Prove the linearity relations for gradients: (a) V(f + g) = Vf + Vg (b) V(cf) =
Question:
Prove the linearity relations for gradients:
Transcribed Image Text:
(a) V(f + g) = Vf + Vg (b) V(cf) = cVf
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 50% (2 reviews)
a We use the linearity relations for partial ...View the full answer
Answered By
Mugdha Sisodiya
My self Mugdha Sisodiya from Chhattisgarh India. I have completed my Bachelors degree in 2015 and My Master in Commerce degree in 2016. I am having expertise in Management, Cost and Finance Accounts. Further I have completed my Chartered Accountant and working as a Professional.
Since 2012 I am providing home tutions.
3.30+
2+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Mathematics questions
-
Prove (L1) (the linearity and additivity rule for Laplace transforms) using integrals. (L1) a, f (t) + a f (t) +...+ a f(t) (L2) f(ct) (L3) 1 (LA) t (L5) teat (L6) " (ne (0,1,2,...}) (17) h(t-to)...
-
State and prove linearity principal for Laplace transform. Also discuss the applications of Laplace transform in engineering field. state and prove Linearily Principal For Laplace t1onstorm...
-
Project, Useful Formulas for Gradients and Laplacians, prove the following formulas and give for each of them two examples showing when they areadvantageous. V(fg) fVg+gVf (f") = nf-Vf V(f/g)...
-
27 13. Name-4 Abdominal Quadrants and 9 Abdominopelvic Regions using the PowerPoint Number Quadrant 1 2 3 4 Number Region 1 2 D. Bladder: E. Small Intestine: F. Spleen: G. Pancreas: 34 5 6 Tolla 7 8...
-
The position r of a particle moving in an xy plane is given by r = (2.00t 3 5.00r)i + (6.00 7.00t 4 )j, with r in meters and t in seconds. In unit-vector notation, calculate (a) r, (b) v, and (c) a...
-
The Abram Manufacturing Company in Rochester, Minnesota, assembles and tests electronic components used in handheld video phones. Consider the following data regarding component T24: The activities...
-
A sail plane with a lift-to-drag ratio of 25 flies with a speed of \(50 \mathrm{mph}\). It maintains or increases its altitude by flying in thermals, columns of vertically rising air produced by...
-
To expand operations, Aragon Consulting issued 170,000 shares of previously unissued stock with a par value of $1. The selling price for the stock was $21 per share. Record the sale of this stock....
-
The annual return on the S&P 500 Index was 12.4 percent. The annual T-bill yield during the same period was 5.7 percent. What was the market risk premium during that year?
-
Prove the Chain Rule for Gradients in Theorem 1. THEOREM 1 Properties of the Gradient If f(x, y, z) and g(x, y, z) are differentiable and c is a constant, then (i) V(f+g) = Vf + Vg (ii) V(cf) = cVf...
-
Let C be the curve obtained as the intersection of the two surfaces x 3 + 2xy + yz = 7 and 3x 2 yz = 1. Find the parametric equations of the tangent line to C at P = (1, 2, 1).
-
a. Suppose that you want to borrow a widget beginning in December of Year 0 and ending in March of Year 1. What payment will be required to make the transaction fair to both parties? b. Suppose that...
-
4.4) The B-field is uniform and perpendicular to the plane of the figure. The conductor has a straight segment with length L perpendicular to the plane of the figure on the right, with current...
-
Use the following information to answer the next question. The driver of a vehicle travelling with a speed of 19.4 m/s approaches an intersection. The driver notices the colour of the traffic light...
-
dB dt Scoop out a small cylindrical region with radius R/2 inside the big cylin- drical region with radius R as shown in the figure. The magnetic field B(t) directed outward varies with time such...
-
Referring to this picture for line charges, if the wire is very long (the length is unlimited), then = 8.23 nC/m and a 1.9 m, then the electric field in P is... N/C. (Write the answer with 2 numbers...
-
Question 5: If the period of a simple harmonic oscillator is halved, but its amplitude is kept the same, what happens to the angular frequency and maximum potential energy, respectively? Assume that...
-
Leaky Pipe, a local retailer of plumbing supplies, faces demand for one of Its SKUs at a constant rate of 30,000 Units per year. It costs Leaky Pipe $10 to process an order to replenish stock and $1...
-
Consider model (9.18). What is the effect on the model parameter estimates, their standard errors, and the goodness-of-fit statistics when (a) The times at risk are doubled, but the numbers of deaths...
-
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n. 2 + 4 + 6 + ... + 2n = n(2n + 1)
-
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n. 3 + 4 + 5 + ... + (n + 2) = 1/2 n(n + 5)
-
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n. 3 + 5 + 7 + ... + (2n + 1) = n(n + 2)
-
Locate the following scholarly articles about bankruptcy in the SUO Online Library. Identify and discuss the most important aspect of the article, as well as any ethical issues. Boettcher, J.,...
-
Alex Corporation reports the following components of stockholders' equity at December 31 of the prior year. Common stock-$25 par value, 50,000 shares authorized, 33,000 shares issued and outstanding...
-
Drawing from the Lambert article, how has corporate internalization of the law service function affected large law firms and the careers of many junior lawyers working in these firms? What do you...
Study smarter with the SolutionInn App