(x²y3 - 5y2) lim (x, y) →(4, 2)

Q: (a) Find the solution of the limit using polar coordinate system. x² + y² x2 + y2 lim(x.y)-(0,0)

A: To find the solution of the limit using polar coordinate system lim(x,y)→(0,0)x2+y2x2+y2 We have the…

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

A:

Q: 7. et² -e-y² = }(e - e-1) lim %3D (x, y)→(1,1) x+y

A: To Determine: to prove  lim(x, y)→(1, 1)ex2-e-y2x+y=12(e-e-1) Given: we have a  problem based on…

Q: Expand x'y + 3y - 4 about the point (1, -2) by Taylor' s theorem.

A: Let, the given function be fx,y=x2y+3y-4 and the given point is 1,-2

Q: Vx +1 vx+3 lim det Vx +1

A:

Q: x4-16y+ lim (x,y)¬(2,1) x²–4y2

A:

Q: 2x*y lim (x,y)→(0,0) x8 + 6y²

A:

Q: Find the limits

A:

Q: lim x-4y (x,y)- (0,0) 6y+7x .A does not exist.

A: To calculate the given limit: limx,y→0,0x−4y6y+7x

Q: lim (x,y) (0,0) 2x3 + xy² + y x2 + 7y2

A:

Q: Show that 4z2 z2 +1 1 (b) lim- z→1(z – 1)3 (a) lim : 43B = 00; (c) lim = 00. - - z(I – 2) 0+2 I- 2…

A: We will use the simple calculations using some usual formulae to evaluate these limits.

Q: ขน lim (x,y) → (0,0) x² +10y²

A:

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

A:

Q: |z²–1| 2 1) Use a tble of functional values to evaluate: lim I-1

A: The tables containing the functional values are very useful to approximate a limit. The tables are a…

Q: 4x +4 lim (2,y) (-1,2)` x² + 3xy – 3y2 + 3xy - 3y2

A:

Q: 2x lim(x,y)→(0,0) x² + x + y²

A:

Q: lim xy + 2y - 3x - 6 (x, y) 4, 3) y +3 y-3 2 O 6

A:

Q: 3y +5xy + 2x lim (1) (z3-2) 3y +2.xy 4(x*-y*) (i) lim (10 x -y +1-1 lim (1.)-0.0) (Hint: use…

A:

Q: lim Scy+1 1-secy a) as y→n/2 b) as y→T/4 c) as y→ 3t/2

A: a) y→π2 lim cosec y+11-sec y=cosec π2+11-sec π2=1+11-∞=-∞

Q: (2) (6) xy-y-2x+2 lim (x,y) (1.1) x-1 2x-y-2 lim (xy)-(20) 2x-y-4 lim (x.y.x)-(3,4.1) (xyz) ¹√√x² +…

A:

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

A:

Q: 2-y lim 7+ 6y² y-

A:

Q: lim y approaches 0  ................... [5y3 + 8y2]/[3y4 - 16y2]

A: Consider the given function as limy→05y3+8y23y4-16y2

Q: .2 lim (x, y) (0,0) along y = x2 |3|

A: Substitute y=x2 in the function. Now the limit becomes

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

A: limx,y→0,0x-4y6y+7x Take the path y=mx, then as x→0, y→0 limx→ox-4mx6mx+7x limx→ox1-4mx6m+7…

Q: Along the path x = e find lim (2,y)→(1,0) y²+6zy 3x-y-3

A: To evaluate the given limit: lim(x,y)→(1,0)y2+6xy3x-y-3 along the path x=ey. Here,…

Q: (x,y,z)→(-1,5,3) xy (b) lim (x,y)→(0,0) xª – y²

A:

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

A: We have to solve given problem:

Q: xy lim (x.y)→(4,3)x²+y²

A: find the following limit

Q: x2-x-2 2x-4 2sin(6x–12) 3(x-2) Sx-1 Let f(x)* ,g(x) • and h(x) Vz+2+1 a. Find lim f(x), lim g(x),…

A:

Q: lim 4y° + Jy18 – 1 -00

A: Given that: limy→-∞4y9+y18-1

Q: x° +2y² +x*y lim (* ,y') → (0, 0) x* +3y - x*y

A:

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

A: We have to find the limit.

Q: xy+yz b) lim (xy2)-(0.0.0) x+y2+2

A: To find the limit: L=lim(x,y,z)→(0,0,0)xy+yzx2+y2+z2

Q: x+y lim In ху (xy)-(1,1)

A:

Q: Along the path x = e" %3D find y +4xy lim (x,y)-(1,0) 3x – y - 3 does not exist O -2 -3 2 0 3

A:

Q: Q3) Find: (1) lim, V1+cos 2x (2) lim-2 (x+ 2) 14-x2

A:

Q: xy lim (2,y)→(0,0) x³ + y²

A: Solution is given below..

Q: xy + 1 lim (x, y)→(1, −1) x² − y²

A:

Q: lim 15 13 15z2 Vr? + 8z lim %3D HY8 9-4x Vr? + 8z lim 9-4r /7

A: Given query is to find limit of the expression. Since first three has been filled correctly, solving…

Q: 16+y limy-o

A: The given function is 16+yy-4y. Simplify the given function as follows.…

Q: x*-16y* lim 14. (r,y)→ (0,0) x2 +4y2 xy 15. lim (x,y) (0,0) 3x² +2y2

A:

Q: y+4 lim (x,y )→(2,-4) xy -xy +4x-4x

A:

Q: x2y2 lim (r,y)(0,0) 2r+ y

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: j) lim e- =

A: 2. (j). We have to find the limit:  limx→∞ e-x

Q: x²+x5-2y lim (xy)-(3,9) %3D x-

A: Given limit lim(x,y)→(3,9)x2+xy-2yx-y

Q: (b) lim æ In(x² + y²) (x,y)→(0,0)

A:

Q: lim (x,y)(1,2) 2x +x*y-xy 4x2-y?

A: Given,          limx,y→1,22x3+x2y-xy24x2-y2

Q: lim (x,v)→(-2,0) g(x, y) does not exist given that Show that (x+2)³y² (x + 2)6 + 3y4' 0, if (x, y) #…

A: