12 sin( In x) (b) Evaluate lim,→1 3+5)(x-1)

Q: 2-limx-o(x. secx.cscx)

A: To find the limit of the following.                                     limx→0 (x sec x csc x)

Q: How does the function behave as lim x → 3- for 7/(3(x-3)(5-x))?

A:

Q: 3n Find lim,→0 (1+ )'

A: Here,

Q: lim2

A: Explained below

Q: (12 sin )( In x) (x3+5)(x-1) Evaluate limx→1

A: Here we have to evaluate the given limit .

Q: 2) lim (+5)a00 (-2a+1)50

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

Q: Determine lim X- • ot s/x 7 Sinx

A: limx→0+5x-7sinx

Q: 11) Evaluate lim (1+ 2x)csc(x).

A:

Q: 1. Find the value of the expression lim x²+x+21 X-3 x-1

A:

Q: Ex x-2 XE3, X-2 12) Consider メレ3 2) lim. (f(x) b) lim. (f(x)

A: Topic:- limit

Q: lim (1+ tan 3x)*

A:

Q: x²-1 X If lim x0 x+1 - ax - b} = 2, Find the values of a and b.

A:

Q: lim (2x-5x) is x--2

A:

Q: V5x+4-3 3) lim X-1 x-1

A:

Q: d) (x+27) -3 X lim-

A:

Q: (1 + +)" =- 65. lim

A: To show: limn→∞1+1nn=e

Q: In(2+x) lim, x+-1 X+1

A:

Q: b) 49-(5+ x)² x-2 lim-

A: Use L.Hospital rule to evaluate above limit as in next step.

Q: b) series converges or diverges. 8 n=1 1 (2n)! n=1 use the ratio test to decide whether the nen

A:

Q: /2х-у -2 lim (*) -2.0) 2х- у-4 3.) Evaluate 2x-y#4

A:

Q: 1. lim x-2 (2x + 3)

A: 1. To find the given limit limx→ 22x+3

Q: x* + x² - 1 Find lim XC

A: Please see the explanation below

Q: 3. Prove lim 3x-7= 2 X-3

A:

Q: 3x 2х 2) Lim х-1 х+1° X → 00

A: Given,   limx→∞(3xx-1-2xx+1)

Q: 2. find: en(x?) a). Lim メ-1 b). Lim 1 - cos "x 1-COS 4x2

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.