Use properties of limits and algebraic methods to find the limit, if it exists. (15– 2x for x<7 x²-9x for x27 lim f(x), where f(x) =' X→7 O -1 -14 Does Not Exist 14 1

Q: Determine whether the limit exists. If so, find its value. If the limit does not exist, indicate…

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Q: 4) Find the value of a for which the limit lim x→0 evaluate the limit. sin(ax)-sinx-x x3 is finite…

A: To Find: The value of a for which the limit limx→0sin(ax)-sin(x)-xx3 is finite and then evaluate the…

Q: Let f(x)={−2x+2  x≠1               {2   x=1. What is f(1)? If f(1) does not exist, type: 99999 What…

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Q: 5 if x - 3 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x) = I+…

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Q: Find a value for the constant "a" that will make the function f(x) continuous. f(x) = { ax- if xs2…

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Q: -1- x +3, if x -2 Calculate the following limits. Enter DNE if the limit does not exist. lim f(x) =…

A: Given : fx =-1-x + 3   if x&lt;-23                        if x=-22x+8                if x&gt;-2

Q: Estimate the limit numerically (or graphically). Use oo or -oo for too. Write DNE if the limit does…

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Q: Let f(x)={−2x+2   x≠1               {−5         x=1. What is f(1)? If f(1) does not exist, type:…

A: Given,

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: Using L'Hopital's Rule, we have to find the limit of f(1+ x) – f(1 – x) lim xf'(1) |

A: If the Direct substitution will results the answer in the form 00 or ∞∞ then we can use L'Hospital's…

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

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Q: Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is…

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Q: { if x -1 Calculate the following limits. If the limit doesn't exist but it makes sense cases where…

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

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Q: Q2: (a) By using " L' Hopital rules "; Find the limits of ::- (1) limx¬(n/2)-(tan x)cos x (2) limx-o…

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Q: Find the limit (if it exists) (а) lim x — 5 (b) lim 5 x-243 x2 + 6x + 8 (c) lim x--2 x + 2 sin x (d)…

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Q: 7. Find the limit, if it exists. If the limit does not exist, explain why. - (a) lim sin (2x 6)…

A: solution is given below

Q: limf(x) does not care what happens While a limit exactly at x = c because the limit is concerned…

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Q: 8. Evaluate the limit by using a change of variable. x* - 1 Vx – 2 а. lim 8 x - 8 d. lim Vx – 2 27…

A: According to the L' Hopital rule, if the limit of a rational function, f(x)=N(x)D(x) , is to be…

Q: 8 - x- x2 if x 4 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(æ)…

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Q: 8. Evaluate the limits by previous methods or by L'Hospital's Rule, if applicable: 4x3 +3x 4x b) lim…

A: We have to find limit

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: 5x2 + 10x + 1 20. lim x* + x² + 1

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Q: Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is…

A: We need to see the logic for f(x)

Q: 1. Find the limits. (Don't use L'hopital Rule) V2h+1-1 a. lim h-0 b. lim_(x – 3) -2| x--2 (x-2)

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: 5. Evaluate the limits using any of the methods you know. Show your work. 1-cos 2x а. lim x-0 4sin2x

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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: (4- x - x² if x ≤ 2 2x-7 if x > 2 Calculate the following limits. Enter "DNE" if the limit does not…

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Q: (e= - v2n) V2 x lim x→0+

A: Let L=limx→0+eπx-2x1x Taking ln on both the sides: ln L=lnlimx→0+eπx-2x1x here we can interchange ln…

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

A: NOTE: Refresh your page if you can't see any equations. . find the left-hand side limit of the…

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

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Q: 9 if - 1 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x) = 2 -1…

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Q: 3. Evaluate the limit if it exists: а. lim 8-0 sin-B b. lim(1+x*)*

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

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Q: 5. Evaluate the limits using any of the methods you know. Show your work. In(1+4x) c. lim tan 2x

A: find the limit

Q: 9 -x2 if x 1 .What value of c makes g(x) continuous at x = 1? Show all conclusions. 2 Vx-4 Using…

A: For a function to be continuos, the left hand limit should be equal to the right hand limit.…

Q: S 2x² f(x) = 8 - x for x 2 Compute the left- and right-hand limits at x = 2 and determine whether ƒ…

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Q: Let f(x)={−4x+3   x≠4               {3       x=4. What is f(4)? If f(4) does not exist, type: 99999…

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Q: 1. Find the limit if exists or show that the limit does not exist 1-cos(x+2y²) (x+2y2)2 (a) (b) lim…

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Q: 2. Determine the infinite (∞ or -0) limit as follows: x² – 2 - (a) lim x2- x2 3x + 2 - 4-6 sin x – 1…

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Q: 1c. Use L'Hopital's Rule to find the Limit: lim          (1 - x)tan(pix/2) x-&gt;1-

A: We will use tan z = 1/cot z formula

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: Calculate the limit algebraically. (If an answer does not exist, enter DNE.) x2 + 3 lim x--2 x2 + 3x…

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

A: (1). From the given problem: limx→0-x2-4xx

Q: and b at where? ] Use the &-8 definition of the limit to prove lim(4x-3)=5. X2 Find the & value When…

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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: 4] [2M] Determine whether the limit exist in R for lim xsin(1/x²), (x# 0). x→0

A: Zero

Q: 6 -- if a - 3 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x) =…

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Q: Q5) Find the limit for the following function by using L'Hopital's rule: tanx - tan-11 lim X-1 x2 -…

A: We find limit

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.