Question 18 ( has exactly Show that the equation one real solution. 207e +2023 In z=7²4

Q: Find the derivative of the function. y' = y = etan(e)

A: We use chain rule to find the derivative of the following function.  dftdθ=dfdt·dtdθ also use the…

Q: Given (y)-16-²-², use the total differential to approximate or at (4.1) towards (24,1.05). Round…

A: △x=2.4-4=-1.6△y=1.05-1=0.05

Q: Differentiate the function. f'(x) = f(x) = In(cos(x))

A: The solution is shown below-

Q: Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral.…

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Q: Complete the parametric equations of the line through the point (-1,-8,-7) and perpendicula plane -…

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Q: If f(x) = 3x5 - 10x³ +5, on what intervals is f"(x) > 0? Enter the (disjoint) interval(s) below…

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Q: Find the particular solution to the given differential equation that satisfies the given conditions.…

A: Given differential equation:- x2+y28dy=7xdx+ydy

Q: The​ short-term demand for crude oil in Country A in 2008 can be approximated by q=f(p)=2,443,225p…

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Q: For the demand function q = D(p) = 314-p, find the following. K a) The elasticity b) The elasticity…

A: We need to find out the elasticity, elasticity at p=93 and also the value of p at which revenue is…

Q: The region bounded by f(x) = −3x² + 12x + 63, x = 0, and y = 0 is rotated about the y-axis. Find the…

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Q: Find the equation for the tangent plane to the surface z = 9x² - 6y² at the point (2, 1, 30). OA.…

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Q: A vector with magnitude 4 points in a direction 340 degrees counterclockwise from the positive x…

A: let vector =V given  magnitude=V=4and direction=θ=340°now Vector V=<x,y>=?…

Q: 20,000e 1+ ķ xy-plane, where x and y are measured in centimeters, find the total population of…

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Q: [5-A] [CLO 12] The line ℓ passes through the points (−3, −4) and (5, 1). Give an equation for the…

A: Given: The line l passes through the points -3,-4 and 5, 1. The objective is to find the equation…

Q: Evaluate the limit sin 2x 6x lim x→0

A: N=limx→0sin2x6x∂ ∂x(sinx)=cosx∂ ∂x(xn)=nxn-1

Q: Consider the following vector function.. r(t) = (2√2t, e²t, e-2t) (a) Find the unit tangent and unit…

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Q: A rectangular tank that is 2048 ft³ with a square base and open top is to be constructed of sheet…

A: The given data is: A rectangular tank that is 2048 ft3  Base is square Find the dimension of the…

Q: Arriving at the eighth and penultimate gate, you immediately get to work. "Computer, translate this…

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Q: a) Suppose that lim n-00 ∞ The series Enan n=1 an+1 an 1 == 2 converges ✓ by the ratio test <

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Q: Consider the function f(x) = 12x5 +75x¹ - 120x³ +1. For this function there are four important…

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Q: Find the extreme values of f(x,y) = xy subject to the constraint x² + y² -4 = 0. The extrema are…

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Q: You are planning to make an open rectangular box from a 38-in.-by-75-in. piece of cardboard by…

A: This question is based on application of derivative. First take a square of length x then make a box…

Q: Consider the graph between two curves. Which of the following is the correct set up for the area of…

A: Application of derivative

Q: Evaluate the integral. 6e6t ¹+12° +35 S- 12t dt

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Q: A tank contains 500 gallons of salt-free water. A brine containing 0.25 lb of salt per gallon runs…

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Q: Does the series convergence or diverge 7 n²+5n+6 ∞

A: We have given a series  Let, y=∑n=0∞7n2+5n+6 Using factor form n2+5n+6=n2+2n+3n+6=nn+2+3n+2…

Q: Consider the function f(x) = 1−3x², -3 ≤ x ≤ 1. Use the derivatives to algebraically answer the…

A: Given, As per given question we need to find the extreme points of the function fx=1-3x2 on the…

Q: Evaluate the integral. 2 √√Z T ||||** SS (² cos ²0+z²)r de dr dz 000 2 √Z T S SS (² cos ²0 +2²)r de…

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Q: Find the volume of the pyramid with base in the plane z = -10 and sides formed by the three planes y…

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Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

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Q: 17x³ (In x)² dx =

A: The given integral is: ∫17x3 ln x2 dx

Q: Show that the equationy/= -9y is satisfied for y = cos 30.

A: We are required to check that y=cos3θ satisfies the equation y''=-9y.

Q: Express the integrand as a sum of partial fractions and evaluate the integral. 9 y 2 5 y-y-2 -dy =…

A: Integration

Q: Find the exact area of the surface obtained by rotating the curre around the x - as is 1 16-x1 g= +…

A: Given that , y=6-x , 4≤x≤6 find the area of the surface obtained by rotating the curve around the…

Q: S Du Arriving at the eighth and penultimate gate, you immediately get to work. "Computer, translate…

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Q: 1/9 A disease has hit a city. The percentage of the population infected t days after the disease…

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Q: Find the volume of the pyramid with base in the plane z = -10 and sides formed by the three planes y…

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Q: 3, 3, 1 > and b Let a = . Find k so that a and b will be orthogonal (form a 90 degree angle). k=

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Q: Find and classify the critical points of z = Local maximums: Local minimums: Saddle points: (z² -…

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Q: The Fourth Gate You arrive at the fourth gate, feeling confident in your skills. "It is a good thing…

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Q: A volume is described as follows: 1. the base is the region bounded by y = 9 - 1x² and y = 0 2.…

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Q: If 3 A = -4 -4 8 1 x 4 1 1 Is a singular matrix, then x is 1

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Q: Suppose that the daily profit (in dollars) from the production and sale of x units of a product is…

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Q: 4. Point of Diminishing Returns Assume that an advertising campaign is launched for a new product…

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Q: Let z=f(x,y) = 15x² - 25xy +9y². Find the following using the formal definition of the partial…

A: The given function is: z=f(x,y)=15x2-25xy+9y2

Q: Consider the following problem: a box with an open top is to be constructed from a square piece of…

A: Note: There are multiple sub-questions. No specific question has been asked. So, We will solve the…

Q: Find an equation of the tangent line to the curve at the point (1, -1-). y = x³e-x y =

A: To Find: Tangent line to y=x3e-x, at point 1, 1e

Q: Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded on…

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Q: Find the centroid of the triangular region cut from the third quadrant by the line x + y = -3.

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Q: For y = f(x) = 8x³, x = 3, and Ax=0.04 find a) Ay for the given x and Ax values, b) dy = f'(x)dx, c)…

A: We have, y=fx=8x3, x=3, and △x=0.04 To evaluate : (a) △y for given x and △x value (b) Expression for…