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Using the same function as the previous question, f(x, y) = ln(x² + y), answer the following questions: (a) Determine D,J(2,3) with v = (1,5) (b) What is the angle, in radians, between v and V/(2, 3)?

Using the same function as the previous question, f(x, y) = ln(x² + y), answer the following questions: (a) Determine D,J(2,3) with v = (1,5) (b) What is the angle, in radians, between v and V/(2, 3)?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I already did the first question, but I only need help with the second question and the parts with it, can you please label the parts for question 2 because that is one that I need help with. 

Can you do this step by step so I can understand it better and can you make it clearly to read

## Calculus Problem Set Given \( f(x,y) = \ln(x^2 + y) \), answer the following questions: ### Problem 1 **(a)** Explain in one or two sentences why \( f(x, y) \) is differentiable at the point (2, 3). **(b)** Determine the equation of the tangent plane at the point (2, 3). --- Using the same function as the previous question, \( f(x, y) = \ln(x^2 + y) \), answer the following questions: ### Problem 2 **(a)** Determine \( \mathbf{D_v} f(2, 3) \) with \( \mathbf{v} = \langle 4,5 \rangle \). **(b)** What is the angle, in radians, between \( \mathbf{v} \) and \( \nabla f (2,3) \)?
Transcribed Image Text:## Calculus Problem Set Given \( f(x,y) = \ln(x^2 + y) \), answer the following questions: ### Problem 1 **(a)** Explain in one or two sentences why \( f(x, y) \) is differentiable at the point (2, 3). **(b)** Determine the equation of the tangent plane at the point (2, 3). --- Using the same function as the previous question, \( f(x, y) = \ln(x^2 + y) \), answer the following questions: ### Problem 2 **(a)** Determine \( \mathbf{D_v} f(2, 3) \) with \( \mathbf{v} = \langle 4,5 \rangle \). **(b)** What is the angle, in radians, between \( \mathbf{v} \) and \( \nabla f (2,3) \)?
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