Find the first partial derivatives of the function.

Q: Consider the following function. f(x)=√x-4, x>4 What is the domain of f? (Enter your answer using…

A: Here, the given function is: f(x)=x-4, x>4

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.1 cm/min.…

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Q: Find the indicated nth partial sum of the arithmetic sequence. a₁ = 13, 316, n = 120 120 =

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Q: dr a) -sin³ x b) sin² x Q7. Find the range of the function y= a) x>0 b) x 3

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Q: Find the inverse Laplace transform 01 2 Ou44(1-4) usinh(t — 4) O sinh4(1-4) 0 1 u4cosh4(1-4) 01 4…

A: Given problem:- Find L-1e-4ss2-16

Q: Consider making monthly deposits of P = $250 in a savings account at an annual interest rate r =…

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Q: Find the intervals on which the graph of f is concave upward, the intervals on which the graph of f…

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Q: 7 Find f(x) if f'(x)= and f(1) = 4. X 7 --x-3+19 O B. f(x)= -28x-5 +32 7 O c. f(x)= 3 O A. f(x) =…

A: As we know the Power rule: ∫xndx=xn+1n+1+C ; n≠-1   Given: f'x=7x4 So, we can also write as;…

Q: Use the definition of the Laplace transform to find L{f(t)}. (Enter your answer in terms of s.) 0,…

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Q: Σ 500(1.07)" ΕΞΟ

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Q: Find the critical point of the function. Then use the second derivative test to classify the nature…

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Q: = 4 sec 0. Find the Cartesian equation for the polar curve r =

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Q: Find the following for the given equation. r(t) = (e-¹, 3t², 6 tan(t)) (a) r(t) = (b) r(t): (c) Find…

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Q: Use the graph of f in the figure to the right to complete parts (A) through (M) (assume that f''(0)…

A: Given: f''(0)<0,f''(b)>0 and f''(g)>0 From graph: f'(a)<0,f'(b)=0, f'(0)=0, f'(g)=0 and…

Q: Find dy/dx: 1 II 22²+(²+1)¹

A: Important Formulae:1)ddx(xn)=n xn-12)ddx(1x)=-1x2

Q: Parametric Equations X = 3t², y = 3√t 54m 12 Jse a graphing utility to approximate the integral.…

A: The solution is given below

Q: Determine the height h above the base of the centroid of the cross-sectional area of the beam.…

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Q: Newton's law of cooling states that the rate of cooling of an object is proportional to the…

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Q: A car rental agency rents 480 cars per day at a rate of $20 per day. For each $1 increase in rate,…

A: Solution: Car rented =480 -10x rate =20+x

Q: The population of a community is known to increase at a rate proportional to the number of people…

A: NOTE: Refresh your page if you can't see any equations. . the population growth function is given by…

Q: A company manufactures and sells x cellphones per week. The weekly price-demand and cost equations…

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Q: Convert the given exponential function to the form indicated. Round all coefficients to four…

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Q: A car rental agency rents 210 cars per day at a rate of $30 per day. For each $1 increase in rate, 5…

A: Topic- Application of derivatives

Q: theres three steps.    A manufacturer of upholstery can sell 33 yards of fabric at a price of $1.63…

A: the demand function D(x)= m(x-x1) + p1 where m= (decrease in price)/(increase in production) p1=…

Q: d the following for the given equation. r(t) = (et, 6t², 8 tan(t)) (a) r(t) = (b) r"(t) = (c) Find…

A: Topic:- application of derivatives

Q: Problem 2 √√x-3 x-9 For the function above, please find the following: a) The domain of the function…

A: NOTE: Refresh your page if you can't see any equations. . as we know, the denominator cannot be…

Q: 4. If x= sin² and y = 1 when x = 0, then find the value of x when y = 3. 0 O 8 None of these

A: Topic- differential equation

Q: Ive the equation on the interval 0≤0<2 tan 0-√3=0 www. What are the solutions to tan 0-√3=0 in the…

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Q: [ª* z² cos(4x) dx =

A: We will  integrate the expression.

Q: Suppose that f(x,y,z)=(x,y,z)=2x+4y+3z at which x^2+y^2+z^2≤3^2 Absolute minimum of…

A: Please see the below picture for detailed solution.

Q: Find the differential of the function f(x,y)=−x2+3xy−8y2f(x,y)=-x2+3xy-8y2 at the point (3,−2)(3,-2)…

A: Given.

Q: Question 8 of 25 > Find the derivative of the function f. 3 √x f(x) = O At

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Q: Question 15 A box with a square base and no top is to have a volume of 4 cm³. Find the least amount…

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Q: Hours (x) Bacteria (y) 0 1853 1 2221 2 2714 3 3056 4 4078

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Q: 1. Find the particular solution to y' = 3sin(x) given the general solution is y = C - 3cos(x) and…

A: Topic - differential equations

Q: If f(x, y, z) = 1, then fff f(x, y, z)dV gives the volume of V.

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Q: Evaluate (2x² - 4x + 1)² dx. √

A: Given data:- ∫x32x3-4x+12dx

Q: Consider the following function. x + 2 x-1 What is the domain of f? (Enter your answer using…

A: Points to remember. Every polynomial is a continuous function. If f(x) and g(x) are continuous…

Q: Evaluate the following indefinite integrals using U-Substitution. Thank you! 6. ∫ x3 (2-x2)12 dx

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Prove Vf(r) f'(r)r r

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Q: Answer true or false. If f is not piecewise continuous on [0, co>), then L{f(t)} will not exist.…

A: Existence of laplace transform Theorem: If F(t) is a piecewise continuous function on every finite…

Q: tan (sin-1)=

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Q: - A gardener has 120 feet of fencing to fence in a rectangular garden. He wants one side of his…

A: According to the question: l+3w=120 or l=120-3w a)The area A of the garden is:           A=lw…

Q: (8z i + 9x j + 2y k) = (i k )i + ( i )j + (

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Q: A manufacturer can produce 2700 cell phones when a dollars is spent on labor and y dollars is spent…

A: Given problem:- A manufacturer can produce 2700 cell phones when a dollars is spent on labor and y…

Q: Answer true or false. If f is not piecewise continuous on  [0, ∞>),  then  ℒ{f(t)}  will not exist.

A: Given problem:- If f is not piecewise continuous on [0, ∞),then ℒ{f(t)} will not exist.  True…

Q: Calculate the present value PV (in dollars) of an investment that will be worth $1,000 at the stated…

A: Given the query is to find the present value of the investment.

Q: Use the Fundamental Theorem of Calculus to find the "area under curve" of f(x) = 8x + 4 between x =…

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Q: f(x) is continuous on (-∞,∞o). Use the given information to sketch the graph of f. f'(x) +++ 0…

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Q: Write the linear regression equation that represents this set of data, rounding all coefficients to…

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