(4x – 5y) lim (x,y)→(1,1) 5x² – 7y O -1/2 O 1/2 Limit DNE

Q: Evaluate the following limits: 1-cos¹(x) (i) lim zsin(2x) (ii) lim In (√) +1 2²-1 (iii) lim sin(x) -…

A: Given :limx→01-cos4(x)sin(2x)lim x→1 lnxx2-1lim x→π4 sinx-22cosx-22lim x→01+tan(2x)1x

Q: lim (4x – 3y)= -11 Prove that (r.,v(-2,1)"

A:

Q: Show lim (x,y) (0,1) In (x²+2y²-1) e2x² + y²-2

A: What is Limit of a Function: The limit of a function in mathematics is a key idea in calculus and…

Q: Evaluate lim (x,y,z)→(π,0,3) ze -2y cos(2x)

A:

Q: x2 – 1- y lim (x,y)→(1,0) X – Vy +1

A:

Q: II. Let g(x, y) = 47² +9y² (2x-3y)2 1. Show that lim (z.) (0,0) g(x,y) does not exist. 2. Is g(x, y)…

A: To show :- limit g(x,y) does not exist at (0,0)

Q: 1: Find the limit 6x°y5 lim (x,y)¬(0,0) x6 +y10

A: See the attachment

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: 2. Show that sin (2x²y) lim (x,y) →(0,0) x² + y² does not exist.

A:

Q: Find Lim-0.0 (r² + y²) In(x² +y²) '(xy)(0,0)

A:

Q: Question 2. Find lim sin (1 – 3e-/")e-/2. (Justify your solution.)

A:

Q: Q2. Find the x² + y² lim (x, y)→(0, 0) √√x² + y² + 1 − 1

A: We have to solve above question and find  limit

Q: xy – Y lim (2,y)(1:0) x2 + y² – 2x + 1

A: We have to solve given problem:

Q: Find the limit or show that it does not exist t y lim (x,y)→(0,0) x² + y²

A:

Q: Evaluate X - 4y - lim (x,y)→(0,0) 6y +7x

A:

Q: xy In(r+1) rª + 3y? if (x, y) # ( g(x, y) = if (r, y) = ( %3D

A: In this question we will use basic concepts of calculus i.e concepts of limits in two variables. We…

Q: t3 + 8 . tan(t + 2) Let F(t) j+ (t* – 1) e“-4k , find lim F(t). t+2 t+2 t-2

A: Limit of a vector point function

Q: lim (1,4)→(0,0) r2 + y8

A:

Q: (4x 5y) (z,y)→(1,1) 5x2- 7y lim O 1/2 O 1/2 O Limit DNE

A: We need to evaluate the following limit limx,y→1,14x-5y5x2-7y

Q: lim (x, y) → (4, -2) x2y + xy2 x? – y2

A: The given expression of the limit is: lim(x,y)→(4,-2)x2y+xy2x2-y2

Q: Find lim (x2 + y?)ln(x² + y?) (x,y)-(0,0)

A: To findlim(x,y)→(0,0)(x2+y2)ln(x2+y2)