1. Evaluate the following limits (if it exists) (a) lim X3 Vx+6-x (b) lim ズ→1 Vx-1+x2-x ズー3 xー1 2x (c) lim (* (d) lim ズ→1 Jx2+1 xー1

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

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Q: # 3) lim (2x - 4x2 - 5x+6) X→-3

A:

Q: Show that lim(5x+2)=-18 x-> -4

A:

Q: 21 f(x)= 3x2 +4x +1 and g(x) = x2 -2x-3, then what is lim f(x) *→19(x)?

A:

Q: 7). lims X-1 メ→ド X-1

A: The value of the limit is, 4  The detailed solution is as follows below:

Q: xV1-3x lim | V1-4x3 I-00 %3D

A: Suppose L is limit value of given Limt

Q: Find the one-sided limit

A: To find:limx→-4- x2+2x+4

Q: B. Factoring method 1. Lim x-3/x2-18x+45; x= 3 2. Lim x2-64/x+8 ;x= -8 3. Lim x2+8x+16 ;x-1

A: There is the solution.........

Q: 6x5 + 1 lim x→00 2x5 +3x2 + 4

A:

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

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Q: Find lim f(x) if, for all x > 1, X-00 12-16 4√x f(x). < зех x-1

A: Step 1: Step 2: Step 3: Step 4:

Q: limx→∞42x3+2x2-2x/353+x2+4X+5=   What is the limit?

A: Given expression is We need to find the limit.

Q: V1-x3 16. lim х+1+ V1-x2

A: limx→1+1-x31-x2

Q: .3 2x -3x lim Зx3 +4 Typ (Туp

A:

Q: +64 1. lim (3x-x² + 2) = 6. lim X-3 X-4 4x+16A 2x2-x-3 x+1 2. lim 7. lim X-1 х+1

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Given f(x) = 3/(4-x)3 , evaluate limx=4+ f(x)

A:

Q: V1-x3 15. lim x-1- V1-x2

A: the given limit is: limx→1-1-x31-x2 we have to evaluate the given limit.

Q: Evaluate lim f(x), f(x) = (3x² + 5x − 1, (7x² - 2x - 3, x ≤ 2 x > 2

A: Topic:-  limit and continuity

Q: Evaluate the limit

A: The given limit is limx→ -∞ 3x7+x5-154x2+32x.

Q: limx²+x+I -| Glim 5-x? 5-22 - 2 ズー1 lim -6 -1

A: 4) limx→0x2+x+1-1x00 form=L'Hlimx→012x2+x+1(2x+x+1)-01=limx→02x+x2x2+x+1=0

Q: 4x2-x- V9x2 –x lim

A: Given: limx→∞4x2-x-9x2-xx

Q: x²+6x+9 4. lim X--3 x+3

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Q: 2 lem -9 ズ→ス x-4

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Q: 5. Find limf(x) x4-3 a) f(x) = 5x4 %3D 6x4 - 3 b) f(x) = 3x3 2x3 - 9 c) f(x) = %3D 3x5

A: We have to find limx→∞fx for a fx=x4-35x4b fx=6x4-33x3c fx=2x3-93x5 Since all above limit has ∞∞…

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.