13. Sketch the graph of f (x) = }" Sx² + 1 if x < -1 if x > -1 and use it to evaluate lim_ ƒ (x) and X→-1- lim f(x) x→-1+

Q: 3-v49 B) Without using L'Hopital's rule, find: lim

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Q: 1 Find lim +3 using limit rules. 2.

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Q: 2. Construct a table of values to investigate 1 if x -1

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Q: Estimate the one-sided limits for the function below.  f(x)=(11−x)/(x−8)^2   lim f(x)= x--&gt;8+…

A: Given function is

Q: 10. Find the indicated limit. x²5x - 14 lim x→7 x - 7 Show any work necessary

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Q: 11. Use L'Hopital's rule to find the following limits. x² + 3x-4 x-1 (a) lim x-1 In x xx-1 (b) lim

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Q: Clearly show why evaluating lim x (In x)2 requires repeated application of L'Hopital's rule. Show…

A: We have to evaluate the limit of the function fx=xlnx2 using the L' Hopital's rule. To find the…

Q: Calculate the limit limx→13√x−1x−1.

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Q: 2. Evaluate the limit: TC 1000 lim x-7- (x-7)2 lim x→8+ (8 - x)3

A: the given limit is: limx→7-πx-72-limx→8+10008-x3 we have to evaluate the given limit.

Q: find the limit.  lim(x-->2^-)    ln(-1/x-2)

A: Here we have to find the left hand limit at x = 2.

Q: Fill in the blank/s:

A: A function f(x) is said to be continuous at a point x = a, in its domain if the following three…

Q: Using L'Hopital's Rule, we have to find the limit of f(1+ x) – f(1 – x) lim xf'(1) |

A: If the Direct substitution will results the answer in the form 00 or ∞∞ then we can use L'Hospital's…

Q: Transform the function lim x+5x² +3- x²) into an equivalent quotients to en apply L'hopital's rule.

A: Given that limx→∞x4+5x2+3−x2. Multiply x4+5x2+3+x2 by numerator and denominator both…

Q: /1+x – /1 – x lim |æ|

A: Proceed as shown below...

Q: Find lim (2+x)" * using L'Hôpital's rule. 1/x

A: Given the given expression is limx→∞2+x1x.

Q: Estimate the limit numerically to two decimal places or state that the limit does not exist.

A: We have to evaluate the following limit: limx→2x-2ln3x-5 The above limit is in 00 form. Therefore we…

Q: Suppose neither limx→0 f(x) nor limx→0 g(x) exists. Show that limx→0 [f(x)g(x)] may exist.

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Q: Evaluate without use of Hopital's rule: tanx-sinx 1) lim-0

A: using expansion of trignometric function

Q: Estimate the value of limx→2 x 2 + x − 6 x 3 − 8 to 3 decimal places by making a table with the…

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Q: Extend L'Hopital's Rule to evaluate lim (x2 - x) x-+

A: See the attachment.

Q: iv. lim x' -2x² X -00 v. lim 3x – Vx* – 2x +3 lim I-0 x vi.

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Q: Find the Limit: 1. lim (2x + 5) x--7 3. lim(-x + 5x 2) 5. lim 8(t - 5)(t - 7)

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Q: Limit as x approaches 2 of (x3-8)/(x-2)

A: Obtain the value of the limit as follows.

Q: Use l'Hopital's Rule to evaluate the limit. x2 - 9x + 20 19) lim X→5 X - 5

A: Consider the limit  limx→5x2−9x+20x−5

Q: 2. Use L'Hospitaľ's Rule to find lim (1+ x)*

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Q: Lhopitals

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Q: 1a. Use L'Hopital's Rule to find the Limit: lim         (xsinx + x2 - 4x2)/x - 2pi x-&gt;2pi

A: Let's understand the L’Hospital’s Rule If where a is any real number, infinity or negative…

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: In(1-x)+ x Evaluate lim using L'Hopital's rule. x-0 x?

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Q: Numerically determine the limit 8+x3 limx--2 2+x

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Q: Estimate the limit numerically  limx→4 √x−4/x−16=

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Q: 6. Without graphing the function on your calculator, find the limit. Use L'Hopital's Rule where…

A: Solution of the problem as follows

Q: Lim of √x, as x approaches to 4. Prove using epsilon delta deffinition

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Q: Evaluate the limit 6| lim x→6 x - 6. If the limit does not exist enter DNE. Limit =

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Q: 3 - – If lim f(x) = 3.5 and lim,-2+ f(x) = 6. 5 , the function has a double sided %3D x→2- limit or…

A: Given,          limx→2-fx=3.5 and limx→2+fx=6.5We know that,           Condition of double sided…

Q: 6. ) Express the limit as a derivative and evaluate. x2021 - 1 lim x - 1

A: we have to solve the limit problem

Q: 2. Use L'Hopitals's rule to find lim (-).

A: Given that: limx→0+1x-1ex-1

Q: Use ľ' Haspital's Pulle lim 1-1=0 by L lim X 3-1 メう

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Q: Analyze the function. +Cx)= Domain: Range: Equation of Asymptote: Intervals on which f(x) is:…

A: As this is a multiple subpart question, according to the Bartleby answering rule, only first three…

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

A: answer

Q: 3- If lim f(x) = 3.5 and lim,2+ f(x) = 6.5 , the function has a double sided x-2- limit or one sided…

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Q: Estimate the limit numerically  limx→4 x^2−2x−8/x^2−3x−4=

A: We have to find limit

Q: limit as x approaches infinity of (-1)x+1

A: Apply the limit.

Q: 3 - If lim f(x) = 3.5 and lim,-2+ f(x) = 6.5 the function has a double sided %3D limit or one sided…

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Q: 2. Evaluate the limit by Use the definition of the derviative to compute the derivative of f(x) = 1…

A: Given,

Q: 3-Vx2+9 Without using L'Hopital's rule, find: lim-

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Q: 5) Find the indicated limit if it exist. а) lim X-2 3- Vx+ 7 2 - x x' +1 b) lim x-- x+1

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Q: B) Without using L'Hopital's rule, find: lim 3-Vx2+9 x2

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Q: Calculate the limit limx→∞(1+6x)x.

A: limx→∞ (1+6x)x   = limx→∞ (x+6x2) = limx →∞ x + limx → ∞ 6x2 = ddx x + ddx 6x2 = ddxx + 6× ddx ×…