Find div F and curl F if F(x, y, z) = x²i – 7j + yzk. div F= curl F=

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A: Topic:- geometry

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Q: АСTIVITY 2 FINDING OTHER TRIG VALUES Given some initial values, apply the different trigonometric…

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A: Explained below

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Q: - In(a°y*) + x2 Consider z as a function of the variables x, y which is denoted by z and let P(1,-1)…

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Q: Kuya Bill is selling 'Bill phones'. If the cost for selling r phones is given by 10000 C(r) = 120x +…

A: Given, Cost function, C(x) = 120x + 10000/x - 2000 Price Dand function, p(x) = 1000 - 2000/x2 + 200x

Q: 2. Show that if x and y are two vectors, then

A: Replace x→ by u→ &amp; y→ by v→     Graphing software do not accept label x, y To show: u - v ≤u±v≤u…

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Q: A lighted candie burns outr according to the equation y'(1) =ky (1) where y is the length (in…

A: see below the answer and explanation

Q: Evaluate F. dr F(x, y) = 5xi + 8yj C: r(t) = ti + v4 - tj, -2 sts 2

A: Calculate drdt. drdt=ddtti+4-t2j      =1i+124-t20-2tj      =1i+124-t2-2tj      =1i-t4-t2j…

Q: Find curl (3z i + 4x j + 7y k). curl(3z i + 4x j + 7y k) = ( i Di + ( i Oj + ( )k

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Q: 4. The path of a baseball relative to the ground can be modelled by the function dlt) = – f² + 8t +…

A: derivative

Q: d d Calculate ri(t) · r2(t)] and ri(t) × r2(t)] first by differenti dt dt the product directly and…

A: We have, r1(t)=3t i+7t2 j+4t3 k , r2(t)=t4k

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Q: (1 — 2x)dx

A: Given,  ∫01(1-2x)dx

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Q: Determine whether the improper integral converges and, if so, evaluate it. (Use symbolic notation…

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Q: Write the augmented matrix for the system of linear equations. 6x +y+ 3z =D 2 9x - 6y- z = 5 x-8y-6z…

A: Explained below

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A: Derivative of function

Q: In t years, the population of a certain city grows from 700,000 to a size P given by P(t)= 700,000 +…

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Q: If xy2 3x2y + C, then what is the value of C at (2,2)?

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Q: Use the function f(a) to fill in the table:

A: Given :

Q: Let 7 (t) = Find a parametric equation of the line tangent to 7(t) at the point (– 27, – 44, 1.792)…

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Q: Suppose that z = f(a, y) is differentiable at the point (1024, 1024) with, (1024, 1024) = 5…

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Q: Ise Stokes' Theorem to evaluate F. dr where C is oriented counterclockwise as viewed from above.…

A: Using stokes' Theorem we have to evaluate given integral

Q: Using the laplace transformation formula, ∫ f(t) e^−st dt evaluate L[8t^2 e^-2t]

A: Laplace transform of the function f(x)Lf(t)=∫0∞e-stf(t)dt