The percentage of movie advertising as a share of newspapers' total advertising revenue from 1995 to 2004 could be approximated by p(t) =  −0.07t + 5.0     if t ≤ 3 0.3t + 12.0 if t > 3 where t is time in years since 1995.   Compute  lim       p(t) t→3−   Compute

Q: Find the slope of the tangent line to the parabola y=4x-x^2 at the point (1,3) 1) using the…

A: Given

Q: In x lim T00 rm m > 0 is

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Q: Note: You may need to assume the fact that  lim M→+∞ Mne−M = 0  for all n.Sales of the text Calculus…

A: To calculate the total future sale of the text.

Q: E valuate Dle followneg: lim メーフ+ 7x" – 4x? + 7x - 2 J +- 3 メ 3x° -8x"+ フメー458 -x一5 x3

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Q: Find lim x→-∞ ex + 1° (а) — оо (b) ∞ (c) 0 1 (d) 2 Does not exist and has no infinite behavior

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Q: Using the Nth term test for divergence, V5n-2 n2 n=1 diverges since lim V5n-2 n² is equal to n→∞ 8.

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Q: In (x +h) – In (x) is When x = 2e, lim h→0 h

A: Substitute x=  2e above

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Q: Find the limit of the exercise below.

A: Factor the numerator using a^2-b^2=(a+b)(a-b) formula. With a=t and b=4

Q: For n > 0, use Taylor's theorem to find (1+x)!/n – 1 lim 3.

A: Explanation of the answer is as follows

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Q: Estimate the limit numerically. lim e-13 x13 a. O b. 13 О с. O d. 0 O e. 1 8.

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Q: find the limit of g(x) as x approaches the indicated value.

A: limx→13x2+1gx=∞

Q: Evaluate lim as x approaches negative infinity 3e^2x + 4e^-x / e^2x - 2e^-x .

A: Limit of a function determines the continuity of a function. Three types of limits exist, one is…

Q: Q1) A- Prove that: cotx = - tan-1x B- Find: 1. lịm 2. lim(v9x2 - x- 3x) cotx

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Q: The processor speeds, in megahertz (MHz), of one particular companies processors during the period…

A: Given that the processor speed in Mhz during the period 1970 to 2000 and can be approximated by the…

Q: Find the limit. V17x + h – V17x lim h→0 h

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: Please

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Q: Find lim (√2-t, et-¹, In(t + 1)) t-0

A:

Q: find the limit of g(x) as x approaches the indicated value. lim (4g(x))'/³ = 2 X0+

A: Consider the given limit as limx→0+4gx13=2

Q: In a lim T→0+ 2x

A:

Q: Find the limit as x approaches - 2 for the function f(x) = 12x + 1. %3D lim (12x+1) = X→-2

A:

Q: 2) If x3 s f(x) sx for x in [-1,1), find lim f(x) if it exists. x-0 A) 0 B) Does not exist C) -1 D)…

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Q: Find limit of lim メ-T(x*1) X-1 X-1 O a, 0 Ob. 1 00 d. None of these

A: Given the function limx→1xx−1   (x≠1)∵x≠1

Q: In a model of the nervous system, the intensity of excitation of a nerve pathway is given by I = E[1…

A: Given  that: I=E1-e-a(S-h)E

Q: for |x| > 1, 2x2 fx,(x) = 0, %3D otherwise. Let L = lim P(max{X1,..., X,} < n log(v5)). Determine…

A: Let Xn be a sequence of random variables such that,

Q: find the limit of g(x) as x approaches the indicatedvalue.

A: Given: limx→-310-x2(g(x))1/3=0 Simplify.…

Q: B. Calculate the limits of the following functions.. 1. limx¬-1(2X2 + X + 4) 2. limy--2(y3 + 5y – 1)…

A:

Q: 15) Annual U.S. imports from a certain country in the years 1996 through 2005 could be approximated…

A: Given I(t) = t2+3.5t+48    (1 ≤ t ≤ 9)E(t) = 0.5t2−1.4t+13    (0 ≤ t ≤ 10)

Q: Please find the limit (in terms of the constant a).

A: it is given that

Q: 1 Use a plot of f (x) = 4 Vx - 2 to estimate lim f(x) 4 メ→4 | numerically.

A: Given: f(x)=1x−2−4x−4Estimate:limx→4f(x)=?Graphically  and  Numericallly

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A: To determine the value of the limit.

Q: 3. Is lim f(x) always equal to f(c)?

A: Is limx→cfx always equal to fc The given statement is not necessarily true.

Q: For f(x)=√7x+2, find f′(x) using the definition f′(x)=limh→0f(x+h)−f(x)/h. f′(x)= Using this, find…

A: Equation of the line passing through the points x1,y1 and having slope m is y-y1 =mx-x1.

Q: Use the graph to compute the quantities asked for. y lim, 3 f (x) does not exist -1

A: our objective is to find the limit

Q: Find the maximum value of & > 0 that satisfies the limit claim corresponding to e = 0.3, that is,…

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Q: Determine the limit at infinity. 4x -6x2 + 3x lim - -x - 2x+6 O A. 4 OB. OC. 0 D. 4.

A: Given limit is Dividing both numerator and denominator by x^3, we get

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Q: Find the limit. 4) lim (e5/x - 6x)\/2 x-0+

A:

Q: (6) Draw the graph of a (a) function ƒ satisfying Y S(1) = 2, S is continuous at 1. What is lim,→1…

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A: By L' hospital rule we solve above limit.

Q: + 34, find f '(x) using the definition f '(x) = lim h→0

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Q: Evaluate the limit t3 – t lim t→1 t2 – 1

A: We have to find the given limit.

Q: Q5. Evaluate the limit Vx+h- Vx lim h-0 Vx+h+Vx in the two cases (i) x > 0 and (ii) x = 0.

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Q: Find lim 4(x) (x) / X-0 x 2. Prove that B(m, n)

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Q: For f(x) = 2x³ - 2, find ƒ '(x) using the definition f '(x) = lim f(x+h)-f(x) h h→0 f'(x) = Using…

A: Let's find.

Q: 6) Find lim f(x). X>T/2

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Q: Determine a reasonable estimate for lim hx x-1 3 -5 -4 -3 -1 3 5 2. 1 4. 1. 1. 2. ee

A:

Q: Prove that lim n 00 a" f (x) dx = 0, for any f E R[0, 1].

A:

Q: Find the limit x-1 lim x>I* Vx +2

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.