For f(x) = −x^3 + 1/2x + 8 evaluate limx→∞ f(x) and limx→−∞ f(x). Then give the horizontal asymptote of f (if any). (a) Graph f(x)=(1−x^2, x≠1)(2, x = 1) (b) Find limx→1+ f(x) and limx→1− f(x). (c) Does limx→1 f(x) exist? If so, what is it? If not, why not?

Q: Find the limit for when x -> 4 lim F(x), for f(x)= x2+2 ; x≠4 ; 27; x=4

A:

Q: Find limit of lim x-->0 of f(x)= (e3x-3x-1)/(4x^2

A: Given limx→0e3x-3x-14x2

Q: Find the limit V3x(x-1) lim→1 |x-1|

A: we have limx→1-3x(x-1)|x-1| this is 00 indeterminate term

Q: Suppose limx →4 ƒ(x) = 0 and limx →4 g(x) = -3. Find lim x →4 g(x)/ƒ(x) - 1

A: We first distribute the limit

Q: B. Find the value of the limit. 1. lim *+1)²(x-1) x1 x³+1 x²–4 2. lim x1 x2-3x+2 x²-4 3. lim x2 x-2

A:

Q: Find the limits a) lim x2 - 4x + 3 x2 - 1 when x approaches 1 b) lim 6x + 100 7x2 100 when x…

A: We have to find the limit

Q: Consider limx-4 f(x), where f(x) 14x+ 9. Find a maximum value of 6 such that: If(x) 65< 0.006 if |x…

A: Plug f(x)=14x+9 in the given inequality and simplify.

Q: The process by which we determine limits of rational functions appliesequally well to ratios…

A: Solution:Givenlimx→∞ x-34x2+25To find the limit valueFormula:ab=ab

Q: lim x² ln x x-0*

A:

Q: Estimate lim→-4 f (x). Estimate lim-→-2 f(x). Where is f(x) discontinuous?

A: Since you have asked multiple part question, we will solve the first 3 part of the question for you…

Q: 2. Write the equation of a function that is discontinuous at x=5, but lim f(x) exists, and is…

A:

Q: Draw a graph where lim x→2 f(x) exists but f(x) is discontinuous at x = 2. Name the type of…

A:

Q: Q2 e valuat of the fallowing 2. ☺ lim L(x +3)t -16] xーース ☺ lim -25 X+5 メー5 lim |-X 3+X 9. X-3 メー] O…

A: To evaluate the given limits.

Q: Find the indicated limit. 2x lim (- Vx2+1 X00

A: Find the indicated limitlimx→∞(2xx2+1)

Q: Suppose neither limx→0 f(x) nor limx→0 g(x) exists. Show that limx→0 [f(x)g(x)] may exist.

A:

Q: Evaluate in terms of the constant a. lim (2a + x) x→ 0

A: To Determine:  Evaluate in terms of the constant a.…

Q: Find the limit. . lim 2x²-x-3 X-1 x+1 . lim 2+h-vZ x-5 E lim x-5+ x2-25 . lim o. f (x) = fx³ +3 lx -…

A:

Q: 3. Use L'H rule to find lim (1– 2x)/=

A: From the given problem: limx→01-2x1x Let, y=limx→01-2x1x Now taking log on both sides.…

Q: Estimate the limit numerically if it exists. (If an answer does not exist, enter DNE.) lim x→+∞  5x2…

A: Consider the given function:

Q: V2x -1 Using defination of limits, prove that lim Jx- 3 L^ = x4

A:

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

A: solution is given below..

Q: Let ƒ(x) = (x2 - 9)/(x + 3). a. Make a table of the values of ƒ at the points x = -3.1, -3.01,…

A: Simplify f(x) first for x not equal to -3 x y -3.1 -6.1 -3.01 -6.01 -3.001 -6.001…

Q: lim (4x – V16x² + 3x – 5 (4* Зх — 5 00-x

A:

Q: find Vx+4--x-2 1- lim --3 x+3

A: Since we are given with the multiple number of question and our guideline is solve first question…

Q: メ-D4 xー12 In do torminate Form Lim | १ - 3

A: Given:   Limit equation is given

Q: Find the limit 1-ex lim x+0 10x2 – 18x

A: Here we have to use the concept of limit.

Q: what is the lim x->0  f(x)-f(0)/x^2 if f(x)=2x^2+1?

A:

Q: Q.5 (a) Find radius and height of right circular cylinder of largest volume that can be inscribed in…

A: (a) First draw the figure,   Let r, h, V be the radius of base, height and volume of the cylinder…

Q: Find the limit of the function lim x → − 2 ( 2 − | x | 2 + x )

A: Topic:- calculus

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: . Is it possible that f(2) = 5 but limx→2 f(x) = 7? If so, what kind of function can satisfy this?

A:

Q: Find the limit. y 6- 5- 4 3- 2 1- 3-2 -1 -1 1\2 3 4 5 -2t limz-0 f (x)

A:

Q: If lim (x approaches 6) (f(x)-4)/(x-3)= 2, how do I find lim (x approaches 6) f(x)?

A: We separate the limit first.

Q: Suppose limx →4 ƒ(x) = 0 and limx →4 g(x) = -3. Find lim x →4 xƒ(x)

A: It is given that limx→4fx=0 and limx→4gx=-3.

Q: Use L'H rule to find lim (1 – 2x)/*. -

A: Question is solved.

Q: 3) If lim dt) = 5, can there be a vertical asymptote in the graph of d(f) at t = 0?

A: Given               :  limt→0- d(t)=5   Not Given       :  limt→0 d(t)=? limt→0+ d(t)=?

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: The function f(x) of the below graph is discontinuous at x = -1 because: a) f(-1) does not exist b)…

A:

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: if Væ² – 5x – 6 < f(x) – 1 < v6² – x² then find lim f (x) - | - x-6

A: Given:x2 - 5x -6  ≤ f(x) -1 ≤ 62 - x2To find : limx→6f(x)

Q: Find lim at inf: (x^2 + 2x)/(x - 7) Don't use L'H

A:

Q: If 3-2x sf(x)s3-x for -1sxs1, find lim f(x). lim f(x) =|

A: Calculate left hand limit and right hand limit than find the limit using sandwich theorem.

Q: c) lim -4e-x

A: c) limx→∞-4e-xlimx→∞-4ex

Q: Suppose y = f(x) is defined for all x. Sketch a graph with the indicated property. discontinuous at…

A: See the attachment

Q: Find the limit or show that it does not exist. lim √25t² + 2 − 5t t-x

A:

Q: 3 - If lim f(x) = 3.5 and lim,-2+ f(x) = 6.5 the function has a double sided %3D limit or one sided…

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Q: Evaluate the limit lim x² + 4x – Vx² + x ) and interprete the result in relation to x 00…

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Q: Evaluate limx=0 (e-ax - e-bx)/x

A:

Q: Find g'(x) for g(x)=-x^2+3x+2 by using the limit definition of a derivative.  lim x-->0…

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.