Exercise 16 find the tangent plane to f(x, y) = (x + y) ln(x2 + y2) at the point (1,1) in both standard form and linearized form.

Scalar form:

Linear form:

Step-by-step explanation:

We need the partial derivatives of the function f(x,y):

Notice we need to use product rule: (uv)’ u’v+uv’ where here:

Therefore:

We evaluate them in the given point (1,1):

We also need to evaluate the function f(x,y) at (1,1):

Then we plug the pieces into the formula of the tangent plane:

Here: , so:

We collect everything on the left side to get:

Which is the scalar form of the equation of the plane

Then we distribute to get:

Then simplify by combining like terms:

Finally move the constant to the right side to get the linear form:

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.

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step-by-step explanation: