: Limit of given function

Q: Evaluate the limit of the following algebraic functions. x*+3x3-x²+x+4 2. Lim X--1 x+1

A: Find the limit of the following function

Q: What is the limit of f(x) = 8 as x approaches n? (If an answer does not exist, enter DNE.

A:

Q: For which of the following functions does the limit as x → 2 exist?

A: Given: 1.limx→2x-2x-22.limx→2sinx3.limx→2x2-4x-24.limx→2x2+16x-225.limx→2x2+x2x-16.limx→2tanπx4

Q: find the limit of rational function (a) as x→0 and (b) as x→ -o. 5x8 – 2x3 + 9 h(x) 3 + x – 4x5

A: [a]limx→∞5x8−2x3+9−4x5+x+3 Therefore, limx→∞5x8−2x3+9−4x5+x+3=∞

Q: 2x 2-3х-9 lim x-8 4x2+29

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Q: find the limit of rational function (a) as x→0 and (b) as x→ -o. 2x + 7 x3 – x² + x + 7 f(x)

A: Given that, f(x)=2x3+7x3-x2+x+7 Factoring out x3 on both numerator and denominator we get,…

Q: What is the limit when x is approaching negative infinity when the function is (8x+2) / (4x-5)

A: Given

Q: find the limit of rational function (a) as x→00 and (b) as x→ -o. 9x4 + x 2x4 + 5x² – x + 6 h(x)

A: Given h(x)=9x4+x2x4+5x2-x+6 a) To find limit of h(x) as x→∞ limx→∞h(x)=limx→∞9x4+x2x4+5x2-x+6…

Q: If f(x) = 4, find f'(5), using the definition of derivative. f'(5) is the limit as æ → 5 of the…

A: Given , f(x) =4x2Since derivative at x = a is given byf'(a) = limx→a f(x)-f(a)x-a

Q: lim x X49

A: As we know that: limx→afx=fa Given: limx→ 49x

Q: Evaluate the limit of the following algebraic functions. x4+3x3-x2+ x+4 2. Lim X- 1 х-3

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Q: Given f(x) = 5x² + 2x + 7, find ƒ'(x) using the limit definition of the derivative. f'(x)=

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Q: Find the indicated limits of the following function: 11x3 – 4x2 – 8x - - f(x) = 10 – 10x – 8x3 - lim…

A: According to our company's guidelines I can only answer first three subparts of the question since…

Q: Please see attached -

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Q: Given f(x) = 6/I - 2, find f'() using the limit definition of the derivative. f'(x)=

A: In the question we have to find f'(x) using limit definition of derivatives.

Q: What is the limit of the function f(x) = x ^2 + 2x at the value a = −1?

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Q: Given f(x)=4−4x^2, find f'(x) using the limit definition of the derivative. f'(x)=

A: Given fx=4-4x2

Q: Given the function y = (x2 – 5x + 6)/(x-2), (x#2), find the left-side limit and the right-side limit…

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Q: Given f(x) = 2 /x + 2, find f'(x) using the limit definition of the derivative. f'(x)=

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Q: If f(x) = 4x + 2x + 6, find f' (2), using the definition of derivative. f' (2) is the limit as x →…

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Q: If the limit of a function f at x-3 equals -4, then which of the following are true?

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Q: Given f(x) = 5VI + 1, find f'(x) using the limit definition of the derivative. f'(x)-|

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Q: Given f(x) = 3 – 4x°, find f'(x) using the limit definition of the derivative. f'(x)=

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Q: х2-3х-4 - 3x- lim x-4 х— 4

A: The given problem is solved below in detail.

Q: Find the limit. im 2-4 a. f (x) - 2

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: If f(x) = v3+ 3x, find f'(5), using the definition of derivative. f' (5) is the limit as x → 5 of…

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Q: Find the limit of x^x as x approaches 0 from the right.

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Q: Given f(x) 7 find f'(x) using the limit definition of the derivative. f' (x)=

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Q: Given f(x) 8 – 3x2, find f'(x) using the limit definition of the derivative. f'(x)=

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Q: Q2/ Find the limit of the following function: 3x2-x 1. limx→0 2x2+7x 2+3x 2. limx→∞ 7x2-5°

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Q: Find the limit of f(x) = 9x+9/8x+8     as x approaches infinity and as x approaches negative…

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Q: 2x/y lim (x,y)>(0,0) 5x² +2y

A: Let L is the value of Given Limit.

Q: (x+2)(x² – v²) lim (x.5)(L1) /x² – y² +1-1 (x,9)(11)

A: The solution of given problem is followed by

Q: Q3: Find the limit for the following functions: - Vx-2 1- lim x-4 x-4 (2x-3)(Vx-1) 2- lim x→1…

A: Apply d'hopital rule

Q: Given f(x) = 2x + 6, find f'(x) using the limit definition of the derivative. f'(x)=

A: The given function is:fx=2x+6To find f'x

Q: lim (3x2 – 5x + 9) X-4

A: Given query is to find the limit of the expression.

Q: Given f(x) = 4/x – 5, find f'(æ) using the limit definition of the derivative. f'(x)=

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Q: Find the limit of f(x) = 4x+8/7x+3 as x approaches infinity and as x approaches negative infinity.

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Q: f(x)=X÷2x if x 23 3x ifx<3

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.