LIMITS 1. Evaluate the following limits, if they exist. If they do not exist, but approach too, indicate th Indicate vertical asymptote(s) if any. You MAY NOT USE L'Hopital's Rule. (a) lim I→3 x2 - r - 6 2 - 4r +3 [Ans:

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A: To expand the quotient by partial fractions.

Q: exercise

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Q: dy by implicit differentiation. dx E. Find 1 ー+ー=2 х у 1 x² +y? = xy 2. 1.

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A: We can solve as follows

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Q: 29. Prove the following derivatives by using the definition of derivative. (a) (") = n. dx nxn-1

A: topic - derivative and limits

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Q: ;Which sequence is increasing ? 7n-21 4n -7n+2 4n 4n+2 7n 7(-1)" 4 None of the others

A: We need to determine which sequence is increasing.

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Q: D. Find the area of the region bounded by the given curves. Breaking 1 NEWS x2 = 4y 3 y? = 4x %3D

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A: Solution: So what we need to do to get the desired polynomial is to calculate the derivatives,…

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A: First we find unit vector of v.

Q: Question 2 Let us calculate the definite integral | (2 + a? + 1)°(6æ² + 4x) da

A: Given,            ∫x3+x2+156x2+4xdx

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Q: 3 5 dx

A: To calculate the value of the given integral.

Q: Given the function f(x) =

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A: The objective of the question is evaluate the vector with given magnitude and same direction vector.

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A: Here we have to integrate the given Integral.

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A: The given function f(x)=x5-4x-3-4

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A: This is a problem related to integration. Based on the general formula we will answer the question.

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Q: Find the average value TEX of the function f (x) =4sin cos on - 2 the interval [1,4].

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A: This question is based on exponential Function.

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