Find the value of the following limits: Vx +1 - lim x -1 /2x x2 – x lim v9 n2 – n – 3 n

Q: Find the limits lim х2 — 1 as a. x→1+ b. x→1 c. x→-1+ d. x→-1

A: we have to find the limit    the given expression is

Q: Use the graph of the greatest integer function, y = [x], to find the limits given below. Ay 4- [0]…

A: [.] the greatest integer function returns the closest integer less than or equal to the given…

Q: Find the limit. (If an answer does not exist, enter DNE.) (x + Ax)² – 5(x + Ax) + 3 − (x² − 5x + 3)…

A: Given :lim∆x→0x+∆x2-5x+∆x+3-x2-5x+3∆x

Q: find the limit of g(x) as x approaches the indicated value. 3x2 + 1 lim = X g(x)

A:

Q: Find the limits: Vx – 1 lim x→1 x - 1 а.

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

Q: Find the limits lim (V² + 3 + x) X -00

A:

Q: Q4)A) Find the following limits (for two only). x+1 1. limx→-1 х2-х-2 1-Vx 2. limx→1 1-x 2х 3.…

A: Part 1,Given,           limx→-1x+1x2-x-2

Q: lim V3x² – 6 X-2

A: The given problem is,           limx→23x2-6 Here the function is continuous and defined at x=2, so…

Q: Find the limits by rewriting the fractions first.

A:

Q: Find the limit. 3e - 3 V1 + t - 1 4 lim 1 +t/

A: We have to find the limit of this Vector. If the limit 0/0 form, then we can use L' Hospital rule.…

Q: find the limit of g(x) as x approaches the indicatedvalue.

A: Given,          limx→25x4+2gx=∞

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) x² – 6x +7 -x² + 6x – 11 if…

A:

Q: Find the indicated limit given that lim f(x) = 5 and lim g(x) = 2. xa lim V3f(x) + 6g(x) xa

A:

Q: Find the limit. lim (Váx + 6 + 1)

A: The given limit is limx→56x+6+1

Q: Find the limit. lim (x, y) -(1,-10) y#-10 y+10 x2y + 6y + 10x2+60

A: Given limit, lim(x,y)→(1,-10)y+10x2y+6y+10x2+60

Q: Find the limits x2 - 3x + 2 lim x - 4x as a. x→2+ b. x→-2+ c. x→0 d. x→ 1* e. What, if anything, can…

A: We are entitled to answer three sub-parts. Please resubmit the question which you wish to get…

Q: Find the limit. V17x + h – V17x lim h→0 h

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: Find the indicated limit 2x lim( Vx +1 10)

A:

Q: Use the graph of the function f to find the limits at the indicated value of a, if the limits ex a =…

A:

Q: Find the limit as x approaches - 2 for the function f(x) = 12x + 1. %3D lim (12x+1) = X→-2

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Q: Evaluate the following limits. If needed, enter oo for o and oo for V3 + 9x2 (a) lim 5 + 6x 3+ 9x2…

A:

Q: Evaluate f(4+ h) – f(4) lim h0 where f(x) =5x +7. If the limit does not exist enter DNE. Limit =

A: f(x)=5x+7

Q: Find the limit. (If an answer does not exist, enter DNE.) (x + Ax)² – 2(x+ Ax) + 6 – (x² – 2x + 6)…

A:

Q: Find the following limits if they exist. Must show all work (analytically?): 1. X-2 lim (x) where…

A: Given that: 1. limx→-2f(x), where f(x)=-3x2+8, if x<22x,          if x>-2   NOTE: As per our…

Q: b) lim (1 +2x)³A * x=0

A:

Q: x? + x lim x' + 2x* + x³

A: We have to find  limx→0 x2 + xx5 + 2x4 + x3.

Q: Q4) A) Find the following limits (for two only). x+1 1. lim x--1x²-x-2 1-Vx 2. lim x→1 1-x 2x 3. lim…

A:

Q: Find the limits algebraically: (a) lim vx2 + 2x – 3 x-3

A: Find the limit of the given expression. Given function is continuous at x=3. So we can apply the…

Q: Evaluate the following limits. If the limit does not exist, write DNE. x² –16 b) lim Vx – 2 2 х* —…

A:

Q: Use the graph of the function f to find the limits at the indicated valu 4+ 3. y=f(x) 2 1 2 3 4 566…

A: Given query is to find indicated limit.

Q: Determine the value of the following limits, if they exist. If infinite, specify either o or -o. (If…

A:

Q: Find the indicated one-sided limits, if they exist. (If an answer does not exist, enter DNE.) if x 0…

A:

Q: Q5: Find the limits of: Vx +n - Vn lim n-

A: Given that: limx→0nx+n-nx

Q: Q2: Find the limit r + 3 lim x-3 x + 4x + 3

A: We have to find limit

Q: Find the limits t +3 a) lim (4x3 – 3x² + x – 85); b) lim, t+2 t+1 ; c) lim x +0 1-V1+7x ; d) lim (7…

A: We can solve these problems in this way

Q: Find the limit, if it exists. x2 + 16x + 63 10) lim x--7 10) x+7 A) 224 B) 16 C) 2 D) Does not exist

A: Given, Find limit limx→ -7x2+16x+63x+7

Q: Q4) A) Find the following limits (for two only). x+1 1. lim x--1 x2-x-2 1-Vx 2. lim x-1 1-x 2x 3.…

A: 1. limx→-1 x+1x2-x-2   is of 00form, So apply L'Hospital rule limx→-1 x+1x2-x-2   =  limx→-1…

Q: Q1/ Find the following limits. 1. lim x*+3x-4 2. lim x*- 16 x-1 2 X+2

A:

Q: Evaluate the following limits. If needed, enter oo for oo and -oo for – 0. V5 + 6x2 (a) lim 3+ 10x…

A: Use the substitution and then simplify the limit.

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) x2 - 4x + 18, l-x2 + 4x -…

A: Detailed explanation mentioned below

Q: Use the graph of the function to determine the limit at positive infinity: lim f (x) X00 68. A y 2 3

A: Given query is to find the indicated limit.

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) Sx2 - 4x + 6, X < 3 lim…

A:

Q: (x+2)7(x-5)* lim x→b (x+6)3 (x+8)10 DNE %D

A:

Q: Q4)A) Find the following limits (for two only). x+1 1. lim X-1x2-x-2 1-Vx 2. lim X-1 1-x 3. lim x0…

A: Find the limit for the given function . We use for calculate value of limit L' hospital rule (When…

Q: Find the limits as x→ o and as x → -oo. y = f(x) = 5x3 – x4 lim f(x) = lim f(x)

A:

Q: Find the limits. f(x) = x + 3 g(x) = x2 (a) lim f(x) X→-1

A: A limit tells us the value that a function approaches as that function's inputs get closer and…

Q: Determine the values of the following limits. lim 2a? 2x + 4 lim %3D む+1 lim I -1 x -1

A: To find the value of the following limits.

Q: Find the limit as x approaches infinity of the function V2 – x2 h(x) х3 — х + 1

A: Given:  h(x)=2-x2x3-x+1h(x)=x2 2x2-1x31x3-1x2+1  (Taking highest power of x in the…

Q: Find the limit. (If an answer does not exist, enter DNE.) lim (x + Ax)² – 4(x + Ax) + 9 – (x² – 4x +…

A: In this question we can find limit.

Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0). The multivariable limit of this function as it approaches the points (x0, y0) and is denoted as: