Suppose that lim 2f(x) + 3x – 15 = 5. Find lim f(x)

Q: Suppose that lim 4f(x)+ 2x – 14 5. Find lim f(x). z→1 %3D z→1 x – 1

A: Given

Q: Evaluate the limit. x² +3x - 10 lim-5 2x + 10

A:

Q: Find the limit. lim x→-2 x2-4/x+2

A:

Q: What is lim1 f (x) ? X

A: Find your answer below

Q: Find the limits a) lim x2 - 4x + 3 x2 - 1 when x approaches 1 b) lim 6x + 100 7x2 100 when x…

A: We have to find the limit

Q: Find limx->∞,if for all x>5

A: We apply limx->∞ on all sides.

Q: If 2x - 2s f(x) sx² - 2x + 2 for x 2 0, find lim f(x). x-2

A:

Q: What is lim f(x)? X-1

A: Given graph: To Find: limx→1f(x)

Q: Evaluate the limit: lim 4e10x – 4 13x - x→0

A:

Q: If lim as f(x)-4/x-3=2 as x approaches 5, find lim f(x) as x approaches 5.

A: We have

Q: Use the definition to prove that lim,→∞ x² = ∞.

A:

Q: evaluate the limit lim (x + 1)(3x^2 − 9) x→2

A:

Q: Find the indicated if it exists: lim x to 8;  2x2+3x+1 divided by x4 - x2

A: To find the limit if exists

Q: .) Find the limit or show that it does not exist. lim √25t²+2-5t 1-x

A:

Q: Evaluate in terms of the constant a.

A: We have to find the limit in terms of constant a: limx→02a+x This is determinate limit so we need to…

Q: If 7-6x2 sf(x)s 7-x² for -1sxs 1, find lim f(x). X→0 lim f(x) =

A: If 7-6x2≤f(x)≤7-x2 for -1≤x≤1, we have to find limx→0f(x)

Q: If the lim f(x)-7/x-5 as x approaches 6 = 1, find lim f(x) as x approaches 6.

A: First we use the substitution property of limit and substitute 6 for x .

Q: Evaluate in terms of the constant a. lim (2a + x) x→ 0

A: To Determine:  Evaluate in terms of the constant a.…

Q: Find a number b such that lim- .2. x²-4 =2 x-b x-x -2

A:

Q: If 2x – 2 < f(x) < x² – 2x + 2 for x 2 0, find lim f(x). X-2

A: The objective is to find the limit.

Q: find the limit or explain why it does not exist.

A: We have to find the limit: limx2+5x+5x3+3x2-11x For the given condition, a. as x→0 b. as x→3.…

Q: Find the limit. lim              x2+5/5x3-2 x→+∞

A:

Q: Find the limit. 5) lim /2x + 5 5) x-6

A:

Q: b) limx-2+ 72-4 x²– 4

A: To evaluate: limx→2+x-2x2-4

Q: Find the value of * lim - 1 - 1 1 +x

A: Let us take f(x)=x11+x-1. Then we have to find limx→0f(x).

Q: Find the indicated if it exists: lim x to +infinity;  2x2+3x+1 divided by x4 - x2

A:

Q: what is the lim x->0  f(x)-f(0)/x^2 if f(x)=2x^2+1?

A:

Q: Find lim *2 x -2 In(x- 1) by using the La'Hospital Rule.

A:

Q: lim (3x + 5) = 2, x→-1

A:

Q: Find the limits 2 lim x→0+ x/5

A: Given that limx→0+2x15. As x tends to 0, the denominator of the function 2x15 tends to 0.

Q: Find the limits limx→1+x1/(x-1)

A: limx→1+xx-1

Q: Find lim_f(x), if it exists. If it does not exist, explain why. X--4"

A: Follow the procedure given below.

Q: If 5-4x sf(x)s5-x for - 1<xs1, find lim f(x), lim f(x)%= f(x) =D

A:

Q: If 3x – 2 s f(x) < x² - 3x + 7 for x 2 0, find lim f(x). X3

A: 3x-2≤f(x)≤x2-3x+7

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

A:

Q: If 3x − 1 ≤ f(x) ≤ x2 − 3x + 8 for x ≥ 0, find lim x→3 f(x).

A: Here we use sandwich theorem Also known as squeeze theoremThis theorem states that , if gx≤fx≤hx in…

Q: Find. 1) a. lim f(x) and b. lim f(x). 3- 4-

A: Answer and explanation is given below..

Q: Suppose that limx→ -2 p(x) = 4, limx→ -2 r(x) = 0, andlimx→ -2 s(x) = -3. Find lim x→ -2 (-4p(x) +…

A: Given limx→-2p(x)=-4 , limx→-2r(x)=0 and limx→-2s(x)=-3We need to find:limx→-2-4p(x)+5r(x)s(x)

Q: 3x lim x→∞ √x²+1

A: We can evaluate the limit as below.

Q: If 2x – 2 0, find limf (x). x→1

A: We can use the sandwich theorem to solve this question.

Q: Suppose that limx→ -2 p(x) = 4, limx→ -2 r(x) = 0, andlimx→ -2 s(x) = -3. Find x→ -2 p(x). r(x) .…

A: Suppose that limx→-2p(x) = 4, limx→-2r(x) =0, and limx→-2s(x) =-3.

Q: Find  lim x+8/x-1 as x approaches -2 approaches

A:

Q: If 2x - 2s f(x) S x² - 2x + 2 for x 2 0, find lim f(x) x-2

A: see below the answer

Q: 4x + 12 lim 2 x 3 x²9

A:

Q: Which property of f(x) = x' allows us to conclude that lim x- 8?

A: f(x)=x3 is a continuous function. So, it is continuous at x=2 also.

Q: If 3x – 2 s f(x) sx² - 3x + 7 for x2 0, find lim f(x). x-3

A:

Q: If /10 - 7x sf(x)s/10 -x for -15xs1, find lim f(x). x-0

A:

Q: Find the limit or show that it does not exist. Vī lim 1+4x6 2- x'

A: To find the limit: limx→ -∞ 1+4x62-x3

Q: Use the –δ definition to prove that lim x→1 (3x + 5)/2 = 4.

A:

Q: Q2: Use lim x 0 and lim x 0 to show that lim x = 0.

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.