EXAMPLE 5 A Limit That Does Not Exist numerically. Investigate lim sin graphically and

Q: Find the limit. lim tan x x - (m/2) +

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Q: Find the one-sided limit (if it exists).

A: We will find the limit numerically  Let, x y -0.1 -5.0000025 -0.01 -50 -0.001 -500…

Q: Find the limits

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Q: 4) Find the value of a for which the limit lim x→0 evaluate the limit. sin(ax)-sinx-x x3 is finite…

A: To Find: The value of a for which the limit limx→0sin(ax)-sin(x)-xx3 is finite and then evaluate the…

Q: Question 1 Does (x – 1)? lim (2,1)¬(1,3) (x – 1)* + (y – 3)² - - exist? If it does, evaluate the…

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Q: Question 10 Find the limit, if it exists Limy-9 (x+9) / (1/x+ 1/9)

A: The given limit is limx→9x+91x+19.

Q: Find the limit 18) lim (1- cot x)

A: As you have asked question number 18, So I am solving it

Q: Find the one-sided limit (if it exists).

A: Given: Find the one-sided limit (if it exists).

Q: Find the limit. TX lim cos x → 3 3

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Q: Find the limit. cos(x) – 1 +x2 lim x-0 2x4

A: It is given that, limx→0cosx-1+12x22x4.

Q: 10. Let a be a positive constant. Evaluate lim x(a/x – 1) if the limit exists. If the limit does not…

A: limx→af(x) does not exist. The idea is that there is no number that f(x) gets arbitrarily close to…

Q: Find the limit. lim (1+ sin(3x))/* x→0+

A: Given: u=(1+sin(3x))1x We want to find  limx→0+u=limx→0+(1+sin(3x))1x Since we know that u=eln(u)…

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

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Q: 1) DRAW THE GRAPH OF A FUNCTION WHERE lim,-af(x) DOES NOT EXIST FOR SOME INTEGER a. EXPLAIN WHY THE…

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Q: Question 5 Use the &-8 definition of limit to show that: ( a ) lim(3–2x)=-7 x→5 (b) lim x•cos-

A: Epsilon and delta definition.

Q: lim (e -2x COS 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: find the limit or explain why it does not exist.

A: To find the limit  limx→π sec x = ?

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: Evaluate the limit sin 2x lim 7x

A: limx→0 sinxx = 1

Q: evaluate the limit.

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Q: 1- 2x Prove that lim = -1 using the e, d definition of a limit. 5

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Q: QUESTION 2 Calculate the following limit: lim (x² – 3x – 10)(*-5) X-5+ QUESTION 3 6

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Q: Evaluate the limit sin 3x lim 7x

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Q: Use a table of values (on your calculator) to estimate the value of the limit to at least 2 decimal…

A: Given, limx→1x2+4x-5x-1 Using table of values,  we have to estimate the value of the limit at least…

Q: (-5-x)²+2 if x #-6 Let f(x) = 2x + 14 if x = -6 Calculate the following limits. Enter "DNE" if the…

A: Given  f(x) = -5-x2+2if  x≠-62x+14if  x=-6

Q: Evaluate the limit: sin(13x) lim I-0 tan(7x)

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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: Find the one-sided limit (if it exists).

A: Given: limx→0+x-1x+3 for evaluating given limit, we put x=0+ in given limit

Q: How do you solve question 11 and 12?

A: (11)Given:

Q: QUESTION 4 Compute the limit below. Justify your answer. (5x +8h)2-25x2 lim- h

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Q: Find the limits lim tan-x X-

A: Solution: consider the given limit function; limx→-∞tan-1x Let  tan-1x = y⇒tan y = x when x → -∞…

Q: 1. Find the limī lim In(sin x) X→π-

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Q: QUESTION 2 Prove using the definition of a limit that lim x² + y2 -y = 4. >

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Q: 1. Find the limit. 1-x2 (a) lim VIA +1

A: we have limx→∞1-x2x4+1this is ∞∞(indeterminate form)

Q: Find the limit. sin(x - 5) lim x* + 4x - 45

A: Given : limx→5sinx-5x2+4x-45

Q: 3. Evaluate the limit if it exists: а. lim 8-0 sin-B b. lim(1+x*)*

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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: Determine the infinite limit. lim 3 sec(x) x- (T/2)+ X 00 - 00

A: Given limx→π2+3xsecx, to find the limit

Q: Find the one-sided limit (if it exists).

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Q: Calculate the limit.

A: limx→∞tan-11+x1-x

Q: Question 5- Evaluate the limit. V-1 lim l Vx-1

A: Given: limx→1x3-1x-1

Q: EXAMPLE 4 Investigate the following limit. lim sin

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Q: 1. Calculate the limit numerically. lim(x + 11) x→2

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Q: Find the limit. lim 7 sin(x)

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Q: calculate the limit.

A: