What is the exact area bounded by the curve f(x) = 1/2 X and the x-axis on the interval [1, 8]? Write the value in exact form. Do not write a decimal approximation. Write the exact number that completes this sentence. The area is square units. Do not use the equation editor to write the number.

Q: 1 x² dx So √4-x²

A:

Q: Show that x+iy | g+ix / = 1₁ =1, where X +iy and y+ix are complex numbers.

A: Here, let evaluate x+iyy+ix Using the absolute rule ab=|a||b|: =|x+iy||y+ix|

Q: 6. Evaluate the expression sin cos (77)) 11 tan sin (sin-¹ (²-3)) 13,

A:

Q: f(x) = (x² − 9) -

A: Given :f(x)=x2-923

Q: d. In 1000 x limx→+00 X5

A: Let's evaluate limit.

Q: Sx". .n-1 +n[x²= x" sin x dx = -x cos x + n cos x dx

A:

Q: Calculate the derivative of y with respect to x when sin(x + y) = 5x + 4 cos(y). (Use symbolic…

A: topic- derivatives

Q: Find the integral of f(x³ + 1) Inx dx

A: Given :∫x3+1lnx dx

Q: If the population of a city is 155,000. If the population declines continuously by 5% per year, what…

A: Question-   If the population of a city is 155,000. If the population declines continuously by 5%…

Q: (e) ƒ(x) = x³ (x + 5)²

A:

Q: Find the inverse of the function on the given domain. f(x) = (x-5)^2, [5,00) f-1(x): =

A: The solution is given in the next step.

Q: 1. Evaluate the given integral Q. JR (y - 2x) dA, R where R is the region bounded by x = 0, y = x, x…

A:

Q: lim.. lim X→+∞0⁰ In5 x x² In 1000 X 5 X X→→→→+∞0

A:

Q: 3. Find the member of the curve whose slope at any point is and passes through the point (1, 1)

A: The given problem is solved below in detail.

Q: Write an equation for a rational function with: Vertical asymptotes at x = 6 and x = -4 x intercepts…

A:

Q: 1) Determine the projection of a= [5, -4, 8] onto b = [3, 7, 6].

A:

Q: 4) Given the points A(1, 2, 3), B(5, 4, 3), and C(2, 1, 2), find angle C

A:

Q: F- 2x-7 h(a) √√x +3 the function Find the Domain (11) Range of (11) Show wheather the function is…

A:

Q: 4. Determine whether the following statements are True or False? y = f(x)

A:

Q: What is the expansion of the binomial expression (x + y)⁵ ? What are the binomial coefficients?

A: Solution of given question is written in below steps.

Q: 3√3 dx √3 x² √√x²+9

A:

Q: 5. Determine whether the following statements are True or False? y = f(x) 2 X 0 (a) lim f(x) = 1 (b)…

A: Given graph of y= f(x)

Q: S²₁ A Select one: dw w√w²+3 a. 0.0128 O b. -0.0234 0 с. c. -0.0128 O d. 0.0234

A:

Q: Electric charge is distributed over the disk x² + y² ≤ 11 so that the charge density at (x,y) is…

A:

Q: Find the general equation of the circle of curvature of the parametric equation t+1 X: ; y = ±…

A: This is a problem of finding equation of the circle of curvature. Based on the general formula and…

Q: f (x+2) In (x+2) - 4 tc (x+2) Xt *+ 2

A:

Q: Find the derivative of 4Inloge*

A:

Q: 1. Consider the differential equation y" - ry - y = 0 a) Determine two linearly independent power…

A: answer is in next step

Q: The sum of the lengths of the two diagonals of a parallelogram is 18 m. One diagonal is 2 meters…

A:

Q: whose equation is y³ + 2xy + x² = 9 Using techniques we have learned in our course, perform the…

A: Given query is to find the derivative and equation of the tangent.

Q: a. f(x) = (x² − 9) =

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Perform bisection method on approximating the root of the equation x³ + x²-x + 7 = 0. Use initial…

A:

Q: Evaluate the following limits. a. lim 2x 3x² b. lim x→0+ e-3/x ,2 X² ||

A:

Q: Find the derivative of a composite function using the Chain Rule or General Power Rule.  1.)…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: The average value of f(x, y) over the rectangle R = {(x, y) | a ≤ x ≤ b, c ≤ y ≤d} is 1 fave = (b −…

A: The average value of a function f(x,y)  over  R={(x,y): a≤x≤b,  c≤y≤d}is given by1(b-a)(d-c) ∬R…

Q: 5. y" + 8y + 16y = 0

A:

Q: Find the center of the mass of a thin plate of constant density & covering the region bounded by the…

A:

Q: 1. Evaluate the given integral Q. -2 2y-2 -K² Q Jo 1 = (xy-1) dx dy

A:

Q: Problem #10] A kite 100 ft above the ground is being blown away from the person holding its string…

A:

Q: Find the inverse of the function on the given domain. f(x) = (x−5)^2, [5,∞)

A:

Q: 2 Brad wants to buy a coffee machine for his café. The advertised price is $3200 including GST. When…

A:

Q: Find the linearization L(x,y) of the function at each point. f(x,y) = x² + y² +1 a. (3,4) b. (0,3)…

A: To find the linearization Lx, y of the function at each point.fx, y=x2+y2+1 a 3, 4b 0, 3

Q: Jack has 13 cards printed with the letters from the word “UNDERSTANDING,” so that “U” is in one…

A:

Q: 7π| A d) S_T/A (sin x + cos x) dx

A: We will evaluate the given integral in the following step.

Q: Find the domain of =) = √x² – 3x

A: Given query is to find the domain of the function.

Q: dy dx X2 (1+y2)

A: Let's solve given diffrential equation.

Q: 4. Evaluate the following limits. a. lim X→→→+** 2x 3x² b. lim c. lim -3/x X In5 x x²

A: This is a problem related to limit calculation. Based on the general formula and concepts we will…

Q: Consider the functions z= - ex In y, x = In (u cos v), and y = u sin v. dz əz (a) Express and as…

A:

Q: air resistance can be ignored, how high does it go?

A: Given query is to find the height of the ball.

Q: [x³√₁-x² 2

A: ∫x31-x2dx=∫1-x2x3dx Let 1-x2=t⇒-2xdx=dt⇒xdx=-dt2                         =-∫(1-t)tdt2=-12∫(1-t)tdt…