2h 4. lim h0 2h S(x) dr

Q: e* – 1 lim V1+x -1 x→0

A:

Q: x"+3x+ x*+2 .4 e lim メ→ x'+z x²+3x +l tim メ→。 xとャ! lim x-1

A:

Q: 1. lim (x – 4)(x² + 8) x→5 2(t-10)² 2. lim t→10 t

A: Let P(x) = a0+a1x+a2x2+.....+anxn be a polynomial, where a0, a1, ...., an are real numbers and n is…

Q: X>0০ कलामह ही ही। lim LS 15 X১-০০ 3xt 2 ए

A: The value of limit can be computed as follows.

Q: 2. 2xy lim (x.y)-(0,0) x² + 2y6

A:

Q: Find lim "(x.y)→(0,0) (4 + (x² + y? ) In(x² + y² )) Dose not exist O 1 4

A:

Q: 2x lim x→0 Vx + 1 – 1

A: Given limit expression is limx→02xx+1-1.

Q: x4-16y+ lim (x,y)¬(2,1) x²–4y2

A:

Q: 2x2 – x – 3 (d) lim x→-1 x² + 5x + 4 2x – 8 (e) lim r→4 x2 – 8x + 16 x2 (f) lim r--2 2x + 4

A:

Q: e7x + e-7x _ 2 lim x → 0 5 x2

A: Evaluate the given limit as follows. limx→0e7x+e-7x-25x2=e70+e-70-2502=1+1-20=00 Since 00 is an…

Q: b. lim a-1 ²ln(1-x) X -dx

A: Given

Q: 3. Find the values of the constants a and b such that Va + bx – V3 - lim x → 0 3.

A:

Q: 1. lim (y – 2y+7) 2. lim (y² +5y–1) y→3 y2 3w - 4w+2 3. lim 3w – 2w+7 w² +1 | 4. lim w2 w -5 w-1

A:

Q: X'+2X Lim メーロ 0 @ True eflase laşe 8.

A:

Q: + h 4 (a) Lim×-1'x+1 X (b) Lim h→0 V5h + 4 – 2 -2 - t3 – 1 3. (c) Lim t-1 t-1 II

A: To show the given limits, we use the algebraic indentity and rationalization of a fraction.

Q: tan( xy) lim (х.у) >(0.1) х"у+x = ? 1 (b) 2 1 (c) 3 (a) 0 (e) 1

A:

Q: 1) lim Ax) = -2 x- 5 2) f'(5) = DNE

A:

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

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

Q: 1 c) lim x+0 \ex-1 X.

A: the given expression is: limx→01ex-1-1x…

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: 2-у 4. lim y-4 y2-8y+16

A: 4. limx->42-xx2-8x+16

Q: (H.W) sin(t +4t+3) (7) Lim t -9 (H.W) t-3

A:

Q: 4x e lim x→0 r2

A: The series expansion of ex is ex=1+x1!+x22!+x33!+x44!+...

Q: 1 1 V13+x 3 h. lim X→0 X + 4

A:

Q: 7 - 3y2 e. lim y00 7y2 + 3y f. lim tan-(e/) х2 + 3x — 10 g. lim x-3 х2 — 2х

A: Each parts are solved below.

Q: d. lim h(x) Preview e. lim h(x) = x→00 Preview f. lim h(x) = 00--x

A:

Q: xsinx lim x→0 e*+e¯x-2cosx

A: Since, we have been given up the expression:-limx→0 x sin (x)ex+e-x-2 cos (x)-(i)Since,on applying…

Q: .2 lim (x,y)→(0,0) x² + y²

A: Consider the given: limx,y→0,0x2x2+y2Let y=mx

Q: d) lim (xe”* +1)/ x->0*

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: |x² +1 if x 0 x→0

A:

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: 19. lim x→2- x² – 4 eas y + 6 21. lim y→6+ y2 – 36 -

A: Given that limx→2- xx2-4 limx→6+y+6y2-36

Q: x2 – 4 lim h→2 Vx – V2 /9 + h – 9 - lim h→0 h

A:

Q: b. lim X-0* e -3/x 2 X²

A: Please see the attachment

Q: e2x -1 (1) Lim y² – y-6 (2) Lim yー2 y -4 Vx-3 (3) Lim xー→9 1 1 x 9

A: Given: limx→0e2x-1x, limx→-2y2-y-6y2-4, limx→9x-31x-19 We know that limx→0ekx-1kx=1…

Q: /10-х - 2 8. lim x-2 х+2 А. 1/12 В. -1/12 С. -12 D. DNE

A: The given function is 10-x3-2x+2. We have to find the limit of the given function at x=2.

Q: 1 х — 1 x +1 h 4 (a) Lim (b) Ļim h→0 V5h + 4 – = -2 x→0 2 5 t3 – 1 = 3. - (c) Lim t→1 t-1 || +

A: Reduce the equations by rationalization or by algebraic identities to put the limits and get the…

Q: х — 1 If y = lim x→0 Vx + 3 – 2 The value of y = 4. %|

A: Given:

Q: j) lim e- =

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

Q: h +2h (d) lim 3h -h' +5x+4 (e) lim x' +x-12 -3x +5x+4 lim 4x +x-12

A:

Q: 2xy lim (x.y)-(0,0) x² + 2y6

A:

Q: b-4+ Jb 3x(x – 4) Answer "True" or "False" for the following: In(x – 1) Ji 3x(x – 4) In(x – 1) |…

A:

Q: 1/x 2 In(5x) H lim 2 5x = lim lim lim X- V 5x 5x 2 5x

A: The solution of given problem as follows:

Q: 4x° – x lim x' +5 (d) x² – 49 lim Vx+2 - 3 (e)

A:

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

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

Q: 1 lim(2x + 1)zx =? X→0

A: In the given question, the concept of Limit is applied. Limit The limit formula is employed to…

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.