Let (z, y, z)= + z ln (y + 2) be a scalar field. Find the directional derivative of at P(2,2,-1) in the direction of the vector 12 4 Enter the exact value of your answer in the boxes below using Maple syntax. Number

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A: f(x,y)=x2+5xy+y2−22x−13y+27fx(x,y)=∂∂x(x2+5xy+y2−22x−13y+27)Using the power Ruleddxxn=nxn−1

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A: Note:-Since you asked multiple questions, according to our policy we can answer only first question…

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A: We need to find out the derivative of the composite function.

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A: Given:a region that is bounded by To find:centroid of the region.

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A: f(x)=2tan⁡xx

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Q: graph linear inequlity  11t > 7

A: The required answer is given below.Explanation:

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A: Given :- f(x) = x/3To find :- f(x) =

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Q: 4. Solve the difference equation Yn+25Yn+1 +4yn = n² with initial conditions y(0) = 2, y(1) = -1.

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A: The given function is where d is diameter and length is L.Here, L=12 and d=22

Q: = = 80 minutes, the bacterial The doubling period of a bacterial population is 10 minutes. At time t…

A: Initial population:312.5 Size of bacteria after 3 hours: 81920000Explanation:

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Q: ƒ' (4) = If f(x) = 3√√√x(x³ − 2√x + 2), find f'(4).

A: Given that

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A: Note:As per our guidelines we are supposed to answer only first 3 subparts if there are multiple…

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A: Explained in detail in the below.Explanation:Given that, α is a double root of λk + ak−1 λk−1 +...+…

Q: 5 Similar to 8 ft wire page KX wire 326 : 83 11 ft > with different numbers. [use Calc.] ➜ 15 ft…

A: The given figure

Q: f(x) = 1-x², ax + b, ((x-1)³ + 2, x ≤ 0 0 1

A: f(x)={1−x2,x≤0ax+b,0<x≤1(x−1)3+2,x>1

Q: pls solve using differential calculus

A: Below complete solution is Given.Explanation:

Q: a. Σ=zk2 b. Σ=1(1 + j)3 (1+j)³

A: To re-write the sigma notation as a summation and to perform the indicated addition.

Q: (BC Topic) Which of the following infinite series diverge? n N I. Σ n=1 3n+1 1 n=12n²-5n+3 III. BWT…

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Q: let f(x) = (x-3)^-2. find all values of c in (1, 7) such that f(7)-f(1) = f1(c)(7-1)

A: There is no number c in (1,7) such that  f(7) - f(1) = f'(c) (7 - 1)    If you face any problem in…

Q: a n = sin n n 2²

A: For the sequence given below, to determine whether it converges or diverges. If it converges,then to…

Q: 2. Find the solution of the initial value problem 1 = y+t² sint, y(x)=0. dt t

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Q: y = f(x) N The figure above shows the graph of the twice-differentiable function f and the line…

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Q: Differentiate and simplify each of the following. a) f(x) = 8x³ +7x² − 3x+14 c) f(x)=(x²+1)'(7x +…

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Q: Consider the following theorem. If f is a differentiable function of x and y, then the directional…

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Q: Evaluate the following integral or state that it diverges. Ĵ dx 2 -∞ x + 225 Select the correct…

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Q: (BC Topic) What is the sum of the infinite series Select one: O a. diverges e-n O b. O c. O d. e H…

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Q: dw dt Problem #5: Let w = 5x² + 2y², where x(t) = −3+2t and y(t) = 4t - 1. Use the Chain Rule to…

A: Given  where

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Q: Differentiate the following function: ƒ'(x) = f(x) = ex + x²

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Q: A bank features a savings account that has an annual percentage rate of r = 2.9% with interest…

A: (A) a = $2,000 (the initial deposit)r = 2.9% (annual interest rate)k = 4 (since interest is…