12. lim X00 *A + x

Q: 5. Evaluate lim sin(x)-(x² +3x– e*). 1-0

A:

Q: 1. Compute lim. ( ). 1 x→2+ 2 x² – 2x. where c is a real number. You may need to discuss according…

A: limx→2+1x−2−cx2−2x

Q: 42t lim t+0 4 - 1 - 1

A:

Q: lim [r – In(4x + 7)] x→+0

A: To find the limit

Q: 2х + x 1. lim

A: Consider the limit  limx→02x+xx

Q: x³ + x² - x - 1 lim X→1 X-1

A:

Q: Evalate the limit 6. lim (e + x)²/x

A:

Q: 2. 5 Lim X: CSC JZ% メラ。

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

Q: 39. Find lim f(x) if, for x > 0, 4x? – 5 4x6 + 3 - < f(x) < x6 x2

A:

Q: 21: The final value of :* lim (In(x))?

A:

Q: 32. lim x + x - 2 x2 - 1 2,

A:

Q: 2+ 1 ** Evaluate lim - X+ oL dt A B none of these 1- e? 1 4

A: Given that,  Now taking the integral term,

Q: 16. lim x¹/ x→0+

A:

Q: Evaluate (a) lim (e(5+∆x) − e5)/∆x  ∆x→0 (b) lim ((πx)2021 − 1)/π x − 1 x → 1/π

A: (a) Given limit:   According to L’Hospital rule:

Q: 10) lim (In x)2/x X00

A: Evaluate the limit in the following way:-

Q: 4. Evaluate: lim (a² + e-*)(= cac r) エー→0+

A:

Q: .3 c) lim ス(x+1)

A:

Q: c. lim In³ x

A:

Q: 1. Show that z³+y³ lim (x, y) (0,0) 1² + y² does not exist.

A:

Q: 10sin (Tx) In (xº) q(x) What is lim g(x)?

A: solution :

Q: lim x In(2x) x→0+

A:

Q: lim In (x°) x2

A: We have to evaluate the given limit.

Q: Find the limit.

A: We can find the limit of an expression by applying the limit point as value of the variable in the…

Q: lim (In x) x→0+

A: Given,          limx→0+lnx

Q: 16. Evaluate using L'Hospital's Rule. x3-216 a. lim X-6 (In x) b. lim 4x2

A: Given, Part a: limx→6x3-216x-6 If we put x=6 we get an indeterminate form, Therefore by using the…

Q: lim In(x+3) 4) 1

A: Evaluate :     limx→∞ln3xlnx+3

Q: 27+x- 5 Compute lim II-2 x+2

A:

Q: 23) lim x In x X-0*

A:

Q: 5. Lim xsinx x+0+

A:

Q: 4.lim 1252x-7+2 Sーズ 5. lim e*+1 X-4

A: Let's find.

Q: 21) lim x-4/In x X-0+

A:

Q: (b) lim (r + 1) In x

A:

Q: 1 Assume that lim xn +oo. Prove that lim n-00 n +o0. n-00 k=1

A: Given limn→∞xn=+∞

Q: (1+x)" - 1-nx | lim where n is a natural number. r2

A:

Q: 2 In x lim x→+∞

A:

Q: lim In(10x) x-0t

A: To find the below right-hand limit.

Q: 22) lim (In x)4/x X-00

A:

Q: In(x) lim x+0o x1/8

A: The given limit is,

Q: 5. Show that lim –nx² e dx = 0.

A:

Q: 399. [T] lim e(x - 1) x-1 x-1

A:

Q: 1² +1 Use the e-N definition to prove that lim = 1. x² + x + 1

A:

Q: 3. Show algebraically that lim x* – 2 – x = 0

A:

Q: 4. Evaluate the following limits. 2* a. lim 3x² -3/x e b. lim x+0 x² 2 In5 x c. limx→→+00 x² 1000 In…

A: This question is related to topic limit of function.

Q: Find the limit.

A: Given,

Q: ni eoulav sd no 2x + 5 13. lim x→-2+\x + 1八 +x ber

A:

Q: d. lim+ In 1000 X X5

A:

Q: ƒ (₂) If lim fx x-0 = L then which of the following must be true?

A:

Q: 25 –1 lim x→1 r3 –1

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.