Only one of these calculations is correct. Which one? Why are the others wrong? Give reasons for your answers. a. lim x In x = 0:(-00) = 0 b. lim x In x = 0•(-00) = -oo X-0 In x c. lim x In x = lim -0" (1/x) -1 x-0* In x d. lim x In x = lim -0" (1/x) X-0 (1/x) = lim 0 (-1/x) = lim (-x) = 0

Q: Next, we check the limit when approaching from the right. As x approaches −10 from the right, we…

A: The given limit is ,limx→-10+5x+50x+10

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Q: 3. Evaluate lim, tan (2 x) if it exists. Provide evidence to back up your answer.

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A: We have to find limit

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Q: mpute lim x→0 In (1+ x)

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Q: 1. (a) Suppose you know that lim f(x) exists and that lim f(x) = 7. Do you have enough infor- mation…

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Q: If lim f(x)=-2 x-->0+, lim f(x)=3 x-->0-, and f(0)=-2, what can you say about lim f(x) x-->0?

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Q: Calculate each of the following limits, or explain why it does not converge. You may use any…

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Q: 8x+4-4cos?x+tanx Q1) Find lim x-0 4sin2x

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Q: 21: The final value of :* lim (In(x))?

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Q: It is known that lim-0 eAt-0 for A What can you say about e? Justify.

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Q: 7. Find the limit, if it exists. If the limit does not exist, explain why. - (a) lim sin (2x 6)…

A: solution is given below

Q: Only one of these calculations is correct to evaluate the limit lim xtanhx x-0+ Select one: lim…

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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: lim f(x) x--> 3, where f(x) = {2(x+1), if x < 3 or 4, if x = 3, or x^2 - 1, if x > 3}…

A: First we find the limit of f(x) from left side and right side .

Q: Suppose that ƒ is an odd function of x. Does knowing that limx →0+ ƒ(x) = 3 tell you anything about…

A: Given that f(x) is an odd function.  So, f(-x)= -f(x) Given that lim x →0+ ƒ(x) = 3

Q: Once you know lim x-->a+ f(x)  and lim x-->a-  ƒ(x) at an interior point of the domain of ƒ,…

A: If we know the right and left-hand limit of a point then we know the limit at that point.

Q: Only one of these calculations is correct to evaluate the limit lim xº Select one: lim xe → take In…

A: The first option is incorrect as ∞∞≠0. For the second option, after taking ln, the expression e^x is…

Q: Using e – N description to prove that lim - = 0.

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Q: Find the indicated limit, if it exist:  lim x to 4;  x-4 divide by square root of 2  - 2

A: To determine: limx→4  (x-4)/(x^(1/2)-2)

Q: Only one of these calculations is correct to evaluate the limit lim x* Select one: O lim x* + take…

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Q: Only one of these calculations is correct to evaluate the limit lim x* x-0+ Select one: O lim x* +…

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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: If limxS1 ƒ(x) = 5, must ƒ be defined at x = 1? If it is, must ƒ(1) = 5? Can we conclude anything…

A: The limit of a function is very significant in differential calculus. When the independent variable…

Q: Evaluate, Lim x-->-2+  ((x+2) cot (x2+5x+6))

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Q: lim (In(x))* ?

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Q: If lim f(x) =5 x-->1- and lim f(x)=5 x-->1+, what can you say about lim f(x) x-->1? What can you say…

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Q: 1. Using L'Hospital's rule, evaluate lim(1 – x²).

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Q: Evaluate the limit: lim --> 0 (ex+3x)1/x

A: It is an indetermined form of questions in case of limit. Which will be solve easily by below given…

Q: 30. Use the fact that lim x→0 sin x X = 1 (shown in video) to show lim x-0 1 - cos x X = 0

A: we will find the required.

Q: Use a table of values to estimate the value of the limit. If you have a graphing device, use it to…

A: We will use property of limts

Q: 15. Investigate In (x + 1) In (x + 999) lim lim and In x In x Then use l'Hôpital’s Rule to explain…

A: L' Hopital's Rule is used in the following cases,

Q: 4. Find the following limits. Remember, show your work. x2 + 2x – 8 a. lim x+2 x2 -x - 2 b. lim sin…

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Q: Approximate the value of et – 1 lim x→0 2x2 + X by substituting in 3 different values of x that get…

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Q: determine the limit limh→0[(x+h)2-x2]/h by treating x as a constant. determine the limx→0cos(2x)/x…

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Q: Using the L'Hospital Rule, calculate: (In[tan(2x)]\ lim In[tan(7x)]

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Q: 9. Build a table to estimate lim sin 1 (Hint: Use multiples of T) (x³ – 3x2 + +6– 2x) 10. Use a…

A: As per the guidelines we are suppose to answer only one question. Please repost the remaining…

Q: Use a table of values to estimate the value of the limit. If you have a graphing device, use it to…

A: Explanation of the answer is as follows

Q: 1) If lim f(x) = , what asymptotic behavior will be illustrated in the graph of f (x)?

A: 1) If limx→6-fx=∞, then the value of the function fx tends to infinity as x→6 from the left hand…

Q: (b) Consider lim tan(4z). -7z What does the numerator approach as z- 0 ? What does the denominator…

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Q: and b at where? ] Use the &-8 definition of the limit to prove lim(4x-3)=5. X2 Find the & value When…

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Q: Use l'Hospital's rule to find the limit.  lim x→0  ex − 1 − x x2

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Q: Suppose lim f(x) = - 7 and that for all x + 8, x →8 (플+7 + f(æ)) cos 2 f(x) + - 7. Find lim - 7 -…

A: Formula used   *    cos (π2+θ)=-sinθ*      limx→0sin θθ=1

Q: Evaluate lim x->2 (x^2 - 4x + 4) / tan^2 (x^2 - 4) without using L'Hopital's Rule.

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