Let 60, 61. What is the derivative of the function y = b²? In(b) -In(x) 1 1 In(b) ○ b* In(b) eIn(b) X

Q: 4. The diagram is a rectangular prism. Let u = AB, v = AD and w = AE. Express each vector as a…

A: The diagram of the rectangular prism isthe side vectors of the rectangular prism are

Q: 5) Find the general solution of the non-homogenous differential equation: dy = dx x + y +4 4x+4y+8

A: Explanation is given below:(ask in comment for any doubt!! )Explanation:

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS. THIS IS TRUE OR FALSE

A: 11. TRUE 12. TRUEExplanation:Approach to solving the question: Detailed explanation:

Q: PLS HELP ON ALL ASKED QUESTIONS PLS

A: Final answerlines are paralleli have attached the image below Explanation:

Q: PLS HELP ON ALL ASKED QUESTIONS PLS

A: The answers are as follows: 7.The vector equation of the line isr=(7,2)+s(2,−3),s∈R.Option b. is…

Q: I need the equation of the tangent line to the curve at (1,3)

A: Slope is given by as calculated m=3

Q: Let F be a smooth 2-dimensional vector field defined on an open set U in the plane containing a…

A: The objective of this question is to find the curl of a 2-dimensional vector field F at a point P,…

Q: Set 2π 1 +3 up and evaluate the definite integral for the area of the surface generated by revolving…

A: The required answer is 258.85 square units .Please find the attached file for details...Thank…

Q: A rectangle has a length of 7 inches and a width of 8 inches whose sides are changing. The length is…

A: Let the length and width of rectangle be l,bl=7 inches, b=8 inches

Q: y = 1x312, 0 ≤ x ≤ 21

A:

Q: a. · b = . ) Find a ⋅ b if |a| = 2, |b| = 2, and the angle between a and b is - radians.

A: a⋅b≈3.76Explanation:The dot product of A and B is,a⋅b=∣a∣∣b∣cosθ Given the…

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

A:

Q: R A region is bounded by two concentric circles, as shown by the shaded region in the figure above.…

A:

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: Let 4xyz = e². Əz Əz Use partial derivatives to calculate and მე მყ and enter your answers as…

A:

Q: PLS HELP ON ALL ASKED QUESTIONS PLS

A: Angle that vector a = (12,-3,4) makes with the y-axis is  arccos(13−3​)Explanation: For any query…

Q: Determine the value of k for which f'(3)-2, if f(x) = x+*. x-1

A: Given a function,f(x)=x+kx−1To find : the value of k for which f′(3)=2.Using the quotient…

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS.

A: 3)Option C is correct answer  4)Option A is correct answer  Explanation:

Q: Question 3 Find the derivative of f(x) = √√(x+1)(x+2) (2x + 3) at x = 0 using Log- arithmic…

A: To find the derivative of  at   by  using Logarithmic differentiation.

Q: If z = 3x² + y² and (x, y) changes from (1, 3) to (1.05, 3.1), compare the values of Az and dz.…

A: ### Summary:- The actual change in z  as (x, y) changes from (1, 3) to (1.05, 3.1) is 0.9175.- The…

Q: Find the first partial derivatives of 4x - f(x, y) = = 3y 4x+3y at the point (x, y) = (2,4).

A: f(x,y)=4x−3y4x+3y at the point (x,y)=(2,4)Using the quotient…

Q: x f(x) g(x) T(X) g'(x) 3 1 9 9 6 7 4 3 3 2 -5 g(x+f(x)), x=3

A:

Q: A company estimates that the weekly sales g of its product is related to the product's price p by…

A: SolutionA)11/5B)$2166.94C)$2276.86Explanation:Step 1: Explanation for question

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: b) Solve the following first order differential equation 2+ y = y³ (x-1)

A:

Q: The total sales of a company (in millions of dollars) t months from now are given by S(t) = 0.03t³…

A: Ans:Detailed answers in explanation please referAny confusion please ask in clarification will…

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: Let F be a smooth 2-dimensional vector field defined on an open set U inthe plane containing a point…

A: The objective of the question is to find the curl of a 2-dimensional vector field F at a point P,…

Q: Given f(x)= -5^(2x) -6 , determine • the equation of g(x) given that g(-x) = f(2x) • the range • the…

A: Given:  To Find: To determine the equation of .The range of .The x-intercept (if any) of .The…

Q: Find the arc length of the graph of the function over the indicated interval. (Round your answer to…

A: The arc length = 8.352 unitExplanation:

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

A:

Q: Consider the following list of activities with time (in months) Activity A B C D E F…

A: C) Variance of project completion time is  6.0 months2D) The probability of completing is…

Q: Prove that the equation re* = x² - 1 is solvable.

A:

Q: The Integral Test: Suppose f is a continuous, positive, decreasing function on [1, 00) and let an =…

A: The objective of the question is to understand the importance of the function f(x) being decreasing…

Q: Find an equation for the surface consisting of all points that are equidistant from the point…

A:

Q: (x-5)n n=0 • 8 WI 2. Determine the interval of convergence of the power series.

A: The objective of this question is to find the interval of convergence of the given power series. The…

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: Equations are given whose graphs enclose a region. Find the area of the region. (Give an exact…

A: The area is:A=12253​Explanation:The given curves are: f(x)=x3,g(x)=x2+6x To visualize the bounded…

Q: What is the slope of the normal to y = X-2 X+2 *+ at (2, 0)? -4 4

A:

Q: 1) Find the equation of the tangent plane to a)z In (10x² + 2y² + 1) at P(0,0,0) b) z = f (x, y) =…

A: Ans 1)a. z = 0b. z = √2(4x+4-π)/8Explanation:

Q: d) If_lim_ƒ(x) exists, then f(x) must have a horizontal asymptote. x--∞ e) It is possible that…

A: Given, three statements for true and false

Q: Use implicit differentiation to find dy/dx 2xy-y2 = 1

A:

Q: Solve sin(x) = 0.64 on 0 < x < 2π There are two solutions, A and B, with A < B A = 0.6945 B = Enter…

A:

Q: Newton’s law of cooling states that the rate of change of the temperature of an object is…

A: The objective of the question is to show that the function u(t) = T(t) - Tomg, where T(t) is the…

Q: No hand written responses. I need help with a step-by-step breakdown in laymen terms for each part…

A: Answer AOption A , t2​, t4​, t5​, t7​, t8​Answer Blimt→t6​​N(t)=7N(t6​)=7Answer CThe Limit does not…

Q: No hand written responses. I need help with a step-by-step breakdown in laymen terms for each part…

A: a.  limt→∞​C(t)=5 b. In the context of this problem, the limit               limt→∞​C(t)=5…

Q: Please don't provide handwritten solution ....

A: The objective of this question is to calculate the work required to pump all the liquid out of a…

Q: Q.3

A: (a) The series INFINITE SUMMATION n=1 of (n²) / n diverges.(b) The series INFINITE SUMMATION n=1 of…

Q: f(x)= 3ex 2e-5

A: f(x)=3ex2ex−5f′(x)=ddx[3ex2ex−5]Using the quotient rule ddx[f(x)g(x)]=g(x)f′(x)−f(x)g′(x)[g(x)]2

Q: 6. Consider the curve y = 4x². Determine the equation of the line(s) (in standard form), such that…

A: We need to find an equation of a tangent line that passes through the point given.