Use L'Hospital's Rule to evaluate the following limits. ex-1 a) lim (x²-x³)e²x b) lim X118 x−0 tanx c) lim_(tan x) cos x X→(π/2)-

Q: sinh(x)-sin(x) Find lim

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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: Find the following limits: (a) If lim x--> 3 ((?f(x)/2x) +1)?=2,find lim x→3 f(x) (b)  Find lim…

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Q: Use the limit definition of the derivative of the given function at the given value of x (if it…

A: Given functions are

Q: 2. Determine the equation of the following function. State your answer as a piecewise function. y 10…

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Q: If the percent decrease is 25%, what is the common ratio?

A: Common Ratio The common ratio is defined as the amount between each number in a geometric sequence.…

Q: The answer to lim (2 + e-) is Answer:

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Q: If lim f(x) = = co then f (x) XCOS cos² X00

A: Given- If limx→∞fx=∞ then fx=xcos1x To Prove- The above expression.

Q: . Use the Squeeze Theorem to determine the value of limx sin

A: To evaluate the given limit limx→0x4sinπx by using the Squeeze theorem. Now, the Squeeze thorem…

Q: L True False y -2 then x 1 lim f(x) = 0 y = f(x) 3 X

A: We have to find Lim x approaches to 1 f(x)

Q: 1 Evaluate lim Gnx x→1+ 'Inx х-1

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Q: 5. Use L'H rule to find (a). lim Inz2 (b). lim (sin x)(In x).

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Q: Use L'Hopital's rule to evaluate lim(1 – 2 sinh(x)) sch(a).

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Q: Find lim (sinx-lnx) +0+z

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Q: lim 1-e*) X-0 x sin x

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Q: Use L'Hôpital's rule 4. lim x csc x x →0

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Q: Q \ Find the value of 8 > 0 that guarantee lim x-0 csc(1/x) = 0 in terms of ɛ?

A: Definition of limit: We know that, limx→af(x)=L               ...(i) For each ϵ>0, there exists a…

Q: 1 lim x0 X 2 csc² x

A: Limx-0) - csc2x

Q: lim tan-¹(e* + ln x) x→0+

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Q: x - 3 lim I-3 x - 9 x? – 2x – 8 lim x – 4 x³ – 2x? + 1 lim x³ - 1

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Q: Suppose lim f(x) = 60 and f'(x) is positive for all x. Assuming lim f'(x) exists, find its value. X→…

A: I have explained everything with in the solution. Please go through that.

Q: Why is limx→0(cos(x2))=0 but limx→0(cos(x-2)) is not defined?

A: We have to show  but  doesnot existNote: It is given  which is incorrect,  is correct

Q: Let s(x)=sin(x)/x. Explain why it is true that Lim (X-> 2pi) s(x)=0

A: Let  sx=sinxx Explain why it is true that limx→2πsx=0

Q: lim (x+sin(÷)

A: Let, L=limx→∞x+sin1x1x...(1) So, the form the expression is ∞0.