Suppose that (Sn) and (t„) are convergent sequences with lim s, = s and lim t, = t. Then b) lim (ks,) = ks and lim (k + s,) = k+ s, for any k eR.

Q: number 98 in strang and herman calculus 1. Can you provide a full work up as well as an explanation…

A: Given:      limh→01a+h - 1ah

Q: So 8sin(t® )dt Evaluate the limit lim Z-0

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Q: lim x² ln x x-0*

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Q: Find the following limits. You may use any theorem we have proved, such as Arithmetic of Limits.…

A: Given: limn→∞ 6n2-2n412n3+2n2-17n   Property (i) limn→∞f(x)g(x)=limn→∞ f(x)limn→∞ g(x)    ,…

Q: lim , y, z)→ (1, 1, s not exist.

A: We want to find the limit lim(x, y, z)→(1, 1, 1)2x2 - y2 + z2x + y - z

Q: F ind the limit using L'Hopital Rule. lim 4 - 16 3x-16

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Q: Prove the limit statements

A: To prove: =lim     x→04-x=4-0=4=2=RHSHence proved To prove this, we will start from LHS and will try…

Q: 1. Discuss the continuity of f(x) with graph shown below by answering the following questions.

A: Graph of the function is given, we have to the limit at x=0

Q: 47) lim √√3x-2 x-1 48) lim X->>0 x3 + 12x² - 5x 5x

A: To find the limit of a function f(x) when x approaches k, substitute x= k in f(x)

Q: Evaluate the limit lim cos 0-0 cosh (0) - 0

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Q: Using the definition of limit (so, without using Arithmetic of Limits), show that i. limn→∞ (4 + n)…

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Q: Question 4.[4, 4 marks] Evaluate the following limits, 1+ x (a) lim [r – a* In(-")I (b) lim(1- 2r)

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Q: х2—1 lim х-1+ In(x)

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Q: Evaluate the limit using L'Hôpital's rule 7x³ e10x lim x →∞

A: Given query is to find the limit.

Q: Find the limits in Exercis

A: Consider the given limit as limt→4-t-t

Q: a. For each of the following find the limit if it exist. I. II. x- 1 lim X-1 x2 +x- 2 lim (2-* + 3)…

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Q: Evaluate the limit or explain why it does not exist t t- 2-0 √4+t-√4-t x³+1 lim X-1 X+1 Ix-21 lim…

A: Given that some limit problem and we solve this given problem by using general property of limit.…

Q: At x = -3 f(x) = ²² +2x-3 2x+6 x A) limit of the function exists as x apporaches -3 B) function is…

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Q: EVALUATE THE LIMIT OF THE GIVEN FUNCTIONS

A: The value of 1/infinity is 0. So using this knowledge we got into this problem.

Q: The subject is: PrecalculusThe general subject is: Introduction to Calculusand the specific subject…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Evaluate the limit: VE-Va = 7(r-a) エ→a

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Q: (b) lim csc(r)

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Q: Question: Prove that the limit does not exist. -2|3x| lim 3x

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Q: Compute the following limits: 2 3 3h h-2h-2 (a) lim (d) lim h-0 √h+3-√3 (b) lim x-0 12-4 -2 12+10…

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Q: 5) Solve the differential equation given by the Cäuchy-Euler method or equidimensional equation.…

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Q: Find k so that the limit exists x² + (3 – k)x – 3. lim - X-2 x- 2 (a)5 (b) 4 (c) 3 (d) 2

A: We will solve the following

Q: Evaluate the limit as t-> 1 of -2 t 3 2 2 + ²+ + ² = 2² + ( + ²+ 3) ; +[ 0 -² ² + 1) × e - i 2 +²³²…

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Q: Prove: If function f is continuous at a limit point p if and only if the limit as excuse to p is…

A: Given: If function f is continuous at a limit point p if and only if the limit as excuse to p is…

Q: Find the following limits. You may use any theorem we have proved, such as Arithmetic of Limits.…

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Q: Using the definition of limit (so, without using Arithmetic of Limits), show that i. limn→∞ 2/n +…

A: We have to find the limit using definition of limit.