Q.No.1: i. Find the limit y + 6 lim y→6- y2 – 36 ii. Find value of x, if f is not continuous .2 x* + 6х + 9 f (x) = |x| + 3

Q: 10. Find the value of the limit or state that it does not exist (DNE). a) lim f(x)= =(x)s u X -3

A: Given

Q: 2(x-1)* - y² Lex-1)* +2y (d) Show lim does not exist.

A: Limit exist

Q: 2x? +3y2 Let f(x, y) = Set y = mx and show that the resulting ху limit depends on m, and therefore…

A:

Q: 1. Find the limit if it exists. V2 + t – /2 – t - lim t→0 3t

A:

Q: C. Prove that the limit does not exist. 1. lim (xy)-(0,0) x*+3y

A: We need to prove that limit does not exist.Below find the details solution in image.

Q: 2.a²y rª + y? Show the function f(x,y) : has no limit as (x, y) → (0,0)

A: We have to show that the function fx,y=2x2yx4+y2 has no limit as x,y→0,0.

Q: x2 + 0x – 4 lim x-2 x - 2 Enter I for oo, -l for -co, and DNE if the limit does not exist.

A:

Q: 1. Determine if the following limits exist: x² + y5 lim (x,y) (0,0) 1 - cos(x) + y4 (a)

A: Sol: Part (a) limx, y→0, 0x2+y51-cosx+y4Find two different paths to approach the point that gives…

Q: Use the two-path test to prove that the following limit does not exist. x+ 2y lim (x.y)→(0,0) *- 2y…

A:

Q: Find the followings limits:- х — у 1. lim (x,y)¬(3,3) Vx – Jy. 1 2. lim х-0 \xуx + 1 X.

A:

Q: Express the limit as a definite integral. lim 40 E xk A xk; [-5, 1] k=1 1 9x8 dx -5 x9 dx x9 dx x dx

A:

Q: Evaluate f(4+h) – f(4) lim h→0 h where f(x) = -5x – 1. If the limit does not exist enter DNE. Limit…

A: We have to find the limit.

Q: Q2: (a) By using " L' Hopital rules "; Find the limits of ::- (1) lim,-(7/2)-(tan x)" (2) limy-o…

A:

Q: (d) Determine the following limit using u-substitution method: sin(t - 1) lim -1t2 +t – 2

A:

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

A:

Q: (-1)"f" cost =1--+ 4! 2 (2n)! In(1+t) =t-+ 3 -.+(-1)*-"4 +... n Yukarıda verilen cost ve In(1+x)'in…

A:

Q: Compute the limit 1 a2 1 - x2 lim xa x а - What can you say about the derivative of f(x) = ?

A: Given limit :

Q: We have the function if (x, y) # (0,0), xy x²+y² f (x, y) if (x, y) = (0,0), (а) Find lim…

A: We have to find the following given conditions according to the given condition

Q: (2) ykbäi * .. Find the value of Limit Below Vx + 11 – 4 lim x→5 X - 5 3/4 O 2/3 O 7/5 O 1/8 O 7/3 O…

A: Given: limx→5x+11−4x−5

Q: (a) Show that the limit xłycos y lim (x.y)(0,0) 2x4 + y2 does not exist.

A:

Q: Express the limit as a definite integral. lim xk Ax [-3, 2] 4-0 k 1

A: Given

Q: (4-x-x² if x ≤1 if x > 1 2x 5 Calculate the following limits. Enter "DNE" if the limit does not…

A:

Q: 4. Evaluate the limit of as e approaches 0. 2a A 2 B. % CO D. infinity

A:

Q: Use a table of values to estimate tne value of the limit of lim Vx + 4 – 2 f(x) f(x) 2.

A: Consider: limx→0x+4-2x   Let fx=x+4-2x Since we have to calculate limit at 0 of fx=x+4-2x.  Make the…

Q: 1 -1 lím (x,y)→(0,0) tan x² + y?

A:

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

A:

Q: Find the limit. x²y lim (x,y) → (0,0) x² + 8y²

A: limx, y→0, 0x2yx2+8y2

Q: Find the limit V1+t4 dt lim

A:

Q: Find the maximum value of & > 0 that satisfies the limit claim corresponding to e = 0.3, that is,…

A: In the question it is asked to calculate the maximum value of δ for the given function limx→59-x5=8

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

A:

Q: X,xif limF,(t)= F(t) at all t for which Fis Continuous

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 7. Find the limit as x approaches 0. F V I 2 2 O infinity O limit does not exist Oo .

A:

Q: 1 (a) What type of discontinuity does the function g(x)=- have at el/x – 1 x=0 ? Explain. (b) For…

A: This question is from limits and continuity.

Q: 1. In each of the following cases, evaluate the given limit. x2 +5x 14 lim エー→2 - (a) x2 - 2x t - 1…

A:

Q: dy -) using definition with limit of the following: dr 4. Find the differentiation (- y = /2x + 1.

A: We need to find the differentiation of y=2x+1 using the definition of limit. Now, according to the…

Q: 1. a. Describe the level curves of the function f(x,y) = %3D x* + y b. Show that the limit lim (2,y)…

A:

Q: Q2: (a) By using " L' Hopital rules "; Find the limits of ::- (1) lim,-(n/2)-(tan x)cosx (2) lim,--0…

A: L'Hôpital's rule states that for functions fx and gx which are differentiable on an open interval I…

Q: find the limit as x approaches to infinity (x-3 / x+1)^x/a

A: We need to evaluate the value of the following limit limx→∞x-3x+1xa Formula Used:  limx→∞1+mxx = em…

Q: Estimate the limit numerically. x² lim x+4 O diverges to +o 00 O diverges to -∞

A: Given

Q: In(t³ + 1) + t³ + 1 r(t) = 4: then the limit lim r(t) equals 1-0 -i-(4e-²¹-5e²¹)j- - sin³t -k, 13

A:

Q: 1. Investigate the limiting behaviour of x2 lim (x,y)¬(0,0) x2 +3xy +y2

A: It given function fx,y=x2x2+3xy+y2. When x,y=0,0 in fx,y=x2x2+3xy+y2 will result in 00. Set the…

Q: 11. Show that the limit lim (z.y)→(0,0) r² + y4 does not exists.

A:

Q: Find the limit and discuss the continuity of the function. lim sin 1. (K. y)(27, 4) y lim 2. (x,…

A:

Q: 1-cost lim sint et-1 + t t t+0

A:

Q: Show that the limit lim (r.y)(0,0) In(1 – a²) + yª r² + y does not exist.

A: First replace y=mx and then find the limit if the limit is dependent on m then the limit doesn't…

Q: S 10 – x – a? if x 1 Calculate the following limits. Enter "DNE" if the limit does not exist. 2x +…

A: The given function is f(x)=10-x-x2if x≤12x+6if x>1 We have to calculate,  a) limx→1-f(x)=?b)…

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) =…

A:

Q: f(x) lim sin(5x) X I 0 -0.25 3 2 Estimate the limit numerically or state that the limit does not…

A: We have to find out limit

Q: F(x) Let F(r) = | 3e" dt. Find lim if it exists. If the limit does not exist, explain why.

A:

Q: 1-e X x2 +1 X By using the limit comparison test, the integral

A: Using, limit comparison test

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: