x + tan x 2? — 5х — 14 - (а) lim x0 3x + 4x² (b) lim (Do not use L’Hospital rule in part(b)) x7- x2 – 49

Q: (2-4)* Q1: limx-1 sin(x³–1) x-1

A:

Q: lim_(x->1^(-))f(x)={x^(3)+9,x<1}

A: To find: limx→1-f(x)where f(x)=x3+9, x&lt;1. Calculation: We need to find the left hand limit of x=1…

Q: 9. Lim 6x - Sin 2x メ→0 2x +3sin 4X b. lim x²-1 1/2

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Q: Limx-->9 = X -9/ (X)1/2 -3

A: We will first cancel out the irrational factor at the denominator. And then we will check if the…

Q: 1- V1– x2 с) lim x→0 [without using l'Hospital Rule] x2 -1- x – a? d lim x→0

A:

Q: lim                                          (9x/(9x+8))^9x x approaches  infinity using…

A: Given, We have to calculate the limit.

Q: 2. lim (x - Inx)* x)² 2-0+

A: Here, the given limit is: limx→0+(x-ln x)x which is (-∞)0 form.

Q: 1. limx→4 4x-x² 2-√√x t²+3t+2 2. limt-1 2-t-2

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Q: x2 +1 Can L'Hôpital's Rule be applied to lim x→1 2x + 1

A: To check if the L'Hospital's Rule can be applied or not, first we need to find the limit by directly…

Q: lim х>1 \x-1 X→1 Inx,

A:

Q: 2 tan(x)–2x Use L'Hopital's rule to find f (x) = lim 5x3 Note: Retain any fractions in your answer.

A: f(x) = lim(x-&gt;0) (2tanx - 2x)/ 5x3 If any limit takes the indeterminate form 0/0, we can use L'…

Q: 1) lim (2x – 3) = 1 x-2 2) lim|x| = 0 x²-9 3) lim х-з х-3 9 3

A: 1)limx→2(2x-3)=1read : limit x tends to 2, (2x-3) is 1proof:limx→2(2x-3)=2(2)-3

Q: x2+4-2 -6x*+x2+1 (2) limx-0 (3) limx-0 x2 2x4-x

A: we have to find the limit of the following

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

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Q: x²-4 How come lim x-2 x-2 cannot be evaluated using the quotient limit law? How come lim Vx – 2…

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Q: 2 2- limx-1 sin(x3-1) x-1

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Q: e- lim x-3 x2-9 V3x-3 ,x + 3

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Q: Lim 1- Cosx て X-)0

A: Given: L=limx→01-cosxsin2x We know that 1-cos2x=2sin2x…

Q: 10* – 5* – 2* +1 (b). Evaluate lim- VI+x-V1-x (i).Evaluate lim- sin-!

A:

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

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Q: 5. Evaluate lim sin(x)– (x² + 3x – e*). (x³ – 2x2 - 6 + 3x) 6. Evaluate lim X→2 х - 2

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Q: what is the :lim x→-2 (x^2 +3x+1)/x+2 is ?

A: Consider the following limit: limx→-2x2+3x+1x+2 Left hand limit: The function grows without bound:…

Q: Зx2-х-64 17.lim х-4 х2-х-12 10х2-7 18. lim х-о Зx2-х-12 х3-81 19. lim х-0о Зx2+4x+2

A: We will solve the problem.  L.Hospital Rule will be used in the problem.

Q: Final Value Theorem:- 6, lim xin) lim xCt) ヒ→ lim (1-z) Xcz) (火(00)に

A:

Q: x² - 4x +4 (a) lim (b) lim(vx² +3 – x) x2 X+x-3 X +0 V5x? -2 tan 7x (c) lim (d) lim sin 3x ( Do not…

A: Recall: If Right hand limit and left hand limit both exists and equal then limit exists.  i.e,…

Q: general question on why is the lim of x approaches positive infinity of ekx /xn =infinity and lim of…

A: (A)Firstly, we will plug x=inf we will get inf/inf So, we can use L'hospital rule

Q: (1 – V3x lim tan- 3 + x x-00

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Q: 3 - 2x? +x- 2 Use L'Hopital's Rule to evaluate Support your answer graphically. lim X2 x² +x-6

A: To find: The limit by L'Hopital rule. Given information limx→2x3-2x2+x-2x2+x-6

Q: lim メ→02-V4+x Calculate

A: We have to find the limit of the given function.

Q: Inx lim X+o x3 lim- x-0 ex - x2 - 1 lim- 0 sin'3x

A:

Q: z² +et= 1-400 2z-e² 2* - 3* 17. lim- x-0 18. lim cotxln(x+1) x-0 16. lim-

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: sin(2Tx) lim x → 3 x2 – 9 | O -0.6667 T O 0.6667 T O 0.3333 ↑ О -0.3333 п

A:

Q: 1. lim x²-1 al 2. Tく-X b) lim X-Sin 2x +3 c) lim Vey?-x

A: Given- limx→1x2-1x10-1

Q: 1-sinx x²-49 b. lim x→7 x-7 lim C. lim X→00 x²+1 a. X 1-cosx

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Q: (1) lim,-0 √x+9-3 X (2) lim-0 1–c05x x sinx (3) limx-1 x²+3x-4 x-1

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Q: (2-4)² limx-1 sin(x3-1) x-1

A: by using limit algebra and L' hospital rule

Q: 47. lim -4 3x-5x +7 8+2x-5x 2-2 48, lim 49. lim

A: we have to solve given problem;

Q: 26.lim(1 + cosx)2secx x 2 27.lim (G– x) tgx 27.lim ( - 2

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Q: 2- x - sinx 1. lim x00 x + cosx x*+2x-1 2. lim-0 x3-2x2+x

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Q: (2-4* limx-1 sin(x³–1) X. x-1

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Q: lim (4x+cosx) / x ? x---&gt;infinity

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Q: x3–1 х-14x3-х-3 1) lim sin 2x 2) lim x→0 2x²+x 3) lim 1-v х-1 1-х

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Q: 1. lim(8 - Зх + 12х?) x-2 6+ 4t 2. lim t--3 t²+1 2x2-17х+8 3. lim x-8 8-х

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Q: 5. Prove lim 5x + 2 = 17. Your work should include pre-work, and formal proof.

A: To solve the following question on limits

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: x' -x+1 Evaluate (iii) lim 5x' +7 and show work

A: The given limit can be evaluated by taking x3 as common from numerator and denominator

Q: 2х а) lim -1-2x (sin 2x)+² - et b) lim -4x - cos x

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Q: lim lx-1| х>1 1-х ?

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Q: 3] x+8 - 2 i lim

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Q: X-2 lim = 2 a. By L'Hopital's Rule, x→² X²-1 1 1 lim = x→2 2x 4

A: