iz?-z- lim- z2-1 %3D i0 -i O 00

Q: Vh2 + 4h + 5 – V5 (b) lim h->0+ h

A: Given limit, limh→0+h2+4h+5-5h  is in 00form

Q: VП? + 4h + 5 - V5 (b) lim h>0+ h

A:

Q: Va4 – 7x³ – 9 lim læ2 + 7 Z-00

A:

Q: x-4 3. lim I+4 4 VI - 2

A: We need to evaluate the limit of the given function

Q: - 2 lim,→8- х — 8 X

A:

Q: 2x*y lim (л, у) -> (0,0) х8 + 6у2 6y2

A:

Q: 2z 4z +9 Find lim, oo 00 3z2 8

A:

Q: atua 8r? - Зх + 4 lim I 00 2x2 + 7x

A: We are asked to find the limit

Q: lim e5t -1 / t =? t-->0

A: Given,

Q: 4x2 lim (a,y)(0,0) 4x2 + 4y?

A:

Q: Find the limits

A:

Q: esx-1-3x | 10. lim is x2 (A) 0 (B) 1 (C) 4.5 (D) 9 (E) nonexistent

A: The solution for the above question is as shown below.

Q: Q1) Solve:- 5cosx 1) lim 4х-2п 2

A: In question  We have given an expression  5cosx/(4x - 2π) We'll find the value of given expression…

Q: x²+ 4x – 21 - . ... lim х- 3 А. 6 В. С. 10 D. 12 8 Е. 14

A: solution of the given problem is below    ...

Q: x²+ a² – Vx² +b² lim - Væ² + c² – Va2 + d² -

A: Since if we put x tends to zero than it becomes inf/inf form. So use another approach to solve this…

Q: So* - y-³) dy 2.

A:

Q: Find the limits

A:

Q: 10x? .2 +11гу + у? lim (л,у) —(-1,10) 10а2 — 39ху — 4y2

A:

Q: 3 x° + y lim (х,у)>(1,-1) х +у

A:

Q: Evaluate lim→0 6-6e 5x+x ,13 6 13 6 13 6 6 -

A: topic - limits

Q: 2x2 – ry – y? Ty – lim (2,4)-(1,1) 22 – y?

A:

Q: Q1) Solve:- 1) lim Scesz Ar-2 2) lim

A: →When limit is of indeterminate form 00 or ∞∞ , then L'Hospital rule is used.    In  L'Hospital…

Q: x? – 4x Find Lim x-0 3x2 + 6x А. 3 3 2 С. D. 3 B. olo

A:

Q: (2x+1)²-5 lim =? х-0о 2х2+х-1 30 -1

A:

Q: x² – 4x+3 Find Lim A. -- 0.3 C. 0.6 D. 4 B.

A: To evaluate the given limit.

Q: a) Solve lim xe and explain your steps. -2x

A: (a) From the given problem;   limx→∞ xe-2x   It is the 00 form. So, applying the L'Hospital's rule:…

Q: stn (s-1) +5-2 39. lim a. 0.33 C1 d.033

A: Definition and methods help to find the required limit of the given function. A value is said to be…

Q: lim I→-00 12 –6x+3

A: limx→-∞3xx2-6x+3

Q: 13x? - 7x - lim I» 00 6x3 O -13 -0-

A:

Q: Lim 3y +7 y?_2

A: Since you have asked multiple questions, so we will solve only first question for you.

Q: lim 5r' - 40 x→2 x - 4 А. D. 12 В. 8 E. 15 С. 10 4,

A: Since it 0/0 form. Using L' hospital rule,

Q: V3 - 2 lim H:-4 5.

A:

Q: Exc. Eind. Lim (x-1) y3 2

A:

Q: Find the limits

A: To find limitlimh→05h+4−2h

Q: ■ Find the limit.

A: Given;                               limx→2-x2-2xx2-4x+4 Evaluate:              limx→2-x2-2xx2-4x+4…

Q: Exc. Eind. Lim (x-1) y3

A: Solution:

Q: raleuto lim Y-12 XB

A: First rationalize the expression as follows.

Q: 8m3 - 27 2 lim 2m - 3 m- 2

A: a³ – b³ = (a – b)(a² + ab + b²)

Q: ruente x2-2 Зх-7 x+1 lim 3x-5 ||

A:

Q: 3i - lim t-25 (t – 20)2

A: We substitute t=25 in the given expression

Q: (V16x* + 7x – 4x²) = - 4²) = lim x+00

A:

Q: Find:

A: The given expression is limx→-24x2+5

Q: x? - 2y2 lim (x,y)-(0,0) x2 + 2y2

A:

Q: x? — х lim х-1 x2 + 9х — 10 (-5+ h)? – 25 lim h→0 h

A:

Q: -36h2 +216h- 216 lim h-6* h-6

A:

Q: Find Lim 5e*-2x x-0 A. 5e C. 5 D. 0 B.

A: Solution

Q: hand side. Write BOOM 1. lim In e*= 0 X-4

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 4t Vt-t 2-7t/E lim t - 00

A: Simplify the limit

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: