lim (x,y)→(0,0) (3 + (x² + y²) In(x² + y´

Q: a. limr→0 cos(x) b. limx→n

A:

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

A:

Q: iz³+1 lim z--i z²+1 3 2 ylgn ihi

A: Finding the limit by l'hospital rule

Q: lim (x,y)→(0,0) (x² + x²) (х, у) ->(0,0) а. 0 b. 1 с. 1/2 d. Does not exist

A:

Q: lim (1, y)→(0, 0) (r + y +9)e-1/(z²+v²)

A:

Q: 4. Proof Prove that lim x"y" dx dy = 0. n→∞

A:

Q: ev2x-y lim (x,y)→(3,2) x*-4x2 lim (x,y)¬(0,0) \x²+2y²,

A:

Q: lim (x,y) (0,0) Vx²+y² In (x²+y²)2 O is equal to 2 O is equal to 1. O does not exist. O is equal to…

A: We have to find the limit.

Q: Find the limits

A:

Q: Find lim [x +i(2x + y)] z→1-i iz3 – 1 lim z→i z+i

A: a) Given that, limz→1-ix+i2x+y It can be written as, limx+iy→1-ix+i2x+y

Q: lim 17) P - (5, 5, 1) In (z\x2 + y²)

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: 2 i (z-i) lim z→i z2+1 1 O 2i 1 -1

A:

Q: z² + iz lim z3 + 1 z- ob ||

A: We are given : limz→∞z2+izz3+1=limz→∞z2+izz3z3+1z3=limz→∞1z+i1z21+1z3=0+i(0)1+0=0…

Q: lim (4 + (x + y} ) In(x² + y)) (х.у) - (0,0)

A:

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

A:

Q: Show that limxy)H(-2,0) g(x, y) does not exist given that (x + 2)³y? (x + 2)6 + 3y4' 0, if (x, y) #…

A:

Q: Does lim(x,y)→(0,0)y2x2 + y2 exist? Explain.

A: Given, limx,y→0,0y2y2+x2 now check limit on y=mx limx,y→0,0m2x2m2x2+x2 limm21+m2 so m21+m2 is define…

Q: lim (4+ (2? + y°) In(x² + y²)) (1,y)(0,0)

A: Given; lim(x,y)=(0,0)[4+(x2+y2)ln(x2+y2)]

Q: ขน lim (x,y) → (0,0) x² +10y²

A:

Q: Does lim (x,y)→(0,0) x² + y² y2 exist? Explain.

A: Here given  limx, y→0,0y2x2+y2

Q: lim zta sec z is A B 2 D nonexistent

A: Given query is to find value of the limit.

Q: lim (x,y)-(2,4) x² +x/F-2y x-Vy %3D ||

A: Solve the limit

Q: lim zx+xて Xー→3 メ-3

A: Apply L hospital rule

Q: iz° + 1 lim z→-i\ z2 +1 ' z--i

A: To evaluate:

Q: Find the limits in Exercise

A: limx22-1x

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

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

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: z+3 lim- %3D iz Z+2

A:

Q: lim, (V+x+1 - V+1) – Vx² x* + 1

A:

Q: x² + y² lim (x, y)→(0,0) V – 1 x² + y² + 1

A: Given: Let L=limx, y→0, 0 x2+y2x2+y2+1-1 To Find: To evaluate the given limit.

Q: 2. lim (x,y, Z)-) (0,0,0) EYaluate ベtyナスス

A: If limit depends upon the directions then limit does not exist.

Q: Find the limit.

A: We have to find the given limit

Q: xy lim (2,y)→(0,0) x³ + y²

A: Solution is given below..

Q: 2 i (z-i) lim z →i z²+1 1 2i -1 | 1

A: Fourth option is correct.

Q: lim (x,y)-(0,0) x-y+2√x-2√√y √x - √y

A:

Q: 23. lim Vx2 + y² In(x² + y²) (xy)→(0,0)

A: This question is related to limit in two variables.

Q: lim(z – 1) csc TZ Is

A:

Q: sinny -limy-1 y-1

A: Given, limy→1 sinπyy-1   We have to evaluate the limit.

Q: lim does not exist NI

A: Given,  limz→0zz

Q: iz° + 1) lim z→-i\ z² 2 +1,

A:

Q: lim (1,4) (0,0) x2 + y2 Prove that

A:

Q: lim (z,y)→(0,0) (2+(x² +y²) In(x² + y²))

A: We have to find the limit of: lim(x,y)→(0,0) 2+(x2+y2)ln(x2+y2)

Q: lim (2 + (x + y²) In(x² + y³)) y)→(0,0)

A: Here, lim(x,y)→(0,0)2+x2+y2lnx2+y2

Q: x²y²z² lim (x,y,z)→(0,0,0) x² + y2 + z²

A:

Q: Show that (x + 1)² sin y lim (x,y)→(−1,0) (x+1)4 + y² does not exist.

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:

Q: 2 -z+1-i Prove that lim =1- :l+i z- 2z+2 2

A: solution is given below

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.