Ex 11.1.1 Compute lim r

Q: 6. Evaluate limx Sin (3x) 4x

A: let

Q: 1 1 x +4 4 lim

A:

Q: lim z+di = 1 Z-1-21 I lim 2 Z-0 lim 240 (Im²) ² 12₁²2² does. (Rez) --121 - compute 0 lim 7731 Z 27²…

A: We will find the required.

Q: +h)4-44 Q 9 Compute limh-0 h

A: To find:

Q: Find each of the following from the graph. a) lim f(x)= b. lim f(x)= x-2" c) (2) =| 2 3 d) Does lim…

A: To evaluate the indicated limits:

Q: Compute lim x 40+ GE. ta 240

A:

Q: Translate the statement lim f(x) 5 in terms of a rigorous e and N state-

A: Solution Given limx→∞f(x)=5we need to translate the statement in term of a rigorous ∈ and N…

Q: 4. lim ) ズ→1 Xー1

A:

Q: . Compute (1+æ)(1+2æ)(1+ 3x) – 1 lim Preview will appear here. Enter math expression here

A: Solution  is given below

Q: 3. Write down the formal delta-epsilon statement you would have to prove in order to prove the limit…

A: The given limit statement is limx→-23x+1=-3

Q: 6. Determine lim 32. Show your work. a. -16 i b. -6 [-+x C. d. 19 119

A:

Q: Evaluate this limit. x + 2 lim x--2 x2 +x – 2

A: To find the limit

Q: 13. Determine lim (6x-x²). X→-5

A:

Q: 7. Show that lim x³ = c³ for any c E R. X-C

A: To prove:- for any

Q: 4. If tige Lim, show that fg & LUM.

A:

Q: 35. lim 20

A: limx→2 x20-x2 = ?Now, fx=x20-x2 is polynomial and we know that polynomials are continous everywhere…

Q: Compute lim 1+-

A:

Q: 18) lim Xcos- X XI

A:

Q: Find the limit 19sin(5x) lim 28x x-0 a. 5 28 Ob. 95 28 19 О с 28 d. None of these. O e. 95 28

A:

Q: 2. Use the Squeeze theorem to show that lim x-0 ² co(+1)²

A:

Q: 10. Prove that if lim(x,) = x and if x > 0, then there exists a natural number M such that x, > 0…

A:

Q: 1.3 Evaluate lim using the laws of limits. 140 V1+ 3x – 1

A:

Q: Suppose Σto an no an5. What is the value of lim a,? 72-0

A:

Q: 11. If 0 < a < b, determine lim Qケ+! a" + b"

A: First we take comman bn+1  from numerator and bn  from denominator and then we  use lim ban=0.

Q: 6. Prove from first principles (with ac- 6 argument ) that लेग ½ lim 7--1

A: 1x2+1-12=2-x2+12x2+1                               =2-x2+12x2+12+x2+1…

Q: 7. Find lim to talk A. 1 C. -1 B. 0 D. does not exist

A: We have to evaluate the limit.

Q: 1+ x Evaluate lim x x2 In -

A:

Q: Find the limit. x² - 25 lim x 5 x²8x + 15

A: We need to find the limit:limx→5x2-25x2-8x+25

Q: Let 51 =1 and 25n+1=5,+ lim(s,) = Then %3D %3D 11s, Select one:

A:

Q: Show that lim n→∞ k = k

A:

Q: tは lim 1→十8|34 - 1 十

A:

Q: Show that the following: Ifr> 1, then lim Vr -1 = 0.

A: We have to solve given problem:

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: