3. EVALUATE AS AN INFINITE SEMES: 0.5 a. e dx lim x- In (1 + x) b.

Q: Evaluate the following limits.

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Q: e) sec mx – 1 lim

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Q: e2x – 4 3. lim 1→In 2 x – In 2 tanh x 4. lim 1→0+ sech.x – 1 5. lim e"(cschz)

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Q: Evaluate the following limits. 1 - cosh x 1. lim x+0+ ln(x² + 1)

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Use L'Hôpital's Rule to calculate the following limits. te (c) lim t-0 1- e sin z + tan r (a) lim…

A: Part (b) Given limx→1x2-1lnx

Q: Evaluate the following limits, where c and k are constants.

A: Factorise the equation in numerator by splitting the middle term and the equation in denominator by…

Q: In the given equation as follows , determine whether the statement is true or false. If it is false,…

A: f is continuous function on [0,∞) and ∫0∞f(x)dx diverges

Q: 8. Evaluate the limit dx lim C) E) 3 B) 1 D) 4

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Q: Determine the following limits analytically.

A: Given, limx→π3sinπ3-x2cosx -1

Q: Which of the following expres zy 0 = .lim(z,9)¬(0,0) F+ y²

A: Let us substitute: y = mx Then we get, Limit as (x, y) tends to (0, 0), [(xy)/(x2 + y2)] = Limit as…

Q: I. Evaluate the following limits. x sinh x 1. lim x-40 cos 3x – 1

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Q: Choose the correct answer for the following limit So sin t3 dt 2 x4 lim (A) 3 (B) -1 3 (C) 1 8. (D)…

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Q: E valuate the limit below : n lim Ź nうo i =1

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

Q: - Complete the following statement. (x? + 3) dx = lim where Ax = and x; is

A: To complete the statement

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

A: Explanation of the answer is as follows

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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Q: Find the limits

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Q: 4. Use the sandwich theorem to find the following limits: sin x (a) lim cos x (b) lim

A: a) -1≤sin x≤1⇒-1x≤sin xx≤1x⇒limx→∞-1x≤limx→∞sin xx≤limx→∞1x⇒0≤limx→∞sin xx≤0⇒limx→∞sin xx=0(using…

Q: ind the following limits using I sin(Tx) lim -0 tan(ex)'

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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: Use l’Hôpital’s rule to find the limits

A: We have to find the limits of the function by L'Hospital's rule: limt→∞et+t2et-t If we limits are in…

Q: Evaluate the limit, using L’Hôpital’s Rule if necessary.

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Q: Evaluate | re dx by changing from x-limits to u-limits. xet

A: Explanation of the solution is given below...

Q: lim; 0 (, cos t, In t). t+1

A: limt→01t+1, cost, lnt

Q: Find the limit. За + 5 lim x→0 x – 4 O -5/4 O DNE O 3

A: Limit problem

Q: Find the following limits (if they don't exist write DNE, ∞ or -∞ as appropriate): Answer: lim x-3 2…

A: We have given to find limit  Let ,  y=limx→3x2-2x-3x-3 y= limx→3x2-3x+x-3x-3 y= limx→3xx-3+1x-3x-3…

Q: Use L'Hospital's rule to determine the following limit. Use exact values. e1a – 1 4x lim x →0…

A: We apply L-hospital's rule, when we get 0/0 form.

Q: Which of the following limits is equal to x* dx? (A) lim k 1 3+ n00 k=1 n k* 2 (B) lim E 3+ n n n00…

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Q: Find the following limits. Do not apply L'Hospital's rule. ペ-4 lim +2 |x– 2| (i) (ii) sin (3t) lim

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Q: Choose the correct answer for the following limit S sin t3 dt lim 2 x4 (A) (B) (C) 1 8. (D) 4 (E) -4…

A: Given,

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: C-The result of the following limit is sin t² lim 1-0

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Q: Choose the correct answer for the following limit So sin t3 dt lim 2 x4 (A) (B) (C) 8. (D) (E) (F)

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Q: Determine the 2.x2 – 4x + 6 dx using the definition. (hint: lim Rn)

A: Given: ∫12 2x2-4x+6 dx  To find: Value of the limit.

Q: Q3. Compute the following limits if they exist. 1 (d) lim x sin

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Q: OF# Usc the L'Hospital's Rule to compute the limits: B) lim x+5 B00 2x+5* A) lim log, (1+ 2x+x?) and…

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Q: | sin(ln 0) d0

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Q: 2xy lim (x,y)→(0,0) x² + y²’

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Q: Evaluate the following limits by constructing their respective table of values. 1- cos(3t) 4. lim 3t…

A: note: as per our company guidelines, we are supposed to answer 3 sub parts of a given question.…

Q: Use l'Hôpital's Rule to evaluate the limit. 20 lim x sin O A. 0 O B. 1 1. OC. 20 O D. 20

A: Proceed as shown

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: 1 lim x sin x x2 x→0 O 1/5 O 1/7 О 16

A: Given, limx→01x sinx-1x2

Q: 70. J, f(x) dx may not equal lim , f(x) dx Show that 2x dx o x² + 1 diverges and hence that 2x dx x²…

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Q: ind the following limit. x2 + 1 lim (x, y) - (0, 15) arctan + (y – 15)2,

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Q: 11) lim sin²y Y→TT 1+cosy

A: sin2y=1-cos2ya2-b2=(a+b)(a-b)

Q: By using The definilion of the D Lim x (X+1)= o 2) Lin x Cos

A: Given: 1)limx→0x(x2+1)=02)limx→0x cos1x=0

Q: 1+x-e* 1-cos x lim x-0

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Q: tanh r lim +0+ sechr - 1

A: Given problem:-

Q: Choose the correct answer for the following limit S sin t3 dt lim X→0 2 x4 (A) 1

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Q: Express the following limit as a definite integral: where a = , b = and f(x) = lim 84x n n? = √²…

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