Can someone help me solve these problems?

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  • Thread starter khokababu
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In summary, the conversation discusses finding the derivative of a function using the chain rule and using direct substitution. It also involves finding the equation of a tangent plane and using linear approximation to find an approximate value of a function. The first problem involves using the chain rule to find the derivative of a function and the second problem involves finding the equation of a tangent plane and using linear approximation to find an approximate value of a function.
  • #1
khokababu
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0
1. If z=f(x,y)=x3+xey and x=sint,y=logt, use the chain rule to find dzdt in terms of t. Then - by using direct substitution:

express z in terms of t and find dzdt .

2. Suppose that z is a function of x and y, implicitly related by the equation

x2/4+y2+z2/9=3

Find the equation of the tangent plane to the surface f(x,y,z)=3 (surface of ellipsoid) at the point where (x,y)=(−2,1,−3). Then determine the linear approximation to function z in vicinity of (x,y)=(−2,1) and use it to find the approximate value of z(−2.1,1.1)
 
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  • #2
A couple of tips:
1) use ^ to indicate powers I think the first function is x^3+ xe^y but cannot be certain.

2) Show some effort yourself, don't just post a problem without showing any of our own ideas or work.

Can you find the partial derivatives of x^3+ xe^y with respect to x and y? Since the first problem says "use the chain rule" do you know what that is?

For the second problem, you have f(x, y, z)= x^2/4+ y^2+ z^2/9= 3. If you have a surface given by f(x, y, z)= 3, then the tangent plane at (x_0, y_0, z_) (which satisfy the equation f(x_0, y_0, z_0)= 3) then the tangent plane there is given by [tex]\frac{\partial f}{\partial x}(x- x_0)+ \frac{\partial f}{\partial y}(y- y_0)+ \frac{\partial f}{\partial z}(z- z_0)= 0[/tex] where the partial derivatives are evaluated at (x_0, y_0, z_0). Can you find those partial derivatives?
 
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FAQ: Can someone help me solve these problems?

1) What kind of problems do you need help solving?

I am a scientist, so the problems I need help solving are typically related to scientific research, experiments, or data analysis. However, I may also need help with general problem-solving in my field of study.

2) Can you provide more details about the problems you need help with?

Yes, I can provide more details about the problems I need help with. It would be helpful if you could specify the specific topic or area of research that the problem pertains to. If possible, please also include any relevant data or information that may be helpful in solving the problem.

3) How urgent are these problems that you need help with?

The urgency of the problems I need help with may vary. Some may be time-sensitive while others may not have as strict of a deadline. I will do my best to communicate the urgency and any relevant deadlines when asking for help.

4) Are there any specific qualifications or expertise that you are looking for in someone who can help solve these problems?

It would be helpful if the person helping me has a background in the same field of study or has experience with similar problems. However, I am open to anyone who is willing to lend their expertise and has a strong problem-solving ability.

5) How can I help you solve these problems?

There are various ways you can help me solve these problems. This could include providing guidance, suggestions, or resources, or even collaborating on finding a solution. I am open to any form of assistance that you are able to offer.

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