| kx – 3, r<–1 r² + k, r > -1' Given f(x) = find the value of k such that lim f(x) exists.

Q: x sin(2x) 1- cos(x) limr→0 | А. О В. 1 С. 2 D. 4 E. the limit does not exist ||

A: The given expression is limx→0xsin2x1-cosx. Evaluate the limit limx→0xsin2x1-cosx as shown below.

Q: If V 16x <f(x)sx+4 for all positive x-values, then what is lim f(x)?

A:

Q: Find the limits x2/3 + x1 lim X00 x2/3 + cos?x

A: Given: The function is f(x)=x2/3+x-1x2/3+cos2x   To determine: limx→∞ x2/3+x-1x2/3+cos2x

Q: Prove that

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Q: IV. Let f(x) = cos x and t e R+. f(x) – f(t) Vrt – t lim 2 =? x→t -

A: If we have one of the following cases, limx→a F(x)G(x) = 00  OR,  limx→a F(x)G(x)  = ±∞ ±∞ where a…

Q: If f(x, y) approaches 1 as (x, y) approaches (0, 0) along the path y = mx, where m is any real…

A: To check whether the given statement is true or false.

Q: 1. Find the limit if it exists. V2 + t – /2 – t - lim t→0 3t

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Q: The value of the limit lim a) 0 b) 1 c) d) ∞ 1 X x-0 sin x sin x 6 is

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Q: Find the value of the limit lim SINX X 0 2x 02x (a) 0 (b) 1 (c) 1/3 (d) 1/2 (e) 1/4

A: Here we have to find the limit of the function. In the first step use the property of the limit:

Q: 2.a²y rª + y? Show the function f(x,y) : has no limit as (x, y) → (0,0)

A: We have to show that the function fx,y=2x2yx4+y2 has no limit as x,y→0,0.

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

A:

Q: Consider the function f(x) = vx for xE R and 0 <x < 32. Prove that lim,-s f(x) = 4. %3D

A: Given: f(x)=x for x∈ℝ and 0&lt;x&lt;32 we have to prove that limx→16f(x)=4

Q: Express the limit as a definite integral. lim 40 E xk A xk; [-5, 1] k=1 1 9x8 dx -5 x9 dx x9 dx x dx

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Q: Assuming h > 0, compute Vx - Vh lim x→h X-h (a); Vh (b). 2h (c) (d) 2h (0)

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Q: Find the limit. t2 j+ sin(7t) k sin2(t) -2t ¡ + lim t→0 e

A: We have to find the limit: limt→0e-2t i+t2sin2t j+sin(7t) k

Q: Q2: (a) By using " L' Hopital rules "; Find the limits of ::- (1) lim,-(7/2)-(tan x)" (2) limy-o…

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Q: Find the limit. O 75 π O O' O O I 00 D8 - 150 lim sin¹. 5 x X→ 0 ¹7x

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Q: Choose the correct answer for the following limit Q1_V1_M S sin t3 dt lim x-0 1 2 x4 (A) 3. (B) -1 3…

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Q: Find the limit as t-➜0 of r(t)=

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Q: Find the limit. 3 - ti + In(t)j k t-3

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Q: Express the limit as a definite integral. 7 lim n- 0 n 3 1 + (i/n) i = 1 '1 7n dx 8.

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Q: is lim x = inf (xn) as x, y. What Express answer and = 3n lim sup (xn) where Xn = [(-1)³ ]+2?

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Q: 4. Evaluate the limit of as e approaches 0. 2a A 2 B. % CO D. infinity

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Q: Use the Squeeze Theorem to prove lim = 0. x00 x+ e- For x 0, since 0 < e* <1, we have

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Q: f(x) = { S -4x? + 4x for x 0. According to the definition of the derivative, to compute f'(0), we…

A:

Q: 1 -1 lím (x,y)→(0,0) tan x² + y?

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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: Compute the limit as xà0 of f(x)=(sin(61x))/x, if possible.

A: To find:limx→ 0sin61xx

Q: Find the limit V1+t4 dt lim

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Q: X,xif limF,(t)= F(t) at all t for which Fis Continuous

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 4 Find lim cos C→十0 Enter I for o, -I for –∞, and DNE if the limit does not exist. Answer:

A: Topic = Limits

Q: Find the limit of the function along the x-axis xy lim (x.y)-(0,0) x2 + y?

A:

Q: Find the limits by rewriting the fractions first.

A: We have to find the limit: limx, y→0, 01-cosxyxy Rewriting the fraction using trigonometric formula,…

Q: If [ f(x)\dx<∞ show that limf(x)dx=0 k→∞00 1

A: We have to prove that given expression.

Q: Q2: (a) By using " L' Hopital rules "; Find the limits of ::- (1) lim,-(n/2)-(tan x)cosx (2) lim,--0…

A: L'Hôpital's rule states that for functions fx and gx which are differentiable on an open interval I…

Q: Express the limit as a definite integral. [Hint: Consider f(x) = x2.] lim i = 1 n' xp 1.

A:

Q: nd the limit: lim (e-3t i+ j+cos 2t k) sin2t

A: We have to find limit

Q: In(t³ + 1) + t³ + 1 r(t) = 4: then the limit lim r(t) equals 1-0 -i-(4e-²¹-5e²¹)j- - sin³t -k, 13

A:

Q: Find the limit analytically: 2-4x lim 40 5+3x x? - 2.x -15 lim x 5 2. 3. Find dy/dx of:

A: A number M is said to be the limit of a function f(x) at x=a if for any arbitrarily chosen positive…

Q: Q3) If the function (2x + 1 +2 x > h) XSh f(x) having limit at x = h. Find the value of h. Q4) f(x,…

A: Our objective is to solve the above questions.

Q: (4x – 5y) lim (x,y)→(1,1) 5x² – 7y O -1/2 O 1/2 Limit DNE

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Q: Find lim r(t) when 5 In t r(t) = (: 2 tan¬lt, e-2 t 2 tan-t, e 1. limit = (2т, —2, 0)

A: Given    r(t) = 2tan-1t , e-2t , 5 lnttwe need to  find  the limt→∞ r(t)=?

Q: S -2x? + 5x 7x² – 5 for x 0. According to the alternate form of the definition of the derivative,…

A: Given:

Q: f(x) lim sin(5x) X I 0 -0.25 3 2 Estimate the limit numerically or state that the limit does not…

A: We have to find out limit

Q: Find the limit by numerically. 1 lim 1 + |t| |t – 1| t-0

A: To find the limit numerically, consider approximately some values of t which are closer to 0 from…

Q: Find: a. f (0) b. limit of f (x) as x approaches 2 from the left c. limit of f (x) as x…

A: We have to find

Q: Find the limit of f(x) = as x approaches co and as x approaches - oo. 4 -

A: Given,          fx=-4+2x4-6x

Q: Express the limit as a definite integral. [Hint: Consider f(x) = x*.] n lim n5 i = 1 1 7n 2n dx

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Q: Find the limit: lim f(x) as x approaches 0 of Kx2 - tan2 (mx)cos(mx)/x2     (m not =0)

A: Consider

Q: -5x? + 2x for æ 0 According to the definition of derivative, to compute f'(0), we need to compute…

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Q: 1-e X x2 +1 X By using the limit comparison test, the integral

A: Using, limit comparison test

Q: Evaluate the following limits.

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Q: O3: A- Find the limit for the following functions: - tan2x 4х-3 3x3-9x2+x-3 1- lim x→0 sin4x 2- lim…

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Q: S, f(x) dr may not equal lim , f(x) dx. Show that 2x dx x* + 1 diverges and hence that 2x dx ? + 1…

A: