In(1 – x) + x + lim 7x3

Q: 2.x – 3 - Find lim x→-∞ 4 – V5x² – x – 2

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Q: х+4 a) Compute lim X3 (x-5)(x-3)

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Q: Prove rigorously that lim (4 + 8x) = -4. X-1

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Q: 3. Find lim (x² + 3x – 18)/(x – 3)-

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Q: Show that lim Z-2 (2-2)4 || ∞

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Q: Evaluate the limit: x² +6x+8 ]im as x – – > - 4 lim x-4 x+2x-8 2 x ^ 2+ 6x + 8 divided by x ^ 2+ 2x…

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Q: 1-x-x² (c) lim x+∞ 2x²-3x+1

A: The answer is given below:

Q: A) Vx2 +8-3 lim x-1 x+1

A: By using l'Hospital's rule we solve the given problem as follows :

Q: A- The result of the follo 2x² + 3x lim xxx³+x+1 02 Oo O 1 O infinity

A: To find: limx→∞2x2+3xx3+x+1

Q: Find the limnit L. X - 3 1. lim X4 X- 4

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Q: In(x-2) 1- Find , limx→2 In(x² -4)

A: Answer and explanation is given below...

Q: 1. Evaluate. x'- 2x +12 a) lim x² +1 x² -8x + 7 b) lim- x-7

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 19. Evaluate lim (x³ + 2x2 – 3x – 4). x-1

A: Evaluate limx→-1(x3+2x2-3x-4)

Q: O Find 2- X Lim x→2 오-12X X+2

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Q: Prove that lim(4x² – 25) = -9 X-2

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Q: 16. Evaluate using L'Hospital's Rule. x3-216 a. lim X-6 (In x) b. lim 4x2

A: Given, Part a: limx→6x3-216x-6 If we put x=6 we get an indeterminate form, Therefore by using the…

Q: b. limx-3= In(x-2) %3D X-3

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Q: Prove that lim x 2 = 4. x→ 2

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Q: 37. Find lim f(x) if, for all x, -4x+6 < f(x) < x²-2x+7. x→-1

A: As question number 37 is highlighted solving that only.

Q: 1. Find the limit. lim x118 5x³ + 3x² X- 7x²

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Q: O Find 2- X Lim X→2 2- 2X X #2 xY _ 2x² – 8 x² - 4 2 Find Lim x²- 2x²- 8 X->2 Lim 3X X→3 X- 3 -3 X…

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Q: 3 Find x=x-12 lim. x-7-3 x2+ 8x+15)

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Q: Find the exists. 5 x а. lim 3 5x'+1 b. lim 10х-3x +7

A: Given that: a. limx→-∞5x-x3b. limx→∞5x3+110x3-3x2+7c. limx→∞5x2+2x2+3

Q: Ifp(x)=x2-2x-3 and q(x)=x² - 1, then lim 3p(x) X +1 9(x)

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Q: Evaluate the limit: x² - 7x + 3 lim x→∞ x3 - 9x2 + 2

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Q: If f(x) = 3x2 - 4x +1 and g(x) = x² + 2x - 3, then what is lim 9X, g(x). X-1 f(x)

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Q: х-2 Determine lim x→2- 2-V4x-x²°

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Q: Prove that lim(4x2 – 25) = -9 x-2

A: First we use the formula a2-b2=(a-b)(a+b) then put the limit.

Q: a) Evaluate V9x(x² – 3x +2) lim (3х — 3)

A: To find the limit:

Q: In(x-2) 1- Find , limx→2 In(x²-4)

A: The given limit is, limx→2ln(x-2)ln(x2-4)

Q: Determine the infinite limit. x² - 4.x lim 1+4+ x2 - 8r + 16

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Q: The value of k such that x2 lim kx + 7 x→1 x – 1 exists is

A: Given: The limit expression limx→1x2-kx+7x-1, To determine: The value of k such that the given limit…

Q: In(x) (c) lim a5- 10 - 2.x

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Q: 1. Evaluate. 3x -14 a) lim- -4 x-2 r²+x-12 b) lim x-3

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Q: 21. lim V2x-6 -3+

A: Topic  = Limits

Q: limd x²-1 = X- T2+*]

A: Given questions:           Question 1:                                     limx→1+x2-1=?…

Q: 2. Evaluate the limits, if it exists. x²-6x+5 a) lim X-5 X-5

A: Given,  a lim x→5 x2-6x+5x-5  b limt→01+t-1-tt    We have to evaluate the limits

Q: 1. Evaluate. ³-2x² +12 a) lim x--2 x² +1 b) lim -8x+7 x-7

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Q: Evaluate the fallowincx: Lim ー- G+ 76 - 2J反 +- - 4x° 1 x2 メーマ-O 3 -8x+ 7x - 455 -飯 -5 x3

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Q: 2x a. lim x-+3" X - 3

A: limit

Q: 3. Evaluate the lim(2x – 7). x-4 а. lim(2x — 7) %3D 2 x-4 b. lim(2x – 7) = 1 с. lim(2x - 7) %3D7 x-4…

A: Given statement, The limit of a function is the value it approaches as the value of x approaches a…

Q: a) lim 3x + x2 x→1

A: We are asked to find the limit.

Q: 3. Show algebraically that lim x* – 2 – x = 0

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Q: 2. Complete the table and use it to find lim numerically. x-2 x -2x-8 -2 x² +2x x² - 2x-8 x² +2x lim…

A: Explanation and solution is given below....

Q: Prove rigorously that lim (x2 – x) = 6. x→3

A: We have to prove  limx→3x2-x=6 Now let  L=limx→3x2-x

Q: Example 17: find x -1 lim %3D (x-1)Vx² +2x+3

A: we have to find: limx→1 x2-1x-1x2+2x+3

Q: lim ( 7x 12 6. lim 13B

A: In this question we can find limit . Firstly solve quadratic equation of the numerator and cancel…

Q: What is the lim x². In(x) x-0+

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Q: Find all values c such that lim x-2 2c²x 5c +1 x²-3x + 2 - exists. (a real number)

A: We say a limit exists if right hand limit and left hand limits are same. We have…