Find the gradient of the function at the given point. f(x, y) = 4x + 3y2 + 1, (1, 4)

Q: use the properties of the natural logarithm to: A. expand the logarithmic expression: ln (2x/x+2)…

A: A) ln2xx+2B) 5 lnx-7 lny-8 lnz

Q: |*| +1, {0, x = 0 1x-1, x >0

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Q: 1. Find the gradicnt of the following functions (here, i = V-1, and A is a constant) (a) f (x) = 3x.…

A: The objective is to find the gradient.

Q: lim (5x + х+ 3,

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Q: 5. 1 de 9+x2

A: Given query is to find the integral of the expression.

Q: x + 42 series of the function: (x - 8)(x +2)

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Q: r = 3 - 4sine

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Q: Rotate the region specified above by the curve y = x and beneath by the curve y = x^2 from x = 0 to…

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Q: Consider the following x = 2 + t², y = t² + t³. Find the following in terms of t: 1) and enter it…

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Q: A clothing company determines that its marginal cost, in dollars per dress, is given by the function…

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Q: Suppose in the year 2000 a city has population 687 thousand and is declining at a rate of 1.03% per…

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Q: 1 1 (1++)dr

A: To Evaluate: ∫121+1x+1x2dx     Note : ∫1xdx=logx+C∫xndx=xn+1n+1+C

Q: 10 2m | (100x – x³) dæ 16 V = = 27 blank – 104 = 27 (blank – = 27 (blank – 2500) =blank therefore…

A: Basic identity of integration is used

Q: q=D(x)=1080-18x

A: answer is in step 2

Q: There are 13 female board members and 17 male board members. How many ways are there to make a…

A: There are 13 female board members and 17 male board members. How many ways are there to make a…

Q: An instructor wants to create a test that has true-false questions, multiple-choice questions, and…

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Q: A robotic machine fills containers with an acid solution at the rate of 90 + 3t milliliters (mL) per…

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Q: List the domain and the x- and y-intercepts of the following function. Graph the function. Be sure…

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Q: 2. Let g (x, y) = 2x² – y² . Compute 9(1, 2), g (2, 1), g (1, 1), g (–1, 1) and g (2, –1).

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Q: 23. (x- 1) (x + 1)

A: Given: x2(x-1)2(x+1)

Q: 10. Find the first partial derivatives of the following functions (it is not simplify). (a) f(x,y) =…

A: Given query is to find the partial derivative if the expression.

Q: A hot air balloon rising vertically is tracked by an observer located 3 miles from the lift-off…

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Q: a²f If f(x, y) = xey + 8xy, then , is given by: O + 8 O 4xe4y + 8 ○ 웃+8 O 4e4y + 8 O None of these…

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Q: Determine the location and value of the absolute extreme values of f on the given interval, if they…

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Q: A car comes to a stop six seconds after the driver applies the brakes. VWhile the brakes are on, the…

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Q: Find the area of the region under the graph of f(x) = 2x² – 4x + 2 on [-2, 3].

A: Given query is to find the area under the curve.

Q: Sove the following continnity queshans below Let f(x.y) = 2xy? f (xiy) = (0,0) nd Let glan)= f fary)…

A: here we use the simultaneous limit definition and arbitrary path choosing that passes through the…

Q: Given f(x, y) = In(3x² + 5y²) then af dx

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Q: For the function below, determine each of the following. g(x) =. + 6 (a) Find the critical values of…

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Q: 12-2t+tcos(t)-tet-4t2 Given a velocity function v(t) with initial condition s(1) = e, find the…

A: Given query is to find the position function.

Q: QUESTION 1 y=x+1 A в R y=7-x Figure 1 . Refer to the Figure 1, given that region R bounded by the…

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Q: Determine the exact distance from the point P (1,2) to the line (-1,3) + t(2,9), t e R . Show your…

A: Given

Q: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

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Q: 1. Use the four-step process to find f' (x) and then f'(-3) for f(x) = x² - 8x

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Q: If C(x) is the cost of producing x units of a commodity, then the average cost per unit is a(x) =…

A: Use the basic concepts of the average and marginal costs.

Q: A manufacturer determines that the cost in dollars for making "x" calculoodles is C(x) = 1800 + 25x…

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Q: Find a function of the form y = A sin(ka) + C or y = A cos(ka) + C whose graph matches the function…

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Q: Find the minimum value of f(x,y)=66x2+9y2 subject to the constraint x2+y2-784

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Q: In the year 2000, the population of a small city was 50,000. The population grows at a rate of r(t)…

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Q: Set up and evaluate the triple integral in spherical coordinates needed to compute the volume of the…

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Q: Write the infinite series using sigma notation. 7 7+ Σ 7 7 + 625 7 25 125 = U ||

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Q: A bicyclist traveling at 14 ft/sec velocity (ft/sec) puts on the brakes to slow down at a constant…

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Q: 7. An observer stands 200 meter from the launch site of a hot-air balloon. The balloon rises…

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Q: dA when r = 2. dt dr Let A be the area of a circle with radius r. If = 2, find dt

A: Area of the circle with radius r is given by;A=πr2differentiating w.r.t time,dAdt=2πr drdtWhen r=2…

Q: Use the shell method to write and evaluate the integral that gives the volume of the solid generated…

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Q: Use double integrals to find the mass of the lamina ( thin Plate) which occupies the planar region…

A: To find:  The mass of the lamina which occupies the planar region bounded by the straight line…

Q: 1 f(z) = |, + tdt If then f'(x) = 3x^6 f'(-3) = 729

A: fundamental theorem

Q: equation

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Q: 7 sin x Let f(x) 2 sin x + 6 cos x Then f'(x) The equation of the tangent line to y = f(x) at a =…

A: Given problem:- f(x) =7 sin(x)/(2 sin(x) +6 cos(x))  Find:- f'(x) and equation of tangent line at…

Q: If f(x, y) = cos (xy) – 7y, then fx(0, x) = 0. %3D Select one: True O False

A: NOTE: As per our guidelines, I have solved the first problem. If you want the answer of other,…