1. Find all critical numbers of f(x) = x³ ln(x). (a) e5 only (b) e-1/5 only (c) e and 1 only (d) e only (e) no critical numbers 1A 1B 1C 1D 1E

Q: Find the limit. (If an answer does not exist, enter DNE.) √x + 2-9 x - 79 lim X→ 79

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Q: If f(x) = 4 ln(5 + x), ƒ'(x) = ƒ'(1) =

A: f(x)=4ln(5+x)

Q: k+1 For f(x) = = 2x of k if the average value of f(x) over the interval [1, e] equals to 1 is:…

A: Given, the function is fx=k+12xcontinuous on [1,e], and the average value is 1.

Q: What is the sum of the first six terms of the geometric series 2-4+8-... ? α₁ (1-²¹) 1-r Sn = O S6…

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Q: If log₂ (6x + 6) = 2, then x

A: We need to find the value of 'x' using the given expression: log26x+6=2

Q: find the domain of the logarithmic function. f(x)=log7(x-5)

A: The given function fx=log7x-5. We have to find the domain of the function.

Q: Find the first partial derivatives with respect to x, y, and z. w = x7yz2 + xy − 4yz

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Q: Find the exact value of the expression, if possible. (If not possible, enter IMPOSSIBLE.) 63 =…

A: arctan(x) = csc-11+x2x

Q: Use the Law of Sines to solve for all possible triangles that satisfy the giv so that B₁ is larger…

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Q: 5. Find the arc length of the spiral r=0 from 0=0 to 0=27.

A: Arc length for a function of the form r=rθ from θ=θ1 to θ=θ2 is given by ∫θ1θ2rθ2+r'θ2  dθ.

Q: Write down Cartesian equations for the following two polar curves: 5 (a) C₁: r = 2 cos 0+3 sin 0.…

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Q: Find the first partial derivatives of the function. f(x, y) = fy = -7

A: given,  f(x,y)=7yx3we know that,  ∂ ∂x(xn)=nxn-1

Q: Find the inverse Laplace transform. 53+5

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Q: Use the chain rule to find the derivative of You do not need to expand out your answer. 13 3(-5x5…

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Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of 6 F(x) = ['sir F'(x) = x…

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Q: A can of red bull without a top is made to contain 355cm3 of energy drink. Find the dimensions that…

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Q: Determine the equation for the tangent to the curve y= sin(2x + π/3) at the point with x-coordinate…

A: Given

Q: But why if the min/max point is (k^2,0) , it is not a minimum or maximum points?

A: For a function f(x) , function is maximum/minimum if  f'(x)=df(x)dx=0-----1…

Q: Find the domain of the function f(x, y) = ln(36 - 4x^2 - 9y^2) + sqrrt(2x - 3y - 6) and plot the…

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Q: 12. sint√/1 + cost dt

A: let  H=∫sint1+costdt

Q: Find the equation of the tangent line to the curve y = 6 sina at the point (7,3). The equation of…

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Q: Find the exact length L of the curve where y 20. 7y² = (3x-2)³, 1<z≤ 2,

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Q: xy² (x,y)-(0,0) √x² + y² lim I

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Q: Determine whether the sequence converges or diverges. If it converges, find the limit. an =…

A: Explanation of the answer is as follows

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Q: At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 20…

A: At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 20…

Q: Find the tangent planes to the surfaces given by the equations z = 7x^2 - 12x - 5y^2 and xyz^2 = 2…

A: NOTE: Refresh your page if you can't see any equations. . the first surface is so we can write…

Q: Find the average value of f(x) interval [ 14, 14]. fave = Calculator = 14 x over the -

A:

Q: The rate of expenditures on public elementary and secondary schools, in billions of dollars per…

A: st=4.08·e0.074t from 1990 to 2010 , therefore total 20 years

Q: = y. Find the area of the region between the curves 4x + y² = 12 and x = Area between curves =

A: The equation of the curves are as givena) 4x+y2=12 and x=yb) y=4sinx ,y=4cosx form x=0 to x=0.4π

Q: value C = rem can be applied to f on the closed interval [a, b]. (Select all that apply.) f(x) =…

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Q: nd fill in the corresp 11. Find the slope of the line tangent to the graph of y = xy - 8x + 50 at…

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Q: Let f(x) = 2e²+1 +e6. ƒ'(0) =

A: Given that:   f(x) = 2e(x^2+1) + e6.   We find differentiate of f(x) and again we find f'(0).

Q: 3. Find the area inside one petal of r = sin(30)

A:

Q: The height of an object t seconds after it is dropped from a height of 280 meters is s(t) = -4.9t² +…

A: Average velocity = total distancetotal time Mean Value Theorem The mean value theorem states that…

Q: 2. Part 2 - Find the error(s) and solve the problem correctly. Convert the polar equation to…

A: r=-4cosθ

Q: Find the length of AB. 6 in A AB = [? ]in B 030° Round your answer to the nearest hundredth. Enter

A: Radius=6in Central angle=30

Q: f(-2)=-13 and g(-2) = 11

A: f-2=-13 and g-2=11

Q: Find the point on the sphere x²+y²+²=3364 that is farthest from the point (-14,13,23). X )

A: To find the point on the sphere x2+y2+z2=3364 that is farthest from  the point -14, 13, 23.

Q: Find the following using the table below. x 1 2 3 4 f(x) 4 2 3 1 f'(x) 1 2 4 3 g(x) 4 2 3 1 g(x) 4 3…

A: The function and its derivative values are given in the table. To find the values of h'3 if hx=fx.gx…

Q: 12) Evaluate the following: (a) Evaluate the definite integral: f¹(7 √x + 3x • √x) dx (Leave answer…

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Q: Find the area lying above the x-axis under the parabola y=4x-x^2. Graph it

A: First we find point of intersection of given graph y=4x-x2 with y=0, Then using limit of points we…

Q: Consider the following. √² (6-5) 5x) dx (a) Find an approximation to the integral using a Riemann…

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Q: Use a graphing calculator to graph f near xo and use Zoom and Trace to estimate the y-value on the…

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Q: Determine the equation of the tangent to f(x): 1 tan²x (7›1). at the point

A: Determine the equation of tangent to f(x) = 1/tan2x  at the point( π/4,1).

Q: The weekly revenue realized by a company is approximated by the revenue function = R(x, y) 350x +…

A: Given,   The weekly revenue realized by a company is approximated by the revenue function R(x, y) =…

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Q: Find the exact value of each expression, if it is defined. Express your answer in radians. (If an…

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Q: 6. What is the volume generated by revolving the shaded region around the x-axis? Use disks. y 3 2-…

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Q: Find the local maximum of f(x) Be sure to show your work for x + 2 x² +6

A: