고2+ 21-2+2|-4 f(x) = x2 +x-6 x2 4 x2 + |x- 2| x +2 g(x) = h(x) = %3D x- 2 1- Determine the following limit by utilizing derivative of some functions sin 2.x lim 3x e7 1 lim In(4x + 1) lim 5x 7x

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

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A: Let's find.

Q: 4 (11) lim f(x) = X-0 (12) lim f(x): %3D |-10 -8 -6 -4 4 8 10 X +0 -2 -4

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Q: lim In(r) - 0t

A: Consider the given limit

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A: To find if the limit exists or not. limx→3sin2x-6sin4x-12x2-6x+9 limx→5fx when limx→5fxx-5=3

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A: Given: f(x) :  -7  ;  x ≤ -3 (x+2)3 - 6 ;  -3 &lt; x &lt; 0 ( x -2)2 - 5 ;  x ≥ 0

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A: The given limit limx,y→0,0x2-4y2x2+2y2

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A: Explanation of the answer is as follows

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A: We have to find out the limit of the function. We can apply the l'Hospital rule if limit is in 0/0…

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Q: Hon of the Squeeze Theorem) on the same screen. 37. If 4x-9 ((x) x* - 4x + 7 for x> 0, find lim f(x

A: Given: If 4x-9≤f(x)≤x2-4x+7 for x≥0. find limx→4f(x)

Q: 1. If limit of f(x) -8/x-1=10 as x approaches 1, find limit of f(x) approaches 1

A: As per the company guidelines we are supposed to answer nly first question.Kindly repost the other…

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A: The limits are required to be solved. Each part is solved in detail below.

Q: 13. (a) Estimate the value of lim- X x+√1+3x-1 X √1+3x-1 By graphing the function f(x) = - (b) Make…

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Q: 7. Find the limit, if it exists. If the limit does not exist, explain why. sin(2x - 6) sin(4x - 12)…

A: Since you have asked multiple questions in a single request we would be answering only the first…

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A: The given expression is:

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A: To find :  limx→0x22x-1

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A: When we get indeterminate form , we use L'Hospital rule i.e. differentiating numerator and…

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