Question

Answer the following questions: \begin{itemize} \item For which partial derivative $\frac{\partial f}{\partial x}$ or $\frac{\partial f}{\partial y}$ is the finite difference approximation consistently more accurate? \item Why is the finite difference approximation for the other partial derivative is consistently less accurate? (Hint: What happens to the tan y function near y = 1.56?). \item Share a real-world example that might cause similarly poor approximations using this method. \end{itemize} 1. Finding Exact $\frac{\partial f}{\partial x}$: $f(x, y) = 2 \sin x \tan y$ $\frac{\partial f}{\partial x} = 2 \tan y \sin x$ $\frac{\partial f}{\partial x} = 2 \tan y \sec^2 x$ 2. Evaluate (-3.1, 1.56) $\frac{\partial f}{\partial x} = 2 \tan(-3.1)\tan(1.56)$ -25716.40893 3. Finding Exact $\frac{\partial f}{\partial y}$ $f(x, y) = 2 \sin x \tan y$

          Answer the following questions:
\begin{itemize}
    \item For which partial derivative $\frac{\partial f}{\partial x}$ or $\frac{\partial f}{\partial y}$ is the finite difference approximation consistently more accurate?
    \item Why is the finite difference approximation for the other partial derivative is consistently less accurate? (Hint: What happens to the tan y function near y = 1.56?).
    \item Share a real-world example that might cause similarly poor approximations using this method.
\end{itemize}
1. Finding Exact $\frac{\partial f}{\partial x}$:
$f(x, y) = 2 \sin x \tan y$
$\frac{\partial f}{\partial x} = 2 \tan y \sin x$
$\frac{\partial f}{\partial x} = 2 \tan y \sec^2 x$
2. Evaluate (-3.1, 1.56)
$\frac{\partial f}{\partial x} = 2 \tan(-3.1)\tan(1.56)$
-25716.40893
3. Finding Exact $\frac{\partial f}{\partial y}$
$f(x, y) = 2 \sin x \tan y$

Show more…

Answer the following questions:

* For which partial derivative (∂ f)/(∂ x) or (∂ f)/(∂ y) is the finite difference approximation consistently more accurate?

* Why is the finite difference approximation for the other partial derivative is consistently less accurate? (Hint: What happens to the tan y function near y = 1.56?).

* Share a real-world example that might cause similarly poor approximations using this method.

1. Finding Exact (∂ f)/(∂ x):
f(x, y) = 2 sin x tan y
(∂ f)/(∂ x) = 2 tan y sin x
(∂ f)/(∂ x) = 2 tan y sec^2 x
2. Evaluate (-3.1, 1.56)
(∂ f)/(∂ x) = 2 tan(-3.1)tan(1.56)
-25716.40893
3. Finding Exact (∂ f)/(∂ y)
f(x, y) = 2 sin x tan y

Added by Brandi R.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Supreeta N

06/12/2023

Step 1

Using the differentiation rules, we get: ∂f/∂x = 2 tan y sec^2 x Show more…

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Can you help me understand the layout for this? Finding the exact partial and then evaluate. (I was able to get as far as the screenshot but I think I'm doing it wrong) Assume the function f is defined as f(x, y) = 2 sin x tan y Use differentiation rules to find the exact partial derivatives ∂f/∂x and ∂f/∂y, and evaluate those exact partial derivatives at (-3.1, 1.56). Use the finite difference formulas to estimate ∂f/∂x and ∂f/∂y at (-3.1, 1.56) for three different values of the mesh size h = 0.01 h = 0.001 h = 0.0001 Answer the following questions: For which partial derivative or {:(delf)/(dely)) is the finite difference approximation consistently more accurate? Why is the finite difference approximation for the other partial derivative is consistently less accurate? (Hint: What happens to the tan y function near y=1.56 ?). Share a real-world example that might cause similarly poor approximations using this method. Finding Exact (delf)/(delx) : f(x,y)=2sinxtany ¿2tanysinx (delf)/(delx)=2tanysec^(2)x Evaluate (-3.1,1.56) (delf)/(delx)=2tan(-3.1)tan(1.56) -25716.40893 Finding Exact (delf)/(dely) f(x,y)=2sinxtany Answer the following questions: of of For which partial derivative or is the finite difference approximation consistently more Or Dy accurate? Why is the finite difference approximation for the other partial derivative is consistently less accurate?Hint:What happens to the tan y function near y=1.56? Share a real-world example that might cause similarly poor approximations using this method of Finding Exact f,y=2sintany 2tan ysin Evaluate -3.1,1.56 of =2tan3.1tan1.56 25716.40893 of 3.Finding Exact dy f=2sintan

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