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Problem

Find the limits in Exercises $1-12$. $$ \lim _{…

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Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 Problem 21 Problem 22 Problem 23 Problem 24 Problem 25 Problem 26 Problem 27 Problem 28 Problem 29 Problem 30 Problem 31 Problem 32 Problem 33 Problem 34 Problem 35 Problem 36 Problem 37 Problem 38 Problem 39 Problem 40 Problem 41 Problem 42 Problem 43 Problem 44 Problem 45 Problem 46 Problem 47 Problem 48 Problem 49 Problem 50 Problem 51 Problem 52 Problem 53 Problem 54 Problem 55 Problem 56 Problem 57 Problem 58 Problem 59 Problem 60 Problem 61 Problem 62 Problem 63 Problem 64 Problem 65 Problem 66 Problem 67 Problem 68

Problem 4 Easy Difficulty

Find the limits in Exercises $1-12$.
$$
\lim _{(x, y) \rightarrow(2,-3)}\left(\frac{1}{x}+\frac{1}{y}\right)^{2}
$$

Answer

$\frac{1}{36}$

Related Courses

Calculus 3

Calculus 1 / AB

Thomas Calculus

Chapter 14

Partial Derivatives

Section 2

Limits and Continuity in Higher Dimensions

Related Topics

Partial Derivatives

Applications of the Derivative

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Problem 1

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Problem 5

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Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

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Problem 27

Problem 28

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Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

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Problem 41

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Problem 43

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Problem 46

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Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

Problem 59

Problem 60

Problem 61

Problem 62

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Video Transcript

in this multi variable limit problem, we could use direct substitution. Justus we would with a one variable limit problem. And so we'll end up getting 1/2 plus a negative 1/3. Or we could just go ahead and say minus but 1/3. And then we might as well just go ahead and convert these so we could do it all by hand and we'll come up with our common denominator here, multiplying top bottom the first fraction but three. So we'll end up with 36 multiply second fraction, top bottom by two minus 26 And so, at this point, you could see we'll end up getting 1/6 all squared. And from there that would just go ahead. And where the numerator spread the denominators or a final solution is 1/36.

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George B. Thomas, Maurice D. Weir, Joel Hass, Frank R. Giordano

Thomas Calculus

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