Find the implicit equation of the tangent plane to z = ln(x² + 1) + y² at the point (0, 5, 25).

Q: Let SS be the universal set, where: S={1,2,3,...,28,29,30} Let sets A and B be subsets of S, where:…

A: S={1,2,3,...,28,29,30}Let sets A and B be subsets of S, where:Set A={4,5,6,9,13,20,24,28,30}Set…

Q: Given the matrix find A. Write A as input your answer below: a1 = 012 021= 022= H EI I EE A³ - [:…

A: The matrix is given by A = 220-3 To evaluate: The value of A3

Q: (a) If y=f(x) = 7e²+3x² - 20x-5, find the derivative f '(x).

A: given that,   y=f(x)=7ex+3x4-20x-5,   find the derivative of f(x)? formula:   ddx(xn)=nxn-1

Q: PZ π/2 54 3 2 1 -2 -3 -4 -5 Find lim f(x) = The graph of the function f(x) = tanx is given above for…

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Q: find f + g, f - g, f # g, and fgfor each pair of functions. State the domain of each of these…

A: Given, fx=3x2+x+1gx=3x

Q: Find the exact length of the curve. x = 5 + 12t², y = 6 + 8t³, 0≤ t ≤ 3 12117-1)

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Q: At t = 0, a train approaching a station begins decelerating from a speed of 104 mi/hr according to…

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Q: 1. Find the center on the line y = x and passing through the origin. differential equation…

A: Need to find out the differential equation that represents the circles with center on the line y=x…

Q: Write an equation for each line. 15. through (2, 2), y-intercept 10

A: since you have posted multiple questions i can do first question as per our company guidellines.…

Q: 15. Evaluate each expression using the given table of values: -2 -1 1 f(x) 1 0 -2 1 2 g(x) -1 b.…

A: To use the table of values for finding the values of given function.

Q: 1. Separation of variables/ a. xy³ dx + (y + 1)e-*dy = 0

A: Here we have to solve the given differential equation

Q: Integrate [8³e³ 13 ft³e est dt t³ est dt. =

A: The solution to find the integral  of given integration is as follow.

Q: A population of bacteria is growing according to the equation P(t) hours. Estimate when the…

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Q: Evaluate the sum 50 Σ(2 · k + 5) = k=1 50 Σ5₁(2. k+5). k=1

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Q: Evaluate the following integral. 48x² (x-21)(x+7)² dx Find the partial fraction decomposition of the…

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Q: Evaluate the following limits. If needed, enter oo for ∞ and -oo for - 00. 32x 3 - 6x (a) lim 16 (b)…

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Q: Question 26 Solve for the value of constant C in the equation: (2x + 3)y' = y + (2x + 3)¹/2 when x =…

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Q: Use the Lagrange multipliers to find the maximum and minimum values of f(x, y) = 2x + y − 2z subject…

A: Given function fx,y,z=2x+y-2z Let gx,y,z=x2+y2+z-2025

Q: If the rational function y = r(x) has the horizontal asymptote y = 8, then y → Need Help? Read It as…

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Q: Find the derivative: f(x) = (4 sin x + 8 cos x)tan -1 X

A: To find the derivative of given function.

Q: State whether the equation is ordinary or partial, linear or non-linear, and give its order and…

A: See this solution in below.

Q: The length of a stalactite (in mm) has been measured at the beginning of every fourth year since the…

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Q: Consider the following limit statement: lim (9x-3) 15 x → 2 Find the corresponding value of 6 when &…

A: givenlimx→39x-3=15

Q: Let p, q and r be the propositions: p: Wild foxes have been seen in the area. q: Hiking is safe on…

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Q: 0 PERTA C 2000 A television camera at ground level is 2000 feet away from the launchin to take off…

A: Let distance between camera and rocket =s ft

Q: A coroner arrives at a murder scene at 7 p.m. She finds the temperature of the body to be 84 3°F.…

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Q: Problems: 1.(x³ + xy² − y)dx + (y³ + x²y + x)dy = 0 2. (ex siny + ey)dx - (xe-y-e* cosy)dy = 0

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Q: Example 2 (Calculator Active): For 0 ≤ t ≤ 10 days, the rate that a company sells t shirts, in 100's…

A: Given query is to find the rate shirt sold after 5 days .

Q: 1/2 d lim f(x) = Z→** d lim z→ (2T) e graph of the function f(x) = cscx is given above for the…

A: Given query is to find indicated limits.

Q: hich of the following equations can be made into a linear differential equation? DA. (x² + xy)dy -…

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Q: Given the plane л: 2x + y - 3z - 2 = 0, and the lines l₁: 2 - Z-4 y-1 x+1 x==¹=24 and ₂: *1 = y…

A: (b) Given two lines l1: 2-x=y-12=z-43 write it in standard form…

Q: Solve for the value of C in the equation: (2xy¹ey + 2xy³ + y)dx + (x²y4eY - x²y² - 3x)dy = 0 when…

A: uation Given differential equation of the formMdx+ Ndy=0

Q: Find all the critical numbers of f(x) = 2x4-4x³+3x²+2, then determine the local minimum and maximum…

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Q: (5) Find the center of mass of the region bounded by y = sin x between x = 0 and x = 7 above the…

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Q: Calculate the slope of the line that passes through (-11, -6) and (1, -4). O - 1 O -16 1 O 6

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Q: Which of the following is NOT true about the linearity of differential equations? O A. Which of the…

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Q: Suppose Use this to compute the following limit. Limit= Number What Theorem did you use to arrive at…

A: Snadwich TheoremSqueeze Theorem:  If g(x)≤f(x)≤h(x)  for all x in an interval containing a point…

Q: Given the following functions: f(u)=u^5/2 and g(x)=x^6+1. Find f(g(x))= f′(u)= f′(g(x))= g′(x)=…

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Q: True or False: The following function is continuous on R. True O False f(x) = if x sin x 44

A: Given function:- fx=sinxif x<π4cosxif x≥π4

Q: 3. Elimination of Arbitrary Contants 1. y = peax cosbx + peax sin bx 2. y = C₁x + c₂ex ; a and b are…

A: Here we have to eliminate the arbitrary constants of the equation y=ϕeaxcosbx+ψeaxsinbx…

Q: Generate differential equation by elimination of arbitrary constants. 2. y=x+c₁e* + c₂e-*

A: Given: Now,    y'=x+c1ex+c2e-x' =1+c1ex-c2e-xy''=x+c1ex+c2e-x''=c1ex+c2e-x

Q: 1. y' + ytanx = COSX; y(x) = (x + c)cosx; y(π) = 0

A: y'+ytanx=cosxy(π)=0proove that  solution isy(x)=(x+c)cosx

Q: Uranium-238 (0-23 has a hall-me of 4. and determine that 67% of the original U-238 remains; the…

A: We will find the age of rock.

Q: Filling a Conical Tank Water is poured into a containerin the shape of a right circular cone with…

A: Volume of the cone=13πr2hGiven:-Radius of the base of cone=4 feetheight of the cone=16 feet.and…

Q: Find the given limit (x² - 1)(y² - 4) lim (x,y) →(1,2) (x - 1)(y-2)

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Q: Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.…

A: Here we can create the required polynomial function in the below steps.

Q: what is the answer to the problem

A: We want to use implicit differentiation to find partial derivatives.

Q: Given f(x) = 4x¹n (x) " f'(9) _ answer the following:

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Q: (a) Using a graphing utility, graph f1x2 = x3 - 9x for- 4 ... x ... 4.(b) Find the x-intercepts of…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: A car sharing service offers a membership plan with a $30 per month fee that includes 10 hours of…

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