Given f(x, y, z) = √√−7x + 3y – 3z, find fx(x, y, z) = fy(x, y, z) fz(x, y, z) = =

Q: 16. Find the value of the constant k so that the function f(x) = { kx-5 if 0 < x < 2; is continuous.

A: We are given a piecewise function and we need to find out the value of the constant k such that the…

Q: Use the function f and the given real number a to find (f ¹)'(a). (Hint: See Example 1. If an answer…

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Q: Consider the following. x² + y² = 81 (a) Find two explicit functions by solving the equation for y…

A: Find the two explicit function sloveing equationx2y2=81

Q: A rock thrown vertically upward from the surface of the moon at a velocity of 36 m/sec reaches a…

A: According to company policy we are allowed to provide solution for only first 3 sub parts. If you…

Q: Find the slope of the y = sin(x) K 3 A 2 -2 y 2 1 NIR 1516 Need Help? 2 y = sin(4 x) M^^^ X 2 л…

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Q: What is the largest set of real values r such that the sequence limn→∞r converges (a) 0≤r ≤ 1 (b) −1…

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Q: The integral 27 12xe-x² dx can be done with the substitution u = e X and du = xe X dx.

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Q: A rocket accelerates by burning its onboard fuel, so its mass decreases with time. Suppose the…

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Q: 4. For the graph of the function g below, (a) Does g(4) exist? (b) Does lim g(x) exist? x-4 # -2 4…

A: The given graph of function f is:

Q: For the graph of the function g below, (a) Does g(4) exist? (b) Does lim g(x) exist? x 4 (c) Is g…

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Q: Consider the differential equation y"-16y'+64y = 0. The characteristic equation is The solution(s)…

A: Consider the differential equation

Q: 2. Find parametric equations for the line through the point (7,7, 1) with a direction vector d = A

A: Point (7,7,1)d=[1      6      2]

Q: Solve the differential equation. y"-4y'-5y = 0, y(0) = 6, y'(0) = 6

A: We have to solve the given differential equation with the given initial conditions.

Q: Suppose that the position of a particle is given by s = f(t) = 2t³ + 7t + 9. (a) Find the velocity…

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Q: 6. Kitty starts riding her tricycle 3 ft from her front door; her distances s from her front door t…

A: The instantaneous velocity is given by the change in velocity in a very small time.

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

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Q: f(x) = 3+x 5 Find each of the following. Be careful - you only have 3 tries! a) f(-2) = b) f(1) = c)…

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Q: 13. Evaluate limx→∞ cos(3x²). -5 3x5

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Q: Let C be the curve y = 2x³ for 0 < x < 1. 0.5 Find the surface area of revolution of C about the…

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Q: 9. Evaluate (a) limx→1 2023_ (b) limx→0 x-1 x-sin x ¹x0 4x5-2x³ (c) lim₂-0 3-1-1-2 2x4-3x³

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Q: What are the projections of the point (10,8,-2) on the coordinate planes? On the xy-plane: ( On the…

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Q: y' = y = 5 t 2 1 + + t4 ✔t

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Q: Find dy/dx at the given point for the equation. x = y3 – 5y2 + 2, (-2,1)

A: Given, given point is (-2,1)formula of derivatives are '

Q: Q4. Let x denote the grams of gold obtained in a ton of ore. Consider the two events A = {0 < x < 3}…

A: As per our guidelines we are allowed to answer only three subparts of the given problem. Kindly…

Q: r what value of a is the function f (t) = 08 O-15 O -30 O 24 t -a, -10 < t ≤ 3 t² + 8t, 3 < t < 10…

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Q: 2x² - 1 (a) lim X18 1-x²

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Q: What is the length of the curve for 0 = 0 to 0 = π? Answer: 241.3053 x = 4(cos 0 + 0 sin0) y = 4(sin…

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Q: The trigonometric substitution x - 2 = 3 sec could be useful in integrating a function (i.e., an…

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Q: Find the derivative of the logarithmic function. f(x) = In(-⁹x2) 9x Step 1 Rewrite the given…

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Q: Use cylindrical shells to find the volume of the solid generated by rotating the curve y = 4 ln(x)…

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Q: Find x, y, z, t such that 6 x + y [38]-[48]+[24, ***]. =[ :] tu]. -1 2t 4 t 2z+t

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Q: ketch a possible graph of a function f, together with vertical asymptotes, that satisfies all of the…

A: We will satisfy each conditions with graph of function

Q: (1) If f(x) = x¹0, then f'(x) =

A: According to bartleby guide line we do only first part of multiple questions. please re-post other…

Q: Give a geometric description of the following set of points. x² + y² + z² - 10z≥ − 9 Select the…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: olve the following initial value problem for r as a function of t. dr = (tan (1 + (cos (+¹))1-1…

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Q: form the follo x² + y²-2x-6y= 2

A: Given equation is as follows

Q: Estimate the instantaneous rate of change of f(x) = 3x² +5 at the point: x = 1 In other words,…

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Q: If f and g are continuous functions with f(-1) = 3 and the following limit, find g(-1) _lim [2f (x)…

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Q: Find the points at which the graph of the equation has a vertical or horizontal tangent line. 81x² +…

A: Graph of Equation is81x^2+49y^2+1134x-882y+3969=0Now we have to calculate vertical or horizontal…

Q: Find the growth rate after 10 hours. Afton homme help (numbers) will the 200002 ove

A: Solution-The formula of becteria after t hours is,

Q: Prove that if A is a square matrix, then C = (A-AT) is a skew-symmetric matrix.

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Q: 5. Consider the region R bounded by x = 12(y²y³) in the first quadrant. Use the method of…

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Q: . Let A = 1 03 2 3 4 1 02 Find A-¹ if possible. If A−¹ does not exist, explain why.

A: Given that a matrix A  and we find the inverse of this matix A or A-1.

Q: Check whether the function yesin¹ (5*) is a solution of the differential equation y' + y = - 5x the…

A: The given differential equation is

Q: Solve the initial value problem for r as a vector function of t. d²r dt² Differential equation: = -…

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Q: Find the Laplace transform, F(s) of the function f(t) = (e4t - e5t) ², t> 0 F(s) = S> 4

A: Laplace transform of exp(at) is equal to (1/(s-a)), where s&gt;a.

Q: 4. Find the area of the shaded region depicted below. C 8 2 y = 8x y = 200 x² + y = x X

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Q: Find the Laplace Transform of the function f(t) = te¯t by evaluating the integral -t F(s) foto e 0…

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Q: Solve the differential equation. y"-8y +16y = 0, y(0) = 5, y'(0) = 25

A: We have to solve the differential equation with the given initial condition.

Q: Let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. Find (1) and s'(4). y…

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