Let 60, 61. What is the derivative of the function y = log(x)? 1 -In(x) In(b) b* In(b) 1 In(b) X e* In(b)

Q: Suppose that f(x, y, z) = x²yz - xyz³ is a function of three variables. 1. Find the gradient of f(x,…

A: f(x,y,z)=x2yz−xyz3(1) Using the power ruleddxxn=nxn−1

Q: 12. The population of a city is growing exponentially and can be modeled by the equation…

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Q: Fill in the blanks and evaluate the following indefinite integral. 2x dx = (x+4)2 -S dx = (x+4)2 x+4…

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Q: Find the minimum distance from the point (-2, -2, 0) to the surface z = √√9-2x-2y. (Hint: To…

A: To find the minimum distance from the point .

Q: lim (√√x22x - x) 81x

A: −1Explanation:If you have any questions please let me know in comment box thankyou.

Q: Evaluate the double integral by first identifying it as the volume of a solid. 3 dA, R = {(x, y) |…

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Q: iii) sin(xy)=x³ + x²y. Ex 2. Find the derivative dy for the following then evaluate the derivative…

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Q: The region between the lines y=2x, y=x/3 and x=3.

A: Detailed solution of the problem is given below. Explanation:Step 1: Step 2:

Q: Suppose according to a large research poll in a certain year, 59% of respondents agreed that the…

A: a. To find the probability that a respondent agreed with both statements, we can use the formula for…

Q: a homeowner wishes to insulate  his 1200 square foot house's attic. The total cost C (r) for r…

A: The homeowner should place 9 inches of insulation in the attic to minimize the total…

Q: A company uses the model R(x) = 35x^2 - 5/3x^3, 0<=x<=10   to relate its revenue, R, in…

A: Therefore, the point of diminishing returns for this model is at 7 million dollars.Explanation:To…

Q: ii) siny+x= y.

A:

Q: A manufacturer believes that the cost function 5 C(x) = x²+90x+900 approximates the dollar cost of…

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Q: The 3 × 3 matrix B satisfies the equation B^3 = −B. Show that B cannot have an inverse

A: We proved that, the matrix B cannot have an inverse if it satisfies the equation…

Q: a. If the tank is full, how much work is required to pump the water to the level of the top of the…

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Q: Check that the point (-1, 1, 2) lies on the given surface. Then, viewing the surface as a level…

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Q: Continuous Compound Interest Jesaki Bank offers a 10-year CD that earns 2.5% compounded…

A: 5.8 yearsExplanation:Refer to the attached image for the step-by-step solution:

Q: The total sales of a company (in millions of dollars) t months from now are given by S(t) = 0.05t³ +…

A: Answers :: Part -> (A)S′(t)=0.15t2+1.6t+3 Part -> (B)S(6)=66.6S′(6)=18Explanation:Sol)

Q: Determine the solution to the following system: 3x+20y8z = 15 20x+15y-7z = 28 6x+5y-4z = 7

A: The solution of the system of equations is:x=1y=1z=1Explanation:The given system of equations is:…

Q: Find the EXACT value of the area of the surface obtained by rotating y = x³, for 0≤ x ≤ 2 about the…

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Q: 1. Evaluate fxsec²xdx

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Q: graph  linear inequality t >0

A: The objective of the question is to graph the linear inequality t > 0. This inequality represents…

Q: In order to find the derivative of f(x) = -x³ we use the power rule, which states that the…

A: The given function is

Q: Find the volume of the solid formed by revolving the region bounded by the graphs of y = 3 - x^2 and…

A: Given the region is bounded by the curve and line

Q: 3. Find the limit, if it exists lim x→0 ex - 1 sin(x)³

A: Need to find out the limit, it it exists.

Q: g(x)=x³ sin (√√x) sin(√)

A:

Q: A nose cone for a space reentry vehicle is designed so that a cross section, taken x ft from the tip…

A:

Q: The height of a cylinder is increasing at a constant rate of 8 centimeters per minute, and the…

A: Given a cylinder with its dimensions.

Q: Find the partial derivatives of the function က် ထိ စီ ။ ။ ။ w=v4r2 +882 +7t2

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Q: Z Y X X y Z Suppose y=3 cm, Y=1.5 radians, and X=1.2 radians. Determine the following quantities.…

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Q: (b) Consider the vector valued function r = (1 - t)i + (1 - t)i+ (1-t)k, 0≤t≤1. What curve does this…

A: The objective of the question is to identify the curve that is parametrized by the given vector…

Q: Find the first partial derivatives of the function u(r,t) = 3 sin(r cost)). 1. ur(r,t) = = 2.…

A: Explanation is given below:Explanation:

Q: Macmillan Learning Consider the given graph. 13 4.8 1.79 2.19 Let c = 2, L= 4, and e = 0.8. Select…

A: Consider the given graph.Let .To find the values of such that the following statement holds..

Q: Find the maximum rate of change of f(x, y) = ln(x² + y2) at the point (-5, -2) and the direction in…

A: f(x,y)=ln⁡(x2+y2) at the point (−5,−2)Using the chain ruleddxf(g(x))=f′(g(x))g′(x)

Q: Hello, I am in the middle of an exercise and I am getting tripped up on solving this integral. Could…

A:

Q: let F(x) = f^5 and G(x)=(f(x))^5 you also know that a^4 = 11, f(a)=2, f prime of a =11, f prime of…

A: F'(a) = 880 G'(a) = 880Explanation:Detailed explanation:Understanding the FunctionsF(x) = f^5: This…

Q: Consider the functional S[31, 32] = [ dx [7y² + 24y,y2+21y2² +4y² + 12y1y2+9y3] · - Y₁ = azı 322, y2…

A: Functional separability lets you break down a complex functional (think fancy function) into simpler…

Q: Consider the function f(x) = 1.984x4 - 7.936x³ a. Locate the critical inputs on the interval [2.8,…

A: Please check below Answer Explanation of Question a), b), c),Explanation: Question a): Step 1: The…

Q: 4. Find the inverse of the function, s(t) = √3 - t² - 6

A: To find the inverse of a function y=f(x) , use the following steps .Let y= f(x)Swap the variables x…

Q: The area of the region enclosed by the graphs of x = y² and y = √√30 x where y > 0 is: 632 70√5 3

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Q: Find the nth term of the geometric sequence whose = 2 and common ratio is 3. initial term is a 1 ап…

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Q: The GoldPlus Company determines that the marginal cost for their Aiibe 64GB flash drive is given by…

A: The objective of the question is to find the general and particular solution of the cost function C.…

Q: Using the Laplace theorem, find the determinant of the following matrix : D = [2 1 3}/ [4 5 6]/ [7 8…

A: The objective of this question is to find the determinant of a 3x3 matrix using the Laplace theorem.…

Q: PLS HELP ON ALL ASKED QUESTIONS PLS

A: Solution is attachedExplanation:Step 1: Step 2: Step 3: Step 4:

Q: If f(x, y) = 25 - 4x² - y³, find f×(4, -6) and fy(4, -6) and interpret these numbers as slopes.…

A: ∙  fx​(4,−6)=−32∙  fy​(4,−6)=−108These values indicate how the function changes with respect to…

Q: Find f'(x) if f(x)=7e6x f'(x)= 0

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Q: Verify that there exists a function g: R² → R² such that u = (u,v) = g(x) for the system S4xu² +…

A: The determinant of the Jacobian matrix of F at the point (1,1,−1,−1) is 15, which is nonzero.…

Q: y= (2+6 times x)^x Use Logarithmic Differentiation to find dy/dx

A: Conclusion :  dxdy​=(2+6x)x [(2+6x)6x​+log(2+6x)]Explanation:Step 1: Approach 1 ) Take both side…

Q: Calculate the asymptotes of the following functions provided in the image

A: "Since you have posted multiple questions, we will provide the solution only to the first question…

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS

A: b=23​,c=27​Explanation:Approach to solving the question:  Detailed explanation: