Show that 13x - 12 can be made as small as desired by taking x close to 4. lim(5x + 2) = 17x➔3

Q: If 4x - 9  ≤f(x) ≤ x2 -4x +7 for x ≥ 0  , find lim x->4 f(x) .

A: We apply limit on all the sides of the given inequality.

Q: SOLVE BY LIMIT DEFINITION x-1 d) limx→3 6-2x

A: To find: Value of the limit, d limx→3x-16-2x

Q: Find lim 1+ (if it exists) X→ 00

A: Solving the problem by finding the limit.

Q: If 3x - 4 s f(x) sx2 - 3x + 5 for x 2 0, find lim f(x). x-3

A: Given, 3x-4 ≤ fx ≤ x2-3x+5              for  x ≥ 0 We have to find limx→3fx

Q: For all x ≥ 0, 4x − 9 ≤ f(x) ≤ x 2 − 4x + 7. Find limx→4 f(x). ⇒

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Q: x³ + x² - x - 1 lim X→1 X-1

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Q: Show that 13x - 12 can be made as small as desired by taking x close to 4. lim 3x = 12 x➔4

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Q: Find the following: x+/3 + 9x/5 (2х — 1)4/2 — 3 i. Lim- X-0 6x/2 – 4x'/4 ii. Lim x→5+ х — 5

A: we are solving only part (a) of the question because it contains super subparts. Please upload the…

Q: Find lim,00(e3 +2x)/* 1/x

A:

Q: Find lim?→∞ for (5x2-100x+sin2x) / x2. Thank you!

A: Please see the below picture for detailed solution.

Q: sqrt(5-2x^2)0 f(x).

A: This question we can solve with the help of sandwitch theorem-

Q: Show that lim,→»(1+ e* for any x > 0.

A: To prove:

Q: When demonstrating that lim 4x + 3 = 7 with ɛ = .07 Find the largest value for ɛ that will suffice

A:

Q: Find each of the following limits: x² + 7x (a) limz→-7 49 – x² ' 7x3 + 25x² – 9x + 105 (3x + 1)²(2x…

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Q: If √5 − 2x^2 ≤ g(x) ≤ √5 − x^2 for −1 ≤ x ≤ 1, find limx→0 g(x)

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Q: Find the following: x/3 + 9x/5 i. Lim X0 6x/2 - 4x!/4

A:

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: Find the limit. 16x(3x + 16)² lim 1 4

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Q: 4. Find the following algebraically. -2x – 4x +4 a. lim x³ – 27 x - 2 b. lim V9x² +1

A: SOLUTION-

Q: Suppose a is a constant and if x> 3 f(x) = {x? if 2 <x< 3 x+a ifx< 2. (i) Find lim f(x). X+2+ (ii)…

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Q: Estimate the value of lim 1 + 3x 1 by graphing the function f(x) = x/(/I + 3x – 1).

A: It is given that limx→0x1+3x-1 It is known that if we have limx→af(x)g(x), and after plugging the…

Q: Find lim,x - Vx²+ 2

A: To find the limit

Q: If 3x – 1 0, find lim f(x). X→3

A: Given query is to find the indicated limit.

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: lim x X49

A: As we know that: limx→afx=fa Given: limx→ 49x

Q: 4. Evaluate: lim(x² - 10x) x→6

A: This question can be solved by replacing x by 6 in the expression x2-10x.

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

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Q: Find the exists. 5 x а. lim 3 5x'+1 b. lim 10х-3x +7

A: Given that: a. limx→-∞5x-x3b. limx→∞5x3+110x3-3x2+7c. limx→∞5x2+2x2+3

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

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Q: De nty. lim Bx+5 6+X6-

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Q: lim (3x + 5) = 2, x→-1

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Q: Find the following: x+/3 + 9x/5 (2х — 1)1/2 — 3 - i. Lim- x-0 6x1/2 – 4x1/4 ii. Lim x→5+ х — 5

A: a)

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

A:

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

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Q: . Is it possible that f(2) = 5 but limx→2 f(x) = 7? If so, what kind of function can satisfy this?

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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: If 2x – 2 0, find limf (x). x→1

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

Q: 7x + 5 If 1(x) = find lim,-o 1(x) 8x + 1'

A: t(x) = 7x+58x+1limx→∞t(x)= limx→∞7x+58x+1taking x common= limx→∞x(7+5x)x(8+1x)= limx→∞7+5x8+1x=…

Q: Show that 13x - 12 can be made as small as desired by taking x close to 4. lim(4x 2 + 2x + 5) = 5x➔0

A:

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: 2) lim X+1-x1 メーーt メーー 2x+2

A:

Q: 7x2 + 10x a3 – 1. lim x→2 x2 + x – 6

A: Given, limx→2x3-7x2+10xx2+x-6

Q: Find the following: x1/3 + 9x+/5 х-о бх1/2 — 4x1/4 (2х — 1)1/2 — 3 ii. Lim х — 5 i. Lim х-5+

A: i. Here limit is,

Q: If -a2 + 6x – 7 < f(x) < 2x – 3 for all r, find lim f(x). Cite any relevant theorems used.

A: Given that,  -x2+6x-7≤fx≤2x-3 To determine limx→2fx. By the algebra of limits, If gx≤hx  then…

Q: Find the following: A)) lim x+1 x-3 lim B)) x4 x+1

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

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Q: If /6 – 5x2 sf(x)sV6-x² for - 1sxs1, find lim f(x). N6-5x² lim f(x) = X→0 (Type an exact answer,…

A: Solve by taking limit both side

Q: 10. lim is X-- А. со B. -00 С. -1 D. 1

A:

Q: Show that 13x - 12 can be made as small as desired by taking x close to 4. lim (7x - 4) = 10x➔2

A: Let . Domain of f(x) is R and limit of the function is two. The limit of the function is a real…

Q: Let f(x) = x^2 − 10x. If you construct an ϵ-δ proof to show that limx→5 f(x) = −25, what is the…

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.