Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) lim X-8 3+Vx (1- 6x2 + x³)

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) x2 - 6x + 8 lim X → 2 х…

A:

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) -1 lim (-6 +h)-¹ + 6-1…

A: L'Hospital rule:- If limx→0f(x)g(x) is of the form 00 then limx→0f(x)g(x)=limx→0f'(x)g'(x)Continue…

Q: Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) A -…

A: Given limit is

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) lim (-6 + h)-1 + 6-1 h-0

A: The solution is :

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) 1 lim 5 5 + x x--5

A:

Q: Evaluate the limit, if it exists. (If a answer does not exist, enter DNE.) x2 lim 4x 3 x 3x2 2x- 3

A: Obtain the limit value as follows.

Q: Evaluate the limit, if it exists. (If . an answer does not exist, enter DNE.) u + 2 lim u→-2 u3 + 8

A:

Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) 2 - |x| lim x-2 2 + x

A:

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.). lim h → 0  √(4+h)…

A:

Q: Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) lim…

A:

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) 1 1 lim x 8 X - 8

A: To evaluate the limit of the function given.

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) 2+4x+3 lim X--3 x+ 2x- 3

A:

Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) х - 8 lim X- -00 x2 + 9

A:

Q: Evaluate the limit, If It exists. (If an answer does not exist, enter DNE.) lim (h - 4)2 – 16

A:

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) x2 – 4x + 3 X - 5 - lim…

A: The given expression of the limit is: limx→5x2-4x+3x-5

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) lim (9 + h)-1 – 9-1 h→0

A:

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) x2 + 25 – 13 lim x--12 x…

A:

Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) (36 +x - 6x) lim Xco

A: Given,

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) 3 lim 4 + 6A

A: We need to evaluate the value of given limit

Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) 4x6_ X lim x →∞0 x³ +9

A: We need to evaluate the following limit limx→∞4x6-xx3+9

Q: Evaluate the limit, If It exists. (If an answer does not exist, enter DNE.) 1-t lim t-11- Vt

A: I use Rationalization method to solve this limit

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) 6 - Vx lim x→36 36x – x

A: To find:limx→ 366-x36x-x2

Q: Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) lim…

A: To evaluate the given limit: limx→83+x31-6x2+x3

Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) z3 – 27 lim z+3 z- 3

A:

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) V81 + h - 9 lim

A: 6. The given limit is, limh→081+h-9h. Note that, the given limit is in the indeterminate form. Apply…

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) 25 - t lim t- 25 5 - VE

A:

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) 3 lim t→0\tv1 + t -

A:

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) 3 - Vx lim x-9 9x - x

A:

Q: Find the limit, if it exists. (1+h}l/3_ 1 lim h-0 Does not exist 1/3 3.

A: We will find the limit as following.

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) 2 2 lim

A: Explanation of the solution is given below...

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim X→-2- V x² - 4

A: Given expression is We need to find its limit as x approaches -2-

Q: Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) lim…

A: limx→34x3-3x2+x-3=433-332+3-3=4×27-3×9+3-3=108-27+10=81

Q: Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) lim…

A:

Q: Find the limit, if it exists, or show that the limit does not exist. a) lim (x,y)→(0,0) 3x2+2y2/…

A: (a)-lim(x,y)→(0,0)(3x2+2y2x+1)Put the value (x,y)=(0,0)lim(x,y)→(0,0)(3x2+2y2x+1)=302+2020+1=0…

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) 1 1 - lim x 4 4

A: Let's find.

Q: he limit, if it exists. (If an answer does not exist, enter DNE.) Need Help? x² - 8x lim x→-1 x2 –…

A:

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) 9 lim 1 +t

A: We have to find limit

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) x2 - 7x + 6 lim X → 3 x…

A: To evaluate , limx→3x2-7x+6x-3

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) x2 + 7x + 6 lim х— -6 х*…

A:

Q: Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) 3 +…

A:

Q: Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) 2x2…

A:

Q: Find the limit. lim Vx X-1

A:

Q: Find the limit, if it exists. (If an answer does not exist, enter DNE. lim 7etan(x) x- (1/2)+

A:

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) 5 5 t2 +t lim | t

A: This question can be solved by taking the LCM of the denominators

Q: Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) lim…

A:

Q: Find the limit, if it exists, or show that the limits does not exist. a) lim (x5 + 4.x³y – 5a²).…

A: Given lim(x,y)→(5,−2)(x5+4x3y−5x2)

Q: Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) 5x2…

A:

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) 1 1 lim (x + h)" h-0 h

A:

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) x2 - 3x + 2 lim X → 2 X…

A: To determine:

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) (x2 – 4x + 6, 1-x² + 4x –…

A: Here we find limx→7fx       where fx=-x2+4x-2, x≥7x2-4x+6  x <7if it exist

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: