Multivariable Calculus Question:

1 answer:

3 0

$f(2,-1)=2^2-(-1)^2=3$

so we're considering the level curve

$x^2-y^2=3$

The tangent line to this curve at (2, -1) will be the value of $\dfrac{\mathrm dy}{\mathrm dx}$ at this point. Differentiating yields

$2x-2y\dfrac{\mathrm dy}{\mathrm dx}=0\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac xy$

and so the slope of the tangent would be $\dfrac2{-1}=-2$ .

The tangent line then has equation

$y-(-1)=-2(x-2)\implies y=-2x+3$

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2 years ago

How do you do 44.70 divided by 15 long division

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Since the divisor is 2 digits, start by looking at the first 2 digits of the dividend. Those are 44, so you're dividing 44 by 15 at the first step. The quotient digit is the largest integer that gives a value less than or equal to the dividend (44) when multiplied by the divisor (15). For the first step, that digit is 2.

To find the new divisor, subtract the product of the divisor and the quotient digit (2·15=30) and bring down the next digit of the original dividend. Now, you have a dividend of 147 and a divisor of 15. Repeat the process as above.

The decimal point location in the answer can be found a number of ways. The simpliest is to put it above the decimal point in the dividend. (When the divisor is not an integer, multiply or divide both divisor and dividend by the same power of 10 until it is.)