The base of a solid is the region bounded by y = x^2and y = 2x. The cross-section perpendicular to the x-axis is an equilateral triangle. Find the volume of the solid.

Q: Find a power series representation centered at the origin for the function 1. f(x) 2. f(2) 3. f(x)…

A: To find the power series of the function centered at origin.

Q: find the second derivative of tan( 2x^3)

A:

Q: f(x) = 3x at x = 4.

A:

Q: Find the total derivative given: dy a) z = f(x, y) = 2x + xy - y² where x = g(y) = 3y²

A:

Q: Given the function f(x) = 2x³ + 21x² - 72x-1, determine the intervals where the function is…

A: we will find the required.

Q: Use the Root Test to determine whether the series converges absolutely or diverges. M8 F k=1 gk ***…

A: kk/9k

Q: The graph below shows a rectangular sum of n = 4 rectangles to approximate the area under the line…

A:

Q: The length of the side of a square floor tile is 15 cm, with a possible error of 0.05 cm. Using…

A:

Q: The graph of the quadratic function h(x)=x2−3x+2h(x)=x2−3x+2 is a parabola that opens upwards. What…

A: We have given a quadratic equation  hx=x2-3x+2 hx=x2-3x+322-322+2 hx=x2-3x+94-94+2 hx=x2-3x+94-14…

Q: Suppose that a price-demand function is given by P(x) = 500- 500 - 15x. Calculate the marginal…

A:

Q: Suppose that a price p and demand x are related through the price-demand equation x + 400p = 8,000.…

A: The elasticity of demand at price p is given by Ep = -px·dxdp   (where x is the demand).

Q: x²(x-2) X+6 Answer the following questions about the function whose derivative is f'(x) = a. What…

A:

Q: Problem No. 1: In 2015, there were 233,040 Individuals living in Olongapo City. The population…

A: Problem No. 1: In 2015, there were 233,040 Individuals living in Olongapo City. The population…

Q: If f(x) = 7x² - x + 5 and h = 0, find the following and simplify. (a) f(x + h) (b) f(x+h)-f(x) h ||

A: a) Replace x by (x+h). b) Substitute the required.

Q: f(x) dx, given than = 4 Find the value of 6 f(x) is odd, and ſ≤₂ ƒ(x) dx √₂ f(x) dx =

A: Integral

Q: 19. Find the distance from the point (3, -2,7) to the plane 4x – 6y + z = 5. Show all necessary work…

A: A detailed solution is given below.

Q: Find the midpoint of the line segment joining the points P1 and P2;P1 = ( - 1, 4); P2 = (8, 0)

A:

Q: Find the vertical and horizontal asymptotes of f(x), find the first and second derivatives and draw…

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the…

Q: Evaluate the line integral, where C is the given curve. Jox x sin(y) ds, C is the line segment from…

A:

Q: Part of the playground jungle gym has a metal arch. The arch has various footholds to make it…

A:

Q: The first derivative of the continuous function y = f(x) is given below. Find y' and then use the…

A:

Q: f (3 — e3x)3dx

A: The given integral is: I=∫3-e3x3dx   As we know the Sum rule: ∫fx±gxdx=∫fxdx±∫gxdx And use the…

Q: 1) Use the Substitution Method to find f 12x (3x² + 4) dx . O 20(3x^2+4)^10 +C O 0.2(3x^2+4)^10 +C…

A: The given integral is 12x(3x2+4)9.

Q: Simplify the expression. Write the final form with no fractions. cos²x+1 2 sin²x +1= cos sin

A: We can simplify the expression in the below steps.

Q: Suppose I want to use a "u" Substitution to find f cos x(sin x) dx . What should I choose for u?

A:

Q: by change of variable with u = e, evaluate [√ere da

A:

Q: The graph of h(t) shows the height of a person riding a Ferris wheel t minutes since the wheel…

A: Given: The graph of ht, shows the height of a person riding a Ferris wheel t minutes since the wheel…

Q: Consider the graph of f'(x) below. At what value (or values) of x does f(x) have a local minimum? -6…

A: The solution is given below

Q: Evaluate each expression using the given table of values:

A:

Q: = .. Find the tangent plane and normal line to the surface ƒ (x, y) : (1, 0, 1). xey at the point

A:

Q: Problem #2: Consider the following vector field. Problem #2(a): Problem #2(b): F(x, y, z) = 3yz In…

A:

Q: Consider the series Find s4 and 88 S4= S8 = n=1 4 n +8 Let sn be the n-th partial sum; that is, Sn =…

A: Series

Q: Find the intercepts of the graph of 3x2 - 4y = 48.

A:

Q: Question 12 (D² + 2D + 5) y = 6sin2x + 7cos2x

A:

Q: 1. Find for the following by implicit dy dx differentiation: 33x8 9 cot y = y³ − 33x dy 2. Find…

A:

Q: Consider the matrix A = 2 7 10 2 1 8-5 14 ao 1 do as (a) Reduce A to rref and find its rank. (b)…

A: As per the instruction, we will be answering the first question. If you need answers to others then…

Q: Find the area of the shaded region. A = -6 y = x³ - 15 x (-4,-4) X y 20 10 -10 -20 2 (4,4) y = x 4 6…

A:

Q: observer on the ground sites a plane at an angle of elevation of 42.6°. A

A:

Q: A. For each differential equation, give the dependent and independent variable(s), state whether the…

A:

Q: Determine the radius and interval of convergence of the following power series. Σ(-1)*** 8k

A:

Q: differential equations 2ycos(2x)dx+(sen(2x)-2sen(y))dy=0

A:

Q: Please, I need the answers of other tutors to check, thank you very much! Find the vertical and…

A:

Q: Classify the critical value(s) of ƒ (x, y) = (x² + y) e² as a local maximim, minimum, or as a saddle…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: A cup of coffee at 90° C is put into a 20° C room when t = 0. The coffee's temperature is changing…

A:

Q: Use Euler's method with step size 0.5 to compute the approximate y-values y₁ Y2 Y3 and Y4 of the…

A:

Q: A particle moves along the x-axis with acceleration given by a(t) = cos 1/ cos (1/t) for time t > 0.…

A:

Q: Coefficients Linear in Two Variables (3x + 2y + 7)dx + (2x - y)dy = 0 show complete solutions…

A: The differential equation Mdx+Ndy=0 is said to be exact, if ∂M∂y=∂N∂x. Then the solution of the…

Q: In the derivative, transform into linear equation y = mx + b (the form)

A: Given :  y = mx + b (the form)   To find : In the derivative, transform into linear equation

Q: 6. Use a Table Entry to find the exact value of 0 2x sin(7x) dx.

A: Solve by by parts method

Q: find the domains and ranges of ƒ, g, ƒ>g, and g>ƒ.3. ƒ(x) = 2, g(x) = x2 + 14. ƒ(x) = 1, g(x)…

A: