Answer:
Its not that hard think harder 9
Answer: The approximate f(1.1,-0.1) is 4.92.
Step-by-step explanation:
Since we have given that
![f(x,y)=5xe^{xy}](https://tex.z-dn.net/?f=f%28x%2Cy%29%3D5xe%5E%7Bxy%7D)
at (1,0),
we get ![f(1,0)=5](https://tex.z-dn.net/?f=f%281%2C0%29%3D5)
Partial derivative would be
![f_x=5e^{xy}+5xye^{xy}=5e^{xy}(1+xy)](https://tex.z-dn.net/?f=f_x%3D5e%5E%7Bxy%7D%2B5xye%5E%7Bxy%7D%3D5e%5E%7Bxy%7D%281%2Bxy%29)
So,
![f_x(1,0)=5](https://tex.z-dn.net/?f=f_x%281%2C0%29%3D5)
Similarly,
![f_y=5x^2ye^{xy}](https://tex.z-dn.net/?f=f_y%3D5x%5E2ye%5E%7Bxy%7D)
So, ![f_y(1,0)=5](https://tex.z-dn.net/?f=f_y%281%2C0%29%3D5)
Now,
![L(x,y)=f(1,0)+f_x(1,0)(x-1)+f_y(1,0)(y-0)\\\\L(x,y)=5+5(x-1)+5y\\\\L(x,y)=5+5x-5+5y\\\\L(x,y)=5x+5y](https://tex.z-dn.net/?f=L%28x%2Cy%29%3Df%281%2C0%29%2Bf_x%281%2C0%29%28x-1%29%2Bf_y%281%2C0%29%28y-0%29%5C%5C%5C%5CL%28x%2Cy%29%3D5%2B5%28x-1%29%2B5y%5C%5C%5C%5CL%28x%2Cy%29%3D5%2B5x-5%2B5y%5C%5C%5C%5CL%28x%2Cy%29%3D5x%2B5y)
L(1.1,-0.1)=![5(1.1)-5(0.1)=5](https://tex.z-dn.net/?f=5%281.1%29-5%280.1%29%3D5)
and
f(1.1,-0.1) = ![5(1.1)e^{1.1\times -0.1}=4.92](https://tex.z-dn.net/?f=5%281.1%29e%5E%7B1.1%5Ctimes%20-0.1%7D%3D4.92)
Hence, the approximate f(1.1,-0.1) is 4.92.
Answer: False, True, False, True, True, True
Step-by-step explanation:
Points A, B, and C are coplanar since they're on the same plane but not on the same line.
Both BD and DE intersect since they both have a common point which is D.
The line BD connects both planes.
<span>The ratio of 3 to 4 can be written in all the following ways except 4/3. </span>