Use l’Hôpital’s rule to find the limits in Exercises . x² . 8. lim x--5 x + 5 х — 2 7. lim x→2x2 25 13 – 4t + 15 313 + 3 9. lim -3 t – t - 12 10. lim --1413 – t + 3 5x3 11. lim x00 7x + 3 8x2 2x х 12. lim x-00 12x? + 5x sin t² 13. lim sin 5t 14. lim sin x – x 8x2 16. lim 15. lim X→0COS x x→0 20 – T 30 + T lim 17. lim 18. 0--7/3 sin (0 + (/3)) 0T/2COS (27 – 0) 1 - sin 0 х — 1 19. lim 07/21 + cos 20 20. lim x→1 In x – sin 7x In (csc x) x² 21. lim x>0 In (sec x) 22. lim x>7/2 (x – (T/2))²

Q: Prove that lim 12 √16x +9y¹2 2 6 4x² +3y does not exist by showing that the limits along different…

A: We have to prove that  limx, y→0, 0 16x4+9y124x2+3y6 does not exist.

Q: 4 Find the limit: lim t+0 t 4 et – 1, (Enter undefined if the limit does not exist.)

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Q: x – 4 8. Prove that lim Vx = 2 using the e-d-definition. Hint: Va – 2 = VT + 2

A: The epsilon-delta definition of limits says that the limit of f(x) at x=c is  value  of limit. if…

Q: Use l'Hôpital's Rule to evaluate the limit. .3 8x +7 2, lim X- 1 X1 O A. 11 O B. 19 C. O C. - 16 D.…

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Q: Use the definition of a limit to show that (i) limx→0 (x^2 + 6x + 9) = 9 (ii) limx→−7 and…

A: Authoring guidelines:…

Q: Use l’Hôpital’s rule to find the limits

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Q: 2. Find the limits. limx→-1 sin(x² + 3x + 2) x³ + 1 M

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Q: 5. Consider the limit: lim x² = 16. What is the largest allowable & that will "work" for e = 0.25 in…

A: Given  f(x) = x² To find : Value of delta using definition of limit

Q: 9. Given that limx→3 f(x) = 2 and limx→3 g(x) = −5 compute the following limits: (a) limx→3 2f(x)…

A: Given that limx→3f(x)=2 and limx→3g(x)=-5

Q: 1. Compute the following limits analytically. -24.x +11x +21 а. lim 6x – 7x+12 b. lim (2x²…

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Q: 2. Use the definition of the appropriate limit to show (a) limr→∞(2x² + 4x – 1)/(3r³ + 1) 0. - (b)…

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Q: - x² if x 3 - Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x) = x…

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Q: Find the indicated one-sided limits, if they exist. (If an answer does not exist, enter DNE.) S-x+7…

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Q: 4-ху Find lim (x,y)¬(2,1) x²+3y2 if it exists, or show that the limit does not exist.

A: limx, y→2, 14-xyx2+3y2Plug in the value x, y=2, 1=4-2· 122+3· 12=27

Q: V4 + x – V4 – x lim x-0 O 1/2 О 113 O 1/4 O 1/5

A: To solvelimx→0(4+x-4-xx)

Q: 3, Use the definition of limit (E & 8) to show that lim (2.x+iy)-4i, where z=x+ iy. 21

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Q: Q4)A) Find the following limits (for two only). x+1 1. limx→-1 x2-x-2 1-Vx 2. limx→1 1-x 2х 3.…

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Q: 2. Find the limit or show that it does not exist: lim (2,y)→(0,0) 2x6 + y?

A: We have to find limit

Q: Use the E-8 definition of a limit to prove lim Xy (Xy) →(0,0) x² +y²

A: Consider the equation

Q: x- 2 x <4 Estimate lim Ax) where fx) = %3D x+2 x24 12 10 -8- 8. 6 2 Limit does not exist.

A: Check the value of function nearer to given point of limit if they are equal only then limit will…

Q: Evaluate the limit limx→5 x^2 − 2x −15  /  x−5 Enter I for ∞,  −∞ and DNE if the limit does not…

A: First, we factor the numerator

Q: Use l'Hôpital's Rule to evaluate the limit. 2 - 4x+2 lim 2. X>co X+5x+11

A: The limit of a function limx→Xfx=Y means that value of  function fx can be as close to Y by making…

Q: (4) Find the indicated limits, if they exist: Зх—12 (a) lim→4Jx-2 x²+3x-4 (b) lim→-4 +4x x²+4x 3 cos…

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Q: The limit lim (n+1-vn- (A) equals-x (B) equals 1 (C) equals ( (D) equals +∞ O(E) does not exist

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Q: Calculate the limit and show proof. lim (1,1)(0,0) r2 + y?

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Q: Find the limit (2x + y)² lim (x,y)→(0,0) 4x² + v² (Enter dne if the limit does not exist)

A: WE CAN FIND LIMIT . So , we can find limit along the line y=mx .i.e, we can choose path.If for every…

Q: V-1- x + 5 if x - 2 Calculate the following limits. Enter "DNE" if the limit does not exist. lim…

A: NOTE: Refresh your page if you can't see any equations. . find the left-hand side limit of the…

Q: Q2: (a) By using " L' Hopital rules "; Find the limits of ::- (1) lim-(7/2)-(tan x)cosx (2) limy-0…

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Q: Q3: A) Find the limits below x² + sin²y 1) lim (x,y) (0,0) 2x² + y² 2) lim (x, y)-(1,1) x² - 2xy +…

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Q: Q4)A) Find the following limits (for two only). x+1 1. limy--17-x-2 1-VE 2. limy-1 1-x 2x 3. lim--0…

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Q: Find the limits in Exercise

A: Given : limh→055h+4+4

Q: 44. Does the limit exists? If no, show your solution lim (x,y)-(0,0) In(1 – x²) + y4 x2 + y4

A: Solved below

Q: 2. Find the following limits. Show your work. Vx2 + x – 1 lim (a)

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Q: Use an appropriate definition to prove the following limits. x³ – 16x* = 1 I+0 r°+ 4x² x +2 V9x2 + 4…

A: This is a problem of limit . Based on the formula and concept we will answer the question.

Q: Q4: - Evaluate the limit of the following: x3–1 sin 2x 1-V 1) lim 2) lim x→0 2x²+x 3) lim x→1 1-x…

A: When we get 00form, we can us  L' Hospitals Rule to calculate the limits. In this rule μx→a…

Q: Estimate the limit numerically. x² lim x+4 O diverges to +o 00 O diverges to -∞

A: Given

Q: 9 -x2 if x 1 .What value of c makes g(x) continuous at x = 1? Show all conclusions. 2 Vx-4 Using…

A: For a function to be continuos, the left hand limit should be equal to the right hand limit.…

Q: Find the limit: 4z4 – 4y4 lim (1,9) → (3,3) 4yª z² - y?

A: lim(x, y)→(3, 3) 4x4-4y4x2-y2

Q: If it exists, find Answer: x³ - ze²y lim (x,y,z) (-1,0,4) 6x + 2y3z' Write DNE, if the limit does…

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Q: Let fa)=S(-5-x2 + 23x +19 f Xチー6 if X= -6 calculate the following limits. ENter DNE if the liniit…

A: l

Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (2) limx-o x-³ (tan-¹x - x)

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Q: Evaluate the limit V9n4 + 13n³ – 5n – 10 lim -V25n16 + 5n² – 9n Also, find the asymptotic value of…

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Q: Calculate the limit algebraically. (If an answer does not exist, enter DNE.) x2 + 3 lim x--2 x2 + 3x…

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

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Q: Consider limZy² z-0 x2 i. What value does the limit approach as z approaches 0 along the line y = x…

A: given function limx→02y2x2-x2-y2y2i (i) what value does the limit approah as z approaches 0 along…

Q: 8. Let f(x, y) be the function x3 + y3 xy? Show that the limit lim(9)→(0,0) f (x, y) does not exist…

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Q: 2. Calculate the following limits. sin 3x a) lim х-0 2х(х-3) V4+h-2 b) lim h→0 h 5х-4 c) lim X→∞…

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Q: Find the limit: lim (1,y) → (0,0) x² + 8y?

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Q: 2. Evaluate the limits numerically. x-1 a) lim x-1 vx+3-2 x² +3x+2 b) lim x--1 x2-x-2 cos(x)-1 c)…

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