Find the absolute maximum and minimum values of the function, if they exist, over the indicated interval. Also indicate the x-value at which each extremum occurs. f(x) = 7x²/3; [-27,27]

Q: Find the limit. lim X→0 sin (8x) 7x

A:

Q: 43. y = (2+x)√2+(2-x)², [0,2]

A: Given function:- y=2+x2+2-x2

Q: . Find the polar equations x-3y+2=0

A:

Q: cos x ln(sin x)dx

A:

Q: In this problem, p is in dollars and q is the number of units. (a) Find the elasticity of the demand…

A: pq=16  and p=2demand=pq×dqdp

Q: 15 sin ¹√2x dx = [

A:

Q: 1. Determine whether the sequence converges or diverges. If it converges, find the limit. tan ¹ n A.…

A: Given;  A. an=tan-1n/n B. bn=Cosn.

Q: Evaluate lim x→∞ _x3 _ 5x2 +52 – 2 x² + 4x +3 =

A:

Q: 3√t-1 S (³√t=¹) dt

A: The given integral is:  ∫3t-1t dt

Q: Differentiate. y' = y sec(0) tan(0)

A:

Q: Find the derivative of the function. y' = -1(x - √ ₁ + x²) 1 y = 9 tan-¹(x-

A:

Q: Consider the following. f(x, y) = 9x y A /2 sin(0) 1/2 ([ 0 r = sin 0 (a) Set up an iterated…

A: Given f(x,y)=9x

Q: Find the derivative of the functio y = sin ¹(6x + 1) y' =

A: Given: y=sin-16x+1

Q: Let f(x)= = 4x² tan(x) sec(x) 1. f'(x)= 8x*sinx+4x^2*cosx 2. f'(1)= . Find the following:

A:

Q: ts) Let f(x) = 1. f'(x)= 2. f'(4)= 5x² tan(r) sec(x) Find the following:

A:

Q: Find the derivate of the functions a) F(x) = (7x²-9) (2x + 7) f'(x) = b) f(x) = 8x² - 2 8x +3 f'(x)…

A: To find derivatives

Q: 2. Find dy/dx and d'y/dx² at the given point without eliminating the parameter : x = 6s², y=-25³ 3…

A:

Q: Find all the complex roots. Write the answer in exponential form. The complex cube roots of 16+16i

A: Given:  z = 16 + 16i

Q: Find the distance from the point (7,1,-2) to the line ä(t) = (-5, 0, -2)t + (0, 3, 6). Calculator…

A: We have to find the distance between the point and line.

Q: 2. Find polar coordinates a. (3-√3.3) b. (0, -2)

A: We need to find the polar coordinates of the given points :

Q: Expand the quotient by partial fractions. 6x - 10 x - 4x +3 6x - 10 2 x - 4x +3 (Simplify your…

A:

Q: Differentiate. f'(0) = f(0) = cos(0) sin(0)

A: Please see the below picture for detailed solution.

Q: Graphs of the position functions of two particles are shown, where t is measured in sec notation.)…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: 4. Find the exact and the approximate value of x: 2* = 5*-1. Round answer to three decimal places. N

A:

Q: Estimating the Amount of Paint Required A coat of paint of thickness 0.07 cm is to be applied…

A:

Q: Consider the function f(x,y)=e^4x−x^2−4y−y^2. Find and classify all critical points of the…

A: Given function:- fx,y=e4x−x2−4y−y2

Q: Find the interval(s) where the function is increasing and the interval(s) where it is decreasing.…

A:

Q: - Find formulas for dy and Ay if y = x² − 7x + 4. **** dy Ay

A:

Q: 1. Find the Cartesian coordinates a. 1 2 I b. -√2₁. 2 3 π

A:

Q: Use a substitution to change the following integral into one that can be found in an integral table.…

A: Given Integration: ∫7dvv3+lnv2

Q: Consider the center of mass of the following. A lamina occupies the part of the disk x² + y² ≤ 9 in…

A: The solution is shown below- As per company guidelines only first three parts are allowed to solve.…

Q: 29. Determine the average rate of change of the function over the domain graphed. y -4 20 (-3,-5) 2…

A:

Q: Express the given integrand as a sum of partial fractions, then evaluate the integrals. 1 1 y+2 2…

A:

Q: Using the ratio test to determine the convergence or divergence of the series series. O Convergent…

A:

Q: The gradient of f(x, y) = xy at (x, y) = (2,3) is

A:

Q: Consider the following equations. y = x, y=x²

A:

Q: Find the derivate of the functions of at any Use the form f'(c) = lim f(x) - f (c) for a and b X->(…

A:

Q: Solve the equation y" +4y= S(t-4π), y(0) = 1/2, y'(0)=0

A: The given differential equation: y''+4y=δt-4π, y0=12, y'0=0

Q: 31. The surface area of an inflating weather balloon is described by A(x) = 4x² - 1 where x is the…

A:

Q: An inverted pyramid is being filled with water at a constant rate of 25 cubic centimeters per…

A:

Q: Find the general solution for the differential equation. dv 6- - 12xy - x = 0 y = = 1/2 + Ce=x² y =…

A: Given differential equation:- 6dydx-12xy-x=0

Q: Find any relative extrema of the function. List each extremum along with the x-value at which it…

A: We have to find the monotone intervals and relative extremas.

Q: a) Find all of the critical points of x2 - x - 1 b) Find all of the critical points of x3 - 3x - 2

A: We have to find the critical points.

Q: Consider the following planes. -5x + y + z = 5 15x - 3y + 5z = 25 (a) Find the angle between the two…

A: Consider the following planes -5x+y+z=515x-3y+5z=25a To find the angle between the two planes.b To…

Q: What is the minimum value of f(x) = x^2 - 8 ln x   on the interval [1,5]

A: To determine the minimum value of fx=x2-8 lnx on the interval 1, 5.

Q: Given ƒ"(x) = 6x – 5 - and ƒ'(−2) = −1 and ƒ(−2) = 2. Find f'(x) = and find f(2)=

A: We need to find out the value of f'(x) and f(2) for which the second derivative is given.

Q: Using the ratio test to determine the convergence or divergence of the series series. Divergent The…

A:

Q: Given f(x, y) = 100x + 80y - 2x²- 4y² - xy Evaluate f(10, 9)

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

Q: The functions describes the distances from the origin at time t of an object in rectilinear motion.…

A:

Q: Perform long division on the integrand, write the proper fraction as a sum of partial fractions, and…

A: