Don't use plagiarized sources. Get Your Assignment on

Calculus Assignment | Custom Assignment Help

Just from $13/Page

The linear function that best aproximates ##z=x sqrt(y)## at ##(-7, 64)## is ##z = -56 + 8(x+7) – 7/16(y-64) = 28 + 8x – 7/16y##.

To get this result, we must first notice that ##z## is a function of the two variables ##x## and ##y##. Let’s write ##z=f(x,y)##. So, the best linear approximation ##L_(r_0)(x,y)## of ##f## at ##r_0 = (x_0,y_0) = (-7,64)## is given by

##L_(r_0) (x,y)= f(x_0, y_0) + vec(grad)f(x_0, y_0) * ((x,y)-(x_0,y_0))##

Where ##vec(grad)f## is the gradient of ##f## and ##*## is the dot product.

Geometrically, this linear approxiamtion is the tangent plane of ##f## at ##r_0##. The deduction of this equation is very similar to the deduction of the equation for the tangent line of a real function at a point, with the gradient ##vec(grad)f## playing the role of the derivative.

Now we need to calculate the components of the equations for the linear aproximation. ##f(x_0, y_0)## is simply the value of the function at ##(x_0, y_0)##:

##f(x_0, y_0) = f(-7, 64) = -7 times sqrt(64) = -56##

The gradient ##vec(grad)f(x,y)## of ##f## is given by the expression

##vec(grad)f(x, y) = ((del f)/(del x), (del f)/(del y)) = (sqrt(y), x/(2sqrt(y)))##

So, ##vec(grad)f(x_0, y_0) = (sqrt(64), -7/(2sqrt(64))) = (8, -7/16)##

Finally, we have:

##L_(r_0) (x,y)= -56 + (8, -7/16) * ((x,y)-(-7,64)) =## ##= – 56 + (8, -7/16) * (x+7, y-64) =## ##= -56 + 8 (x – 7) – 7/16 (y – 64) =28 + 8x –

Why Choose Us

Quality Papers

At Myhomeworkwriters.com, we always aim at 100% customer satisfaction. As such, we never compromise o the quality of our homework services. Our homework helpers ensure that they craft each paper carefully to match the requirements of the instruction form.

Professional Academic Writers

With Myhomeworkwriters.com, every student is guaranteed high-quality, professionally written papers. We ensure that we hire individuals with high academic qualifications who can maintain our quality policy. These writers undergo further training to sharpen their writing skills, making them more competent in writing academic papers.

Affordable Prices

Our company maintains a fair pricing system for all academic writing services to ensure affordability. Our pricing system generates quotations based on the properties of individual papers.

On-Time delivery

My Homework Writers guarantees all students of swift delivery of papers. We understand that time is an essential factor in the academic world. Therefore, we ensure that we deliver the paper on or before the agreed date to give students ample time for reviewing.

100% Originality

Myhomeworkwriters.com maintains a zero-plagiarism policy in all papers. As such, My Homework Writers professional academic writers ensure that they use the students’ instructions to deliver plagiarism-free papers. We are very keen on avoiding any chance of similarities with previous papers.

Customer Support 24/7

Our customer support works around the clock to provide students with assistance or guidance at any time of the day. Students can always communicate with us through our live chat system or our email and receive instant responses. Feel free to contact us via the Chat window or support email: support@myhomeworkwriters.com.

Try it now!

How it works?

Follow these simple steps to get your paper done

Place your order

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Receive the final file

Once your paper is ready, we will email it to you.

Our Homework Writing Services

My Homework Writers holds a reputation for being a platform that provides high-quality homework writing services. All you need to do is provide us with all the necessary requirements of the paper and wait for quality results.

Essays

At My Homework Writers, we have highly qualified academic gurus who will offer great assistance towards completing your essays. Our homework writing service providers are well-versed with all the aspects of developing high-quality and relevant essays.

Admissions

Admission and Business Papers

With Myhomeworkwriters.com, we will help you secure a position at your desired institution. Our essay writing services include the crafting of admissions papers. We will still help you climb your career ladder by helping you write the official papers that will help you secure a job. We will guide you on how to write an outstanding portfolio or resume.

Editing

Editing and Proofreading

Myhomeworkwriters.com has a professional editorial team that will help you organize your paper, paraphrase it, and eliminate any possible mistakes. Also, we will help you check on plagiarism to ensure that your final paper posses quality and originality.

Coursework

Technical papers

My Homework Writers harbors professional academic writers from diverse academic disciplines. As such, we can develop homework writing services in all academic areas. The simplicity or complexity of the paper does not affect the quality of homework writing services.