Q.No.4 Let x<-2 x+2' S(x) = • x² - 5. - 2 3 Find the following limits lim f(x) lim f(x) lim f(x) And, also discuss the limits through a graph. X-3

Q: 1-cos(0) lim 02 e-0 1 lim (1 + x)a x-0 If f (x) is continuous at a, then what is the value of lim…

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Q: 8-x-1² if x 2 Calculate the following limits. Enter "DNE" if the limit does not exis f(x) Let f(x)…

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Q: The graph of the function f(x) = tan a is given above for the interval z e [0, 27] ONLY. Determine…

A: Given

Q: 9. Evaluate the limit. lim (1+ sin 3x)1/x x→0+

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Q: 6. Find the limit of f(x) = -- 10 as x approaches co and as x approaches - c lim f(x) = X00 (Type a…

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Q: V-1- x + 2 if x -- 2 Calculate the following limits. Enter "DNE" if the limit does not exist. lim…

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Q: 1 Discuss the existence of the limit lim sin x 0 x

A: To determine: The limit

Q: Q1: Find the Limits of: Тan x 1- lim X+Sin x+VX 2- lim xo X+Sin x 3- lim vx2 + 1- Vx2-x

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Q: 1 Q.3: Discuss the limit of f (x) : at x = 0", 0*,-∞,+∞, with graphs.

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Q: 2 – x – x2 if x 3 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(æ)…

A: Given, fx=2-x-x2 if  x≤32x-7 if   x &gt;3 We have to calculate  limx→3-fx limx→3+fx limx→3fx

Q: a. Find the Domain for y = = /4 -x + ! b. For what value of (k) is the function y-f(x) continuous at…

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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: 12, Show that the following limits do not exist. (а) lim 1 (x > 0), (b) lim (x > 0), x-0x2 x-0 Vx…

A: Given: d) limx→0sin1x2 to prove limit does not exist.

Q: For what value of the constant c is the function f continuous on (-o, 0)? cx2 + 3x if x < 2 f(x) =…

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Q: 1 if x – 2 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x) = x -…

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Q: -1– x + 5 if x - 2 Calculate the following limits. Enter "DNE" if the limit does not exist. lim…

A: limx→-2-f(x)=6, limx→-2+f(x)=6,  and limx→-2f(x)=6

Q: Given that: lim f(x) = 5 x-2 lim f(x) = -5 x--3 lim g(x) = -1 x--2 lim g(x) = -10 x--3 Apply the…

A: To find limx→-38fx+9gx

Q: 1. Find the limits lim (3x – 1) x-1/3 a) | cos x b) lim x 1 - T lim y--5 5 - v c) 3h +1 - 1 d) lim…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: (3) Using the appropriate approach covered in Unit 6 of this Course along with knowledge gained in…

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Q: 8-3x, for x <1 For parts b) and c), let f(x)= %3D x+x, for x21' b) lim f(x) x→1

A: We have to evaluate  limx→1- f(x) For x &lt;1 , f(x) = 8 - 3x

Q: 4. Evaluate the limits of the following functions: a) limsinx x-0 sin x-tan x 6 b) lim x-2 x2+2x-8)…

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Q: (b) Find the following limits WITHOUT using the L'Hopital’s Rule. x²–4x lim x→0- |x| (i) (ii) 2tan?x…

A: Part i,Given,           limx→0-x2-4xx

Q: Question 1. Evaluate the following limits and use L`Hopital`s rule if applicable (10 pts) x - sin x…

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

A: limx→∞2x53-x13+7x85+3x+x

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: * + 2, if x 0' (a) Find lim f(x). (b) Give a simple reason why f is discontinuous at 0.

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Q: Q1) A) Find the tangent equation for the function: f(x) = vx2 + 5 at =2 ? B) Find the limits by…

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Q: 2 – x – x2 if x 5 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x)…

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Q: (c) Find the following limit: Vx +1- 2 lim X-3 x(x - 3) V9x2 + 5 lim x-00 X- 1 cot 0 csc lim sin e

A: Given we have to find the limit

Q: §8 – x – x2 if x 5 Let f (x) = Calculate the following limits. Enter "DNE" if the limit does not…

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Q: Q2.) Find the limit ( 1 lim X+x cos x 1. X→ 0 sin x cos x |x + 2| 2 - lim(x + 3) x-2 x + 2 lim sin…

A: solve using properties of limits

Q: Find the limit. x² + y® sin х - у +7 lim (x.y)→(0,0)

A: Given,

Q: 10 – x – x2 if x 4 - Calculate the following limits. Enter "DNE" if the limit does not exist. lim…

A: Given that fx=10-x-x2if x≤42x-5ifx&gt;4   (1) Find limx→4-fx Left hand limit: For x&lt;4 ,…

Q: Find the limit. lim x→4  sin(x − 4) x2 + 5x − 36

A: To Determine: find the limit of  limx→4sin(x-4)x2+5x-36 Given: welimx→4sin(x-4)x2+5x-36 Explanation:…

Q: 1 Find the limit of lim x (1– e * ). X→ 00

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Q: 4. Find the limit, if it exists or show the limit does not exist: a) b) lim 47,² (x,y)(0,0) x + y…

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Q: -7x2 – 6x + 1 x<0 x 20 f(x) = 3 sin x Enter DNE if the limit does not exist. lim f(x) = 1 lim f(x) =…

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Q: II. Evaluate each of the following limits. ArcTanx — х 1) lim x→0 х3 Тапх 2) lim (#- x)таnx — х)…

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Q: Find the limit of f(x)

A: Given information

Q: V-2-x +4, if x -3 Calculate the following limits. Enter DNE if the limit does not exist. lim f(x) =…

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Q: 2. Complete the table by computing f(x) at the given values of x, accurate to five decimal places.…

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Q: We determined that l'Hospital's rule applies to the limit  lim x→5   x2 − 10x + 25 x2 − 5x

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Q: exV – 1 Let g(x,y) (a, b) = (1,0). Show that lim g(x,y) does not exist. (x,V) - (a,b) %3D %3D x+y -…

A: Firstly it should be proved that limit does not exists and then recognize the two limit values so…

Q: 2. Use the given values to set up a table to evaluate the limits. Round your solutions to sin 3x…

A: limx→0sin3xx

Q: Find the limit. lim X→- 47 Vx+ 15 cos (x+ 4x)

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Q: -x + 1, x > 0 3) Let f(x) = sin x -,x < 0' (a) Find left-hand and right-hand limits as "x"…

A: we have given f(x).  We have to find the left hand and right hand  limit.

Q: II- Calculer les limites suivantes: CS Scanned with Camx³x3+4x-5 0071-x II- Calculate the following…

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Q: Find the limits using any appropriate method. ex-e-x-2x 4.4 #40 lim x-0 x-sinx

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Q: A tank contains 1300 L of pure water.  The solution that contains 0.01 Kg of sugar per liter enters…

A: a) At the beginning tank contains 1300L pure water.

Q: b. For what value of (k) is the function y=f(x) continuous at x-3. x3-3x2-4x+12 x + 3 x-3 f(x) = %3D…

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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.