For problems 5-10, evaluate the limit. Use L'Hô spital's Rule where appropriate. 1- cos x lim lim x'e 5.) 6.) х30 (In x) lim 7.) 8.) lim 1+ x * lim cos 6 1 9.) lim 6→0 1- sin ? 6 10.) In x 2 х—1

Q: Verify that L’Hôpital’s Rule applies and evaluate the limit.

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Q: Tim (X-1)sec(Tix/z) X -

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Q: Evaluate the limit: sin 7z sin 4x lim sin 4z sin 2r

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

A: Given: Plugging the limit directly, we get:

Q: Find the limit: limit of 1-cos3x/cos5x-1 as x approaches 0

A: Given,

Q: 4) Use L'Hosp9tal's Rule to find the limits c) lim tanx)) メ→0 d) lim (ex + メ メ→ o

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Q: 4. Show that In x lim x→1 x – 1 1. (Hint: Note that In In x-ln 1 x-1 and interpret the limit as a…

A: Given: To prove that limx→1 ln xx-1=1 using the limit as a derivativeFormula:…

Q: Evaluate the limit using techniques from Chapters 2 and 4 and using L'Hôpital's Rule.  lim x→0…

A: Evaluate the limit

Q: How do you evaluate the limit:  limx-->0  (sin(4x))/9x WITHOUT using L'Hospital's Rule?

A: A property:L'Hospital's Rule is not necessary here.The following is an important property used in…

Q: find the limit. limit as x approaches 0  sin4x/sin6x

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Q: Compute limit as x goes to infinity of (cos(x))/(x)

A: We find: limx→∞cosxx We solve this limit by using Squeeze theorem. Squeeze theorem states that if…

Q: Compute the limit as x goes to 0 of [tan(x) - sin(3x)] / (x^2)

A: limx→0[tan(x)-sin(3x)]x2=[tan(0)-sin(3(0))]02=00

Q: 2. Calculate the following limits. Justify your answer. (without using L'Hopital's rule Rule or…

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

A: Given: limx→01-cos3xx2 we know that a3-b3=a-ba2+ab+b2

Q: (VT – 1) sin(7x) lim (x – 1)2 x→1

A: Given:  Let y=limx→1 x-1sinπxx-12 To Find: To evaluate the given limit without using L'Hospital…

Q: 4 Find the limit: lim sin(x) (Enter undefined if the limit does not exist.)

A: The given limit limx→04x-4sin(x)

Q: Evaluate the limit (1 – cos x)² sin² . lim x2(1 – e)4 COS X - -

A: Given limit is : limx→01-cosx2sin2xx21-ex4  To find the value of the limit.

Q: tan 11r a) limz 0 sin 3x

A: topic - limits

Q: Determine the following limits analytically.

A: Given: The limit expression limx→π21-sin3xcos2x, To find: The value of given expression.

Q: Evaluate the limit using techniques from Chapters 2 and 4 and using L'Hopital's Rule. sin(9x) lim 7x…

A: We have to find the limit

Q: Only one of these calculations is correct to evaluate the limit lim (sinhx)*

A: See the details solution in below

Q: 3. Find the limit. tan(5x) 0 sin(3x) sin(6x) (2) lim x04x-5x (1) lim

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Q: compute limit as x goes to 0 of (sin(x)-x)/(x^3)

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Q: Evaluate. (a) limit as x goes to 0 -> (tanx)/(2x) (b) limit as x goes to 5 -> (-1)/(x-5)2 (c)…

A: a) The limit can be evaluated as.

Q: how can the limit : limn→∞ (n sin(πn)) be rewriten as, limn→∞π sin(πn/πn/)

A: These two values are not equal

Q: 1 If the given limit is lim(1 + sin x)tan x, Solve using l'hopital's rule and evaluate. (Show your…

A: Apply l hopital rule.

Q: Use direct substitution to find lim tan 0. O v3 O 1 O limit does not exist

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Q: Estimate the limit numerically or state that the limit doES not exist (DNE): sin(9r) lim

A: Evaluate: limx→0 sin9xx

Q: 5. Find the limit or show that it does not exist. sin(x – 1) lim x→1 x´ +x –2 2

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Q: Find the following limits: cos( TX) 5. lim 2-x 3x 6. lim tan 1+x V4x²-5 lim 7. x+2

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Q: lim(cos' x+sin 5x) tan 3x x→0

A: Given- limx→0cos3x+sin5x2tan3x To Find- The value of the above limit.

Q: verify that L’Hôpital’s Rule applies and evaluate the limit.

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Q: Estimate the limit numerically or state that the limit does not exist (DNE): sin(12r) lim

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Q: How do you evaluate the limit:  limx-->0 (1-cos(7t))/(sin(7t))   WITHOUT using L'Hospital's rule?

A: Since the given function is function of  variable t but in question limit is given for variable x.…

Q: . Suppose f(т/3) — 5, f (т/3) — —3,а sin(3та) 2->0 sin(5Tx) . Find the limit: lim

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Q: Determine the limit (if it exists). sinx(1- cosx) lim 2x° x →0

A: Given To Determine limit exists or not

Q: 2 cos(4x) – 4x² – 2 4. lim х-о sin(2x) —х2 — 2х

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Q: Calculate the following limits, or explain why they diverge. x2 – 9 lim 1--3 x+3 lim 2x + sin 3x

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Q: Evaluate the limit using techniques from Chapters 2 and 4 and using L'Hôpital's Rule. sin(2x) lim 5x…

A: Limit: a)    x→0limsin (2x)5x=x→0limsin (2x)2x*52=25x→0limsin(2x)(2x)=25.1=25We know ,…

Q: lim x→0 for sin(4x)/3x

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Q: Find the limit using l’Hospital’s rule(4x-sin(4x))/(4x-tan(4x))

A: The limit to be evaluated is as shown on the white board.

Q: lim e^(sin(2022n)), as n goes to infinite, should this limit exist or not?

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Q: Evaluate the limit sin 7h lim %3D 7h Enter DNE if the limit does not exist. Limit =

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Q: Find the following limit: 3. 1) lim (1--) x00 2) lim (Lnx) 3) lim (x² – 1)cos* X-1

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Q: 1. Use the limit definition to evaluate ,(2 – 3x)dx.

A: The given integral is ∫-122-3xdx

Q: What is the limit as x approaches 0 of 2x/sin(x)

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Q: calculate the limit.

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