Hw e- Chapter faur " Lonits' O Find Lim 2- x X→2 2- 2X X #2

Q: x²-2x-3 lim a. (x-3)3 2-2r-3 x-3 (x-3)' x² - 2x-3 b. lim x² - 2x-3 lim 33 (x-3)3 c.

A: x→3+ limx2-2x-3(x-3)3=x→3+lim(x-3)(x+1)(x-3)3=x→3+limx+1(x-3)2=∞

Q: Determine the value of 6>0 for which lim (3x² – 1) = 47 x+ 4 A 6 = max{ – 4-16 -5, - 4 +/16+ 3 들) 3…

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Q: At x = 3 + Ax, the value of the function is f(3 + Ax) = 17 - + Ax Hence, (3 + A3²) -( 17 m = lim Ax…

A: Solution: The objective is to fill the required blanks

Q: 8) lim 2X - メーラ メ1x (-3

A: Here we have;  A=limx→32x2-x-15x|x-3|

Q: lim2

A: Explained below

Q: х2-2х-3 6. lim х-з х2-4х+3

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Q: x-1-2 2) lim 1 1 Xー 2 2,

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Q: 1 1+ 2x lim x → 0- 1 3 + 2x

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Q: Зх — 4 1. lim 2х+1

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Q: (4+3x2 1. lim x-00 \3-4x2. А. -3/4 В. 3/4 С. -4/3 D. 4/3

A: Given query is to find indicated limit.

Q: What is lim 2 (x - 2)

A: Given

Q: 3 Lim xah

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Q: What is lim ? X-0+ x

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Q: 11) Evaluate lim (1+ 2x)csc(x).

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Q: h) lim x* +x?- 2 I+x+x+x

A: Here we have to find the limit of given function. We can divide it in two function , one in…

Q: t -9 9. lim- -3 2t +7t+3 1 1 11. lim x-3

A: 9) limt→-3t2-92t2+7t+3=limt→-3(t-3)(t+3)(2t+1)(t+3)=limt→-3t-32t+1=-3-32(-3)+1=-6-5=65

Q: Lim X-70 (1 + 1/2 ) ²

A: Solution:  we have, to evaluate

Q: Extend L'Hopital's Rule to evaluate lim (x2 - x) x-+

A: See the attachment.

Q: x*-2x2-x с- lim x-2 , х 2 2 х2-4

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Q: 3x+5, p) The function f(x) is defined by f(x) = • If lim f(x)exists, what is th 1- 2x+b;if x>1

A: If the limit of the function exists , then left hand limit is equal to right hand limit. therefore…

Q: Give an explicit example of each of the following: (a) Two power series f and g in the complex…

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Q: 5 4 2 -a 5 -4 -3 -2 -1 1 2 3 4 5 a 7 -1 -2 -3

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Q: lim.                          x^5 x --> - infinity

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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: 5. Find limf(x) x4-3 a) f(x) = 5x4 %3D 6x4 - 3 b) f(x) = 3x3 2x3 - 9 c) f(x) = %3D 3x5

A: We have to find limx→∞fx for a fx=x4-35x4b fx=6x4-33x3c fx=2x3-93x5 Since all above limit has ∞∞…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.