Let F(x) = (x2 + 3x + 2)/(2 - | x | ). Make tables of values of F at values of x that approach c = -2 from above and below. Then estimate limx→ -2 F(x).

Q: Show that lim (x,y) →(0,0) 16x4 +9y¹2 4x² + 3y6 does not exist.

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Q: What is lim1 f (x) ? X

A: Find your answer below

Q: et +ex -x²-2 Lim- x-0 sin²x-x²

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Q: Use l’Hospital’s rule where applicable to find the limit.

A: the given limit is: limx→08x6+3x4-9x9x7-2x4+x3 we have to evaluate the given limit.

Q: Use the Squeeze Theorem to prove lim,e-*arctan(x) = 0.

A: limx→∞e-xarctanx=0 Now, -π2<arctanx<π2                       ∵Range of arctanx is -π2,…

Q: Find the limit limx→0ax−1x.

A: Given, The limit is,

Q: Use a tble of functional values to evaluate: lim 12 z-2

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Q: Show that lim (x,y)→(0,0) 16x4+9y12 4x²+3y6 does not exist.

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Q: Prove rigorously that lim lxl = 0.x→ 0

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Q: How do you evaluate the limit:  limx-->0  (sin(4x))/9x WITHOUT using L'Hospital's Rule?

A: A property:L'Hospital's Rule is not necessary here.The following is an important property used in…

Q: Find limx→−∞(x2 −1)e4x. Show work.

A: We need to find : limx→-∞(x2-1)e4x

Q: Express the limit as a derivative.

A: To express: limit limx→-1x3+1x+1 as a derivative. Concept used: Definition of derivative:…

Q: Find the limit. (x²-7) (6- cos x) lim

A: Given,           limx→0x2-76-cosx

Q: a. Evaluate limx→5 f(x), where f(x) = { 11x+ (2 +77) Ef x5 f(x) exists.

A: solution is given below..

Q: Is there a value of a for which limx1 3x^2+ax+a+3/x^2+x-2 exists? Enter the value of a if such a…

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Q: Evalute the lim sin5x/x(x-1) as x approaches 0.

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Q: If f(x)=x2−9x−3 , what is limx→3+x2−9x−3 , limx→3−x2−9x−3, and f(3) ?   Is f(x) continuous at 3?

A: Given,              f(x) = x2 − 9x − 3

Q: Find the limits limx→0+x-1/ln x

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Q: lim is: X+ d X Does not exist

A: Use the definition of limit to solve this problem.

Q: Using the ɛ, & definition, prove that lim V = 1. %3D x 1

A: We have to prove the given limit.

Q: Find the limits limx→1+x1/(x-1)

A: limx→1+xx-1

Q: Let ƒ(x) = (x2 - 1)/( | x| - 1). Make tables of the values of ƒ at values of x that approach c = -1…

A: Make tables of the values of ƒ at values of x .

Q: 1 lim sinx x2 x→0

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Q: sin² x lim 0-x X

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: Estimate the limit numerically  limx→4 √x−4/x−16=

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Q: Find the limit. (a) lim x→3 Vx +6 – x x3 – 3x2

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Q: Find the limits limx→0(ex + x)1/x

A: Consider the given limit as limx→0ex+xx

Q: Evaluate the limit. 5 sin(x) – 5x lim x3

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Q: find the lim as x approaches infinity when f(x)= (1-x)/2x

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Q: Find the limits of the functions below a) limx-3 x* sin x b) lim,

A: We can find the limit of both the question as below.

Q: 1. If V5 - 2x² s f(x) s V5- x? for -1sxS1, find lim,-o f(x).

A: Answer and explanation is given below...

Q: Find the limits limx→0+x (ln x)2

A: Consider : limx→0+x(ln2x). Modify the limit function. limx→0+(ln2x)1x…

Q: Find lim 2x sin using the Squeeze theorem. x-0

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Q: Find the limit limx→0ln(1+4x)sin3x.

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Q: Evaluate the limit 5 + 2x lim 8 – 8x x → 0

A: We haven the function is: f(x) = (5 + 2x)/(8 - 8x)  Dividing the numerator and the denominator by x…

Q: Suppose that limx→2[f(x)+x2]=α. Find  limx→1(x+1)f(2x)

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Q: use f(x) to find: limx→0f(x), limx→-4f(x), limx→5+f(x), limx→-4-f(x). the discontinuity that is…

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Q: Consider the function…

A: The graph of f is as follows:

Q: Determine a reasonable estimate for lim hx x-1 3 -5 -4 -3 -1 3 5 2. 1 4. 1. 1. 2. ee

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Q: Compute the limit below. Justify your answer. sin(24x) lim- 39x

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Q: What conclusion about f(x) can be drawn from the equation lim-a+f(x) = f(a)?

A: Given that limx→a+f(x)=f(a)

Q: lim (x²Vx* – 1 – x*)

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Q: lim (Vx2 + 4x + x)

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Q: Find the limits limx→∞(1 + 2x)1/(2 ln x)

A: Given, limx→∞1 + 2x12lnx We know that, limx→ac·fx=c·limx→afx⇒12limx→∞1+2x1lnx Now,…

Q: lim(x,y)->(0,0)  (4x2y)/(x2+y2)1/2

A: Given: lim(x,y)→(0,0)4x2yx2+y2         (1) To compute: The limit.

Q: x-3- – 3VA lim x+0* 0" x- Vx

A: We first try to find the limit  by substitution

Q: Find the limit. lim(v² + x = x) = lim( Vx2 + x – x

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Q: Evaluate limx=0 (e-ax - e-bx)/x

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Q: Use the definition to show that x² - y² lim (x,y) →(0,0) x² - y² 0.

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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.