S 1/x ifsxs1 n*x if 0sx< Given fn : [0, 1] → R, defined as f,(x) = then the point wise limit of f„(x) is

Q: Express the limit as a definite integral on the giveninterval.

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Q: Q3) Find the limit for the following function by using L'Hopital's Rule: x2. e* lim x→0 tan2 x

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Q: if r = -1 Is f(r) = · continuous at r= - -1? (Show your work using limits.)

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 7. Express the limit as a definite integral on the given interval: n lim n- 00 3 tan x; Ax , [0, 1 ]…

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Q: If lim 2 4xk (1-3xk')Axk, a = - 3.b=3· Then the correct expression for the limit as integral is: k…

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Q: Express the limit as a definite integral on the given interval. [9(x†)3 – 4xj]Ax, [2,9] lim n- 00 i…

A: Express the limit as a definite integral on the given interval.

Q: Express the limit as a definite integral on the given interval. n lim x; In(1 + x²) Ax, [0, 1] i = 1

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Q: 6 — х — а? if x 1 - Calculate the following limits. Enter "DNE" if the limit does not exist. lim…

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Q: Compute the following limits if they exist: sin 2x – 2x (a) limit sin 2x - 2x +у x3 + y (b) limit…

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Q: Express the limit as a definite integral on the given interval. n eši -Ax 4 + X; lim [0, 2] i = 1

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Q: Express the limit as a definite integral. [Hint: Consider f(x) = x*.] lim n- 00 dx

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Q: 32? And are

A: {x2                               if x&lt;-2f(x)={x1/5                           if…

Q: Express the limit as a definite integral on the given interval. n lim -Дх, [1, 8] n→* i = 1 (x;)2 +…

A: Definition of definite integral: ∫abf(x)dx=limn→∞∑i=1nfxi*∆x in the interval [a, b].

Q: Express the limit as a definite integral. 4 lim non + (i/n)- (i/n)9

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Q: Express the limit as a definite integral. n 7 lim 8 1 + i = 1 n- o n dx

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Q: V5+s-V5 lim s→0 S

A: lims→ 05+s-5s=lims→ 01s+5+5Plug in the value s=0=10+5+5=125

Q: 1 Q.3: Discuss the limit of f (x) : at x = 0", 0*,-∞,+∞, with graphs.

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Q: Show that the absolute-value function y = t(x) = |x − 5| is NOT differentiable at x = 5. (Hint: by…

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Q: Express the limit as a definite integral on the given interval. lim n - 00 cos(x}) Дх, [2л, 5л] Xi i…

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Q: 3. Express the limit as integral: n lim Σcos (27xt Ar 2(2πχ* ) over [0,1]

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Q: Express the limit as a definite integral on the given interval. n X;* -Дх, [1, 9] lim (x;*)² + 4 n-…

A: limn→∞∑i=1nxi*xi*2+4∆x,    1, 9 Here, fx=xx2+4, a, b=1, 9

Q: Express the limit as a definite integral on the given interval. x lim n- 00 -Ax, [1, 6] (x/)2 + 6 dx

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Q: Compute the limit as x goes to 0 of [tan(x) - sin(3x)] / (x^2)

A: limx→0[tan(x)-sin(3x)]x2=[tan(0)-sin(3(0))]02=00

Q: Express the limit as a definite integral on the given interval. lim (2-5(x,)² + 6(x;")³] Ax, [0, 4]…

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Q: 2. Compute xe" da using a limit.

A: The given which we have to find the integration from 0 to ♾️  f(x) = xex

Q: Express the limit as a definite integral on the given interval. -Дх, +7 [1, 6] lim dx J1

A: The following limit is expressed in the definite integral as shown below

Q: (4- x - x² if x ≤ 2 2x-7 if x > 2 Calculate the following limits. Enter "DNE" if the limit does not…

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Q: Express the limit as a definite integral on the given interval. x; In(1 + x3) Ax, [2, 3] lim 3 dx

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Q: Express the limit as a definite integral on the given interval. lim n- 00 [4(x;)³ – 4x;"]ax, [(2, 7]…

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Q: Express the limit as a definite integral on the given interval. cos(x) Дх, [2л, Зл] X; lim Зл dx 27

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Q: Express the limit as a definite integral on the given interval. lim Ax [О, 6] 9 + X; i = 1 dx

A: The answer is found in step-2

Q: The improper integral f(x)dx can be written as lim f(x)dx + lim_ f" f(x)dx . w--00 w+00 If f(x) =…

A: use the above definition of improper integral

Q: Q.3: Discuss the limit of f (x) = - at x = 0¬, 0*,-∞, +∞, with graphs. %3D

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Q: Let fn: R --> R be defined by : fn(x)= x/(1+nx2), For all n >= 1. a) Show that {fn} converges…

A: step:-1 Theorem:- Let fn be a sequence of functions on I such that for each n∈ℕ, f'n(x) exists for…

Q: Express the limit as a definite integral on t lim n-oLX; In(1 + x;²) Ax, i=1

A: Given that: 1. limn→∞∑i=1nxiln(1+xi2)∆x, [0, 1]2. ∫13(x-4lnx)dx

Q: Express the limit as a definite integral on the given interval. lim Σ Σ x;* -ΔΧ, [1,4] 0-700 (x;*)2…

A: To express the given limit as a definite integral.

Q: Give an example of a limit of the form 0/0 that convergesto 1 as x -&gt; 0.

A: Given: Rx=fxgx is a function such that limx→0Rx is of the form 00 and converges to zero. To…

Q: Express the limit as a definite integral on the given interval. n -Ax, (x;")2 + 6 [1, 5] lim i = 1 5…

A: Given query is to express the limit as definiye integral.

Q: Express the limit as a definite integral on the given interval. lim S 19(x/)³ – 8x;]Ax, [2, 5] 1

A: The definition of definite integral is, ∫abf(x) dx = limn→∞ ∑i=1n f(xi*)△x   in the interval a, b…

Q: Find the limit as x approaches zero of f(x)=tan(x)/x

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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: Express the limit as a definite integral on the given interval. x;* -Ax, (x;')² + 2 lim n- co [1, 6]…

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Q: Express the limit as a definite integral on the given interval. lim x, In(2 + x^)Ax, [3, 4] n- 00

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Q: Let f(x) 2.x – 5 if x > 5 --- Calculate the following limits. Enter "DNE" if the limit does not…

A: Here we have, f(x)=10-x-x2 if x≤52x-5         if x&gt;5 We have to calculate,…

Q: Express the limit as a definite integral on the given interval. lim 8x; + (x;)² Ax, [3, 8] dx

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: If lim 2 4xk (1-3xk)Axk,a= - 3,b=3 Then the correct expression for the limit as integral is: k =1…

A: Let's find.

Q: Express the limit as a definite integral on the given interval. lim (4(x")3 – 3x;]Ax, [2, 6] n- 00 i…

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Q: Does fn converges to L1 and L2 i.e the distance between fn and f goes to 0

A: By the theorem: A metric  on BE is the uniform metric du  . A sequence of bounded functions fn:E→ℝ…

Q: Suppose  f is continuous on [0, ∞) and limx→∞ f (x) = 1 . Is itpossible that  ∫ 0∞f (x) dx is…

A: Consider a function f(x) which is continuous on [0, ∞) with limx→∞f(x)=1. The objective is to…