= 4. Find the linear approximation of the function f(x, y, z) = x² + y²+z2 at (3, 2, 6) and use it to approximate the number √(3.02)2 + (1.97)² + (5.99)².

Q: > #11 Given z = f(x,y) = 3xy , у find the equation of the tangent plane to the graph, when x=1, y=3.

A: Equation of tangent is z=4x−34​y−2Explanation:

Q: Let f(x,y) = x3+2xy-2y2-10x. What are the critical points, and the saddle point(s), local…

A: the critical points are (−2,−1)and(35​,65​) local minimum at (-2, -1)  saddle points at (35​,65​)…

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A:

Q: Question 2 The graphs of a function f and its derivative f' are shown. Identify each curve and…

A: We have graphs of f and f'We have to identify curve of f and f'

Q: (c) [6 pts] In(x + 1) In(1 - x) = 2. I (d) [7 pts] 2.31-2x = 7.64+x

A: Question cx = 0 and 3 Question dx=−3ln(3)+ln(2)3ln(2)+3ln(3)+ln(7)​≈−1.835Another way of expressing…

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A: E(X) = 1.2Explanation:The expected value of a random variable X, denoted as E(X), for a given…

Q: 6. Sketch an even continuous function with all of the following features: • Absolute minimum at -5 •…

A: Function is even continuous  function.  Absolute minimal at -5 Zeroes at 4 and -4y- intercept at -23…

Q: Answer the following questions for the function defined on the interval [-15, 17]. f(x) = x3 ૨૨ 16…

A: Explained in detail in the below.Explanation:Given f(x)=x2−16x3​ Vertical Asymptote is given by…

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A:

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A:

Q: ☐ 1. Find the volume of the solid formed by revolving the region bounded by the graphs = x² about…

A: V=5162π​Explanation:Step 1:

Q: #14. Given the integral SS² y² cos xdxdy (a) Evaluate it. "(with the given order of integration),…

A: a.)∫12​∫02π​​y2cos(x)dxdy=∫12​[y2sin(x)∣x=0x=2π​​]dy=∫12​[y2sin(2π​)−y2sin0)]dy=∫12​[y2⋅1−y2⋅0]dy=∫1…

Q: Find the absolute extrema of f(x) = 7x2 x-5 on the interval [-1, 2]. maximum, f ; minimum, f

A: on the interval Note:As per bartleby guidelines we are supposed to answer only3 sub-parts (if there…

Q: Let us model the number of automobile sales in a developing country as N(t) 158,000…

A: a) 22899 cars at 2010b) 122566 cars at 2020c) cars sales stabilize at 158000 cars.Explanation:

Q: An offshore oil well is 2 kilometers off the coast. The refinery is 5 kilometers down the coast.…

A:

Q: Evaluate the following integrals using partial fraction decomposition, when applicable.

A: 16.51​ln∣x−4∣−51​ln∣x+1∣+Cor,51​ln∣∣∣​x+1x−4​∣∣∣​+C17.2ln∣x+2∣−23​ln∣2x+1∣+CExplanation:Step 1:Step…

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A:

Q: B. Find the distance between the point A(-2,2,1) and the plane 3x 5y+z = 5. - C. Find the equation…

A:

Q: Find all solutions to the quation. sin 0 = 2 Write your answer in radians in rms of it, and use the…

A:

Q: I need help with this problem and an explanation for the solution described below (Discrete…

A: The objective of the question is to find the negation of the given statement. In logic, the negation…

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A: Final answer and explanation are clearly mentioned in the next section.Explanation:Please let me…

Q: #5 Find parametric equations of the I love through points P(-2,4,-1) and Q (-3,-5,6)

A: The parametric equations of the line passing through points P(-2, 4, -1) and Q(-3, -5, 6) are:•x(t)…

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A: The objective of this question is to calculate the mean, median, and mode of the given data set.…

Q: - The Parametric equation of the line that passes through the point A(1, 1, 1) and parallel to the…

A:

Q: Find the volume of the following solids.   The base of a solid is the region between the curve y…

A: The objective of this question is to find the volume of the given solids. The base of the solid is…

Q: Give your final answer in interval notation. Determine the intervals where the graph of f(x)=x+3/x…

A: To determine the intervals where the graph of  is concave upand concave down.Note: Since you have…

Q: The vectors (2,10, 4) and (1, 3, x) are orthogonal if and only if x= -8. Ignore "Give your reasons"…

A:

Q: Solve the following initial value problem for r as a function of t. dr Differential equation: =(2…

A: Given:To find:r(t)

Q: Evaluate the integral L 4 diverges. 2 3x ln x dx or state that the integral

A:

Q: Find the exact length of the curve √x = 1 + 6t² y = 6+4t³ for 0 <t≤4

A: Answer:   6817​−4Explanation:For any query with the solution please ask in the comment box.

Q: 4. Let A, B and C be subsets of the universal set U. Draw the Venn diagram for (CUB)N(Ā-C). U C B

A:

Q: x = −1 + cos(t), y = −2+ sin(t), 0 ≤t<2π . Sketch a graph of 5 4 3 -5-4-3-2-1 2 1 -1 -2 -3 -4 -5+ 55…

A: Orientation of the graph is Counterclockwise.Explanation:

Q: Suppose f(x, y) = x² + y² - 10x - 6y+4 (A) How many critical points does f have in R²? (B) If there…

A:

Q: The distance s, in m, above the ground for a projectile fired vertically upward with a velocity of…

A:

Q: 3. Use implicit differentiation to find and (a) xy+yz = x2 (b) xyz = cos(x + y + z) (c) xy² 23 +…

A:

Q: Integrals of the form sin mx cos nx dx sin mx sin nx dx cos mx cos nx dx can be found using the…

A:

Q: Problem 3. Show that the volume of the largest parallelpiped (i.e., rectangular prism with sides…

A: V = 8abc / 3√3Explanation:Here's how we can find the volume of the largest inscribed…

Q: lim n!en 1/2

A: √(2π) Or. √2 •. √πExplanation:Step 1: Step 2: Step 3: Step 4:

Q: The equation r(t)=(12 sin t) i+ (4 cos t) j +(8t) k is the position of a particle in space at time…

A: The equation  is the position in space in time . To find the particle's velocity and acceleration…

Q: Let g(x, y, z) = x³y²z√√√18-x-y-z.

A: The given function is

Q: Use Linear Approximation to estimate Af = f(3.02) - f(3) for f(x)=sin(). (Use decimal notation. Give…

A: By using Linear approximation to estimate .

Q: End Find the derivative from FIRST PRINCIPLES of A 3) 3 f(x) = 2x+1 nobonut gniwo

A:

Q: Estimate Ay using differentials. y = x 1/2e4x-1, a = 1, dx = 0.1 (Give your answer to four decimal…

A:

Q: 3. (4.4.1 #15) Find the general solution. y" - 3y + 2y = e³ (1 + x)

A:

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS

A: The answers are as follows: (a) The vector equation of the plane is r.(−9,15,10)=−23. (b) The…

Q: The function f(x)- is concave down on which interval?

A: The function f(x) is concave up on the interval I if f"(x) &gt;0 for all x in I.The function f(x) is…

Q: Find all points (x,y) on the graph of f(x) = 2x² - 3x with tangent lines parallel to the line y =…

A:

Q: Solve the system of equations 2x4y+ z = 6 -x+y-z=-2 x - 2y = 2 by converting to a matrix equation…

A: given system of equationswhere

Q: what is the volume of the solid formed by revolving y = 13sinx*cosx between x=0 to x=pi/2

A: Answer written in explanation Explanation:Step 1: Step 2: Step 3: Step 4:

Q: Calculus I May I please have the solution for the following questions? Sketch an accurate graph…

A: Please refer below to get your solutions.Explanation:Sol -&gt; a) Sol -&gt; b) Sol -&gt; c) Sol…