Let k be a positive number. It can be shown that lim be kb = 0. Use this fact to compute o*xe¯k* dx. b te tr

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A: Here we use L'hopital's rule

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Q: Find the limit (if it exists).

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A: →When limit is of the form 00 or ∞∞ then L'Hospital rule is used.     In this rule, take the…

Q: Q.4: (A) Show that Lim t'i = 4 i t >2

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Q: Q: Prove ha中 Lim x" an %3D

A: we have to prove that the following

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A: Let f(θ)=θ cos θ. The limit exists if both the left-hand limit and right-hand limit are equal.…

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Q: 10 11. Calculate (8 – x) dx in two ways: (a) As the limit lim RN (b) By sketching the relevant…

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A: Limit (f1 i + f2 j + f3 k) = Lim f1 i + Lim f2 j + Lim f3 k

Q: Express the limit lim E (5(x;)* – 7(x;)°)Aæ; over [3, 6] as an integral. n→ 00 i=1 Provide a, b and…

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Q: ex Let frx) = cos x - frx)3Dcosx %- O constract hout X-0 ? the 3rat a Taylor poly Par fx) CA

A: The Taylor's series expansion for a function can be obtained using the formula…

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A: Find B=-limx→0+xx-16sinx

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A: The given expression is: limx→∞sin xx

Q: Prove the following. (b) lim( Vn² +1 – n ") = 0 - (c) lim Vn? n) = } 1 2 ||

A: Prove the following limits

Q: 2. Let r > 1. Prove that lim r" = 00,

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Q: x is the distance 1:- Show that the from morm Il x|l o7 2 to

A: We have to show that x of x is the distance from x to 0 Hence, x can e written as x−0 x=x−0 The…

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Q: Evaluate the following limits. sin- (e") 1. lim 2 V1- e20 1 1 x + sin 2. lim

A: On solving this we will get

Q: e n Show that for any &> 0 and S, ₁X₁, lim P(S₁-0 ≥ 8) = 0. =

A: We will use Chebychev's inequality to find the required limit of probability.

Q: Evaluate the following limit. t t lim cos ti-6 sin j+ -k

A: Given query is to eveluate the indicated limit.

Q: lim, ,0 Ttan(1/r)=? O a. Limit does not exists O b.0 O c.00 O d. 2 O e. 1

A: Given, limx→∞xtan1x

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Q: Express each limit as a definite integral: n lim n→∞, i=1 πί sin + (4 2n. 2 5k -1+ 5k lim 2 п k=1

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Q: Given the sequence an 1 [" 1 dx. Then find lim an-

A: an=1n∫1n1xdx, then find limn→∞an

Q: Find the limit. lim_(cos(t), cos(t), t° In(t))

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Q: Let f(2) = C, be the upper half eircle J2| = R in the counterclockwise direction with R>1, and /= ,…

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Q: Calculate the following limit: lim(2r)ª sin(12 ).

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Q: Determine whether the function u below has a limit as x 0o. If it has a limit, find it. u : R0 → R,…

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Q: then evaluate the limit. n vo Ingolal n69 olulny CILCIC 4 4i 16i2 n V 23. (x – x²) dx, R, = -2 Σ | n…

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Q: Find the limits of the Follo CoS \im

A: Given query is to find the limit of the expression.

Q: 4. lim (cos t)e COS

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Q: a²z If z = arctan ), find ( ay?

A: Given,           z=arctanyx= tan-1yxTo find           ∂2z∂x2+∂2z∂y2=?

Q: Find the limit 1- sin z In (100r² + e*) (a) lim (b) lim 1+ cos 2r 100z

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Q: If zo is a pole of f(z) then the residue of f at zo is lim (z – zo)f'(2). Select one: True False

A: Applying residue property we can conclude this...

Q: Find the value of the given limit. lim tan(4x) I I-0 O a) 1/12 Ob) undefined Oco d) 4

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Q: Suppose u is a finite Borel measure on R, which is singular to Lebesgue measure. Show that except…

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Q: Let sin(2t) F(t) = + cos t, Find the limit lim F(t).

A: We have to find the limit

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A: Given a statement

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Q: - Evaluate the following limit 2 sin z – sin 2r a. lim

A: Evaluate the limit limx→02sinx-sin2xx3