3x 15 if x < 3 11. Let g(x) = I V4x + 4 if x > 3° Compute the following or state that they do not exist. a) lim g(x) x-3- b) lim g(x) x-3+ c) lim g(x) x-3

Q: b) Now, follow an algebraic approach to compute the limit 13 – 1 lim 1 I-1 and the limit V9+x– 3 lim

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Q: Match the values on the top with the given limit. A -o BO C 8/9 D +co 9 x2+12 x +9 lim 64 - x2 X- 8-…

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Q: Find the limit. 15) lim V3 + cos2 x A) 2 16) lim (3 sin x - 1)

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Q: find the limit of g(x) as x approaches the indicated value.

A: ltx→-25-x2gx=0As x tends to -2 denominator tends to 1 .    gx≠0 . gx&gt;0

Q: b* – 1 Show numerically that for b = 3 and b = 5, lim аppears to equal In 3 and In 5, respectively.

A: Given : limx→0bx−1x

Q: Solve for the limit: lim \belowx → 3 x2-9 O a. 1. 54 c. 6. 1 54 O d. 1/9

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Q: 1) Find the following limits. Do not apply L'Hospital's rule. x² +x – 6 lim 142 r2 - 2r (a) sin(1 –…

A: 1) a) From the given problem:   limx→2x2+x-6x2-2x   Simply we can write as:…

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

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Q: Evaluate the limit. –1+}² 1.2 COS I lim 2.x4

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Q: Find the following limits: Vx+3-1 i. x-2 x+2 lim 1 + x-1- \]x-1| ii. lim x2 +3x, Vx+-7 lim X→+co…

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Q: Q1) A- Prove that: cotx = - tan-1x B- Find: 1. lịm 2. lim(v9x2 - x- 3x) cotx

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Q: 1. Solve the following limits. (a) lim 1-- V1+ r2 x Inr (b) lim 2-0 I+ In r 2 + sec (3r) (c) lim…

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Q: Let Fexy=4 Find Lim FAt and Lim FEX) X->2* 2 Does l tM fe) exist? Why zis FM cON tin-noss at X=27…

A: Answer

Q: IS In(x² – 1) 6. Evalaute lim x→0 cos(x) - 1

A: To find the limit of the function we have to find right as well as left limit of the function. First…

Q: Find the limits lim x→ -1+ cos-1x

A: We find the limit by substitution

Q: 1. Find the following limits. e3r lim 3.x е (a) (b) lim e3/(2-a) lim In(1x2 - In(1 x (c) _ (d) lim…

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Q: 5x2 + 10x + 1 20. lim x* + x² + 1

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Q: Q2/Find the limiting values: lim Tan (4%) 必→。 O lim 7 7- x2

A: Explanation of the solution is given below...

Q: 2+4x 7. Prove lim = 2 using the e-ô definition of the limit. 3 %3D X-1

A: Hey, since there are multiple questions posted, we will answer first question of the first image. If…

Q: 1. Find the limit (if it exists). (If an answer does not exist, enter DNE.) 2 - x im x² – 4 sin 2x…

A: Find the limit of the given function  1) (2-x)/(x2-4) , when x tends to 2 .  2) sin(2x)/sin(3x) ,…

Q: Find the limit. 2 lim 1+ x4 О А. 2 О В. 0о O C. 0 O D. 1

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Q: Vx + 32 - 5 Limit. lim x--7 X + 7 O 0.1 O Does Not Exist (DNE or tco) O 10 O 1.4 O 5

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Q: Evaluate teh following fucntions

A: Dear Students,  “Since you have asked multiple questions in a single request, we will be answering…

Q: 5. Show that x³y³ lim (x,y) →(0,0) 2x¹2 + 3y4 does not exist.

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Q: 1. Solve the following limits. (a) lim T→-∞ V1 + x² x In x (b) lim x UJ + x 00x 2+ sec (3x) (c) lim…

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Q: Q2/Give a value for each of the following limits: x2 - 4x – 21 1) lim 7 3x2 - 17x – 28 (7+2x)-V5-vZ)…

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Q: Evaluate the following limits: V10 + 6х — 2 (a) lim x→-1 x2 – 2x – 3 1 – sin(x) (b) lim x→5 (2x –…

A: Use l hospital rule for finding the limit.

Q: (c) Find the following limit: Vx +1- 2 lim X-3 x(x - 3) V9x2 + 5 lim x-00 X- 1 cot 0 csc lim sin e

A: Given we have to find the limit

Q: Q3: Find the following limits if exist:- 1-cos 2x (1) limx-0 sin² x

A: If it is required to evaluate the limit limx→af(x)g(x)=00. That is if applying the limit leads to…

Q: Q3. Compute the following limits if they exist. 2 – Vx (c) lim x→4 3 – V2x + 1 -

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Q: Q2/ Find the following limits: 3- 5/27+81 x--00 2/12+Vt²-167 A. lim 1 В. lim-1 x+1 1-sin t С. lim #…

A: We have to find the limit of the following... A. limx→-∞t13-5t2+81142t2+t23-1612B.…

Q: Find lim I→1 x² – 1 Enter inf for oo, -inf for -00, and DNE if the limit does not exist. Answer:

A: In such kind of limit we substitute the value of the limit with sign and then evaluate the…

Q: 1(a)Find y' given that y In(2x + 1) + e**+5 %3D 5x2-1 b) Evaluate lim x00 2x2+1 c) Find y' if x'+ y…

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Q: 4x + 1 Let f(x) = x-2 (b) Use the precise definition of the limit (i.e. M, 8) to prove that lim f(x)…

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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: 1. Evaluate the following limits: x2 V2x2 + 1 Vx2 + 5 (a) (3 marks) lim (b) (4 marks) lim a→3 2* +…

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Q: Find the limit: 1 – cos(x) lim x2

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Q: Evaluate the following (you may use Limit Theorems). x²–4x+3 1. lim X-1 x2-1 2. lim 3t-2 sint+(ei–1)…

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

Q: Is In(x² – 1) - 1) 6. Evalaute lim n cos(x)-1 r lulx2-1) lem lulx²-1)

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Q: Find lim 4(x) (x) / X-0 x 2. Prove that B(m, n)

A: Limit of the bessel function

Q: Find the following limits. √x-3 X-9 x-9 1. lim t²-7t+10 2. lim- t-2 t-2 3. A function f(x) satisfies…

A: Since, you have posted multiple questions, as per guidelines, we"ll solve only first three…

Q: Find the limit. lim X→- 47 Vx+ 15 cos (x+ 4x)

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Q: Which of the following limits does not yield an indeterminate form? a.limx→0 3x^2/x−sinx b.limx→2…

A: (a)lim(x→0) (3x2)(x-sin⁡x)=00form(indeterminant form)(b)lim(x→2) lnx2(x2-5x+6)=00form…

Q: Discuss the continuity of : Q1 x+ for *く0 for osr 2 Q2 1-x lim

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Q: h of the following limits analytically; show your work: O LIVE 9-(3-h)2 (a) limp-0 1 1 (b) limx-1…

A: Please refer the attached image for complete solution.

Q: 5x2 + 10х + 1 :0. lim x4 + x? + 1

A: