2. Let E denote the parallelepiped with corners (0, 0, 0), (1, 2, 1), (2,3,0), (-1,0, 1), (3, 5, 1), (0, 2, 3), (1,3,1), and (2, 5,2). Find the average a coordinate of a point in E.

Q: Use f(x) = log4(16x) and g(x) = 4* to answer the questions below.

A: A. Find f(g(x)) and simplify    B.  Find the range of y= f(x) - g(x)

Q: 3 9 Using sigma notation, write the following expression as an infinite series: 1+ − + · 4 16 n2+ 1…

A: By using sigma notation, to write the following expression as an infinite series.1+34+916+2764+...

Q: Evaluate the following integral in spherical coordinates. √ffe (²+y - (x² + y² +2²) 312 D dV; D is a…

A:

Q: = Find e > 0 such that the area of the region enclosed by the parabolas y 440. C = x² - c² and y =…

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Q: Find the arc length of the curve on the given interval. (Round your answer to three decimal places.)…

A:

Q: Find the initial horizontal velocity and vertical velocity for each situation.

A: According to question,Given,Velocity v= 1200 ftsecAngle with the ground = 42o

Q: 3. Tim ( x ²-1 x2-3x+2/

A: use L'hospital rule limx→1(x2-1x2-3x+2)=limx→1∂ ∂x(x2-1)∂ ∂x(x2-3x+2)∂xn∂x=nxn-1

Q: For the curve determine each of the following: Note: Use a negative for a shift to the left. y =…

A:

Q: Use summation properties and formulas to rewrite and evaluate the sur 37 Σ 60 (i² – 8i + 1) - i=1

A:

Q: A projectile is launched straight into the air with initial velocity vo = seconds after launch is…

A: The given velocity function: vt=100-32t

Q: d. 3 +e=tan(x-y)

A:

Q: Find the Maclaurin series of the function f(x) = 8x³ − 9x² - 4x +9. Determine the following…

A: We need to solve Maclaurin series.

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A:

Q: Choose the correct answer. O A. B. log ₂6. log ₂y + log 2² log ₂6+ log 2y + log 2² C. This cannot be…

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Q: 2. An international airline has a regulation that each passenger can carry a suitcase having the sum…

A:

Q: The function defined by f(x) = ax2 + bx+c has a relative extremum at (1,7) and the graph of f passes…

A:

Q: east one real value of x? =x² +1 لاح * 1T for all real values of c. h(x) = |x| d. j(x)=x²-3x…

A: Function is differentiable everywhere on R if it's derivative is defined everywhere on R.

Q: Confirm that the below limit meets the conditions to apply Hôpital's Rule and then solve the limit.…

A: Answer: The solution is given below:

Q: The rectangular coordinates of a point are given. Plot the point. (-6√2,-6√2) O O -10 -10 (r, 0) =…

A:

Q: X+2 - 9 X-2 = 10x 4-x2

A: Given,             3x+2-9x-2=10x4-x2

Q: in triangle,p is the midpoint of side bc and cq=1/3ca prove that 2 vectors bc+ vectors ca+ vectors…

A: Given: in triangle,p is the midpoint of side bc and cq=1/3ca To find: 2→bc +→ca+→ba=6→pq

Q: Consider the curve x²y + y²x = 6 A) Find in terms of x and y dx B) Write the equation for the…

A:

Q: 8. Jymy) dy ylny/

A:

Q: Determine the open t-intervals on which the curve is concave downward or concave upward. x = 9+7t²,…

A:

Q: 3. Write parametric equations for y = -4x + 1 for the given definitions of x. x = 1²/22 a. x = b. x…

A: Explanation of the answer is as follows

Q: This extreme value problem has a solution with both a maximum value and a minimum value. Use…

A: To find the minimum and maximum value of function using lagrange multiplier.

Q: A wire of length 7 is cut into two pieces which are then bent into the shape of a circle of radius r…

A:

Q: calculus to determine where = 180x³ + 33x² - 12x + 3 ecreasing. your answer as an interval, using U…

A: Given query is to find the interval where function is decreasing.

Q: 2 The function f(x)= x3 does not satisfy which of the following conditions on the interval [-1, 1]…

A: The objective of the question is choose the correct option.

Q: Use an appropriate test to determine whether the series converges. 8 k! Σ k=1 5 k Select the correct…

A:

Q: -2 0 8 4 Determine the x-value where a possible global maximum for a function h occurs on the…

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Q: Suppose that triangle ABC is a right triangle with a right angle at C and hypotenuse c. Also note…

A:

Q: Question 4 > Evaluate the definite integral by interpreting it in terms of areas. 8 L (27. (2x -…

A:

Q: Expand, that is, perform the indicated operations on the differential operator D (xD+2)(xD-2)

A: To expand, that is, to perform the indicated operations on the differential operator D. xD+2xD-2

Q: 9.

A:

Q: r(t) = (−8tª + 5, sec² ti ANNE 9 7 3et - 2tln(t))

A:

Q: 14. Determine the value of a. 0 b. 4 for y= x²(x² + 1)² when x = 1. Show your work. C. 12 d. 16

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Q: Find the magnitude of the cross product A x B for the vectors A = 3.0 + 4.0j and B = 21 Drawing a…

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Q: Consider the curve x²y + y²x = 6 A) Find in terms of x and y dx

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Q: Find the length of the curve over the given interval. Polar Equation Interval r = 2a cos 0 9π X π π

A: To find length of polar curve.

Q: Limits at infinity are associated with O straight lines O vertical asymptotes horizontal asymptotes…

A: To fill in the blanks

Q: Find the Taylor polynomials of orders n = 0, 1, 2, 3, and 4 about x= x and then find the nth Taylor…

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Q: Find the function f with f'(x) = cosx-x³, f(n)=3.

A:

Q: COMPUTE: 5. r' (t)

A: Givenr(t)=-8t4+5t,sec2tπ6,3et-2tln(t)   We are required to find the value of r'(t)

Q: The position of a ball, relative to the ground, which is thrown vertically upward is governed by…

A: The position of a ball, relative to the ground, which is thrown vertically upward is governed by…

Q: Find дз дх if 4z3 + 3xz2 - xyz - 2xy2 + 7 = 0.

A: 4z3 + 3xz2 -xyz - 2xy2 + 7 = 0 we want to find out ∂z∂x

Q: X 1+√x 8.) f(x) = -

A:

Q: Use the following table to answer parts 1-4 below. ▸ Part 1 ▸ Part 2 - Part 3 - If h(x) = 2x +…

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Q: Integration of( 3x2-3yz+2xz)dx + (3y2-3xz+z2)dy + (3z2-3xy+x2+2xz)dz along straight line joining…

A: Given: ∫-13∫22∫31(( 3x2-3yz+2xz)dx + (3y2-3xz+z2)dy + (3z2-3xy+x2+2xz)dz )

Q: Compute the values of dy and Ay for the function y = 4x + 2x given z = 0 and Az =dz = 0.02.

A: