Which of the following is true? А. lim Ax) =- and lim fx)=-0 x→ 3- x → 3* В. lim f(x) = -00 and lim f(x)= ∞ x→ 3- x → 3* С. lim f(x)= ∞ and lim Ax)= -∞ x → 3 x → 3* D. lim Ax)= 0 and lim f(x)= 0 x → 3 x→ 3*

Q: x tan 2x-2x tan x lim- x→0 (1cos 2x)

A:

Q: 2. lim (x - Inx)* x)² 2-0+

A: Here, the given limit is: limx→0+(x-ln x)x which is (-∞)0 form.

Q: Let f(z) 2 = = (-)². Show that lim f(z) does not exist. z➡0

A:

Q: (x² – x – 2)(2x +3). Vx² +5-V3x +3 6. lim =... .2 x2

A:

Q: iv. f(0) = Preview v. lim f(x) = x→7 Preview vi. lim f(x) x→7+ Preview

A:

Q: A) Vx2 +8-3 lim x-1 x+1

A: By using l'Hospital's rule we solve the given problem as follows :

Q: If h(x) →5 as x→ 1 and k(x) → 0+ as h(x) k(x) X→ 1 ? x → 1, then what is lim L

A: solution:-Givenh(x)→5  as x→1k(x)→0+   as x→1

Q: Evaluate using the identity a3-b3 = (a-b)(a2+ab+b2)

A:

Q: 3) If the lim f(x) = 2 and lim f(x) = -1 %3D x-3- x-3+ Then what is the lim f (x) = x→3 %3D a) Why?

A: To find the limit of the f(x) at x=3

Q: |x + 2 x + 2 17. а. lim (x + 3) b. lim (x + 3) x→-2+ x + 2 x→-2 x + 2

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Q: 4x3-2х с) lim x→00 V2x4+1

A:

Q: Show that lim (2,v)>(0,0) **+y D0.

A:

Q: A B C D lim /(x) = 0 x+2+ lim f(x) = 2 x →-2+ lim /(x) = 0 x+2- lim f(x) = -3 x--2 -5-4-3-2-1 Y -3-…

A: Find limit of function

Q: 1. lim x- 2x + 6

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: Determine the following limits by inspection and choose the correct option from those given: x+1 I.…

A: To find the limitsI) limx→ 0x+1x2exII)limx→- 3+2x-1x+36III)limx→∞x-x

Q: Which of the following statements is true? ху- 4y 1 A lim 2 (x.y) (4,0) x2-8x+y² + 16 V2x+y-3 lim…

A:

Q: Let h(x)

A: hx=x2,      x<23,       x=22,       x>2 Now, The left hand limit at x=2 is,…

Q: 4. Show that im (XM) (110) хуу (x-4)² + y² does not exist.

A: see below the calculation and explanation

Q: x²-1 2. limx-1 1-x

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: valuate 10-Vx a. lim x→100 x-100 b. lim (-2x+4)²–4 1 c. lim *+2 5 x→3 x-3 X-3 3-x

A: Given that:

Q: Given the function f(x) = Which f the following is/are true? (x- 1)(x + 1) 1. lim f(x) = +00 2-1+ 2.…

A:

Q: 4-X 1) Lim メ→4 5-x²49 2.

A: To evaluate the below limit. limx→ 44−x5−x2+9

Q: e graph of y = f(x) is shown. Assume f'(x) is continuous. 8 7 6 5- 4 3 2 -7 -6 -5 -3 -2 -1 nd xf(x)…

A: Given query is to find indicated limit.

Q: (4+ 43) (x + 43) -(16 + 43)x limy→ -43 limx. x + 43

A:

Q: x+5, x<1 f(x)= - x+7, x21 19) a. lim f(x) b. lim f(x) c. lim f(x) x1* (2 15

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.