3) For: f(x) = 10x + 96 and g(x) = x² + 8x + 16 A) At what two x-values is f(x) = g(x) (show algebra or the graphing method) B) Which function is bigger between the x-values you found in part A C) Give the simplified Definite Integral that will find the exact area enclosed by the grap of f(x) and g(x). D) Find the exact area enclosed by the graphs of f(x) and g(x) Show your work(method).

Q: 1) The distance, travelled by a car, f(x), in meters, after x hours, can be represented by f(x + 20,…

A: Disclaimer: Since you have asked multiple question, we will solve the first question for you. If you…

Q: Use a trigonometric substitution to integrate the function f(x)=x√x² - 9 x². Check your work by…

A: put put x2-9=sin2t⇒2x dx=2 sin t cos t dtNow∫x (x2-9) dx=∫sin2t [sin t cos t dt]=∫sin2t. cos t .dt…

Q: Evaluate the integral dx fax √2x-x1

A: Given: I=∫dx2x-x2   As we know the common integral; ∫11-x2dx=sin-1x+C

Q: Differentiate the following function In z I y = 0 - 1/1/(x-²) I 1-ln z O O 1-r ln r r³ 0 1 I

A:

Q: 1 Evaluate the integral S√I+2x f dx

A: We have definite integral  Substitute 1+2x=z2  to make integration radical free as I have done…

Q: 1 Determine the definite integral of 4 3(Vx) xp (DE + x^)S

A: Let I=∫49x+13xdxApply the Sum Rule:…

Q: Consider the aleatory variable X with densidad: f (x) = (1/6)x 2 ≤ x ≤ 4 a)…

A: Let X be a continuous random variable with the range [a, b] then the probability density function…

Q: Find y in terms of x. dy =x+ 5, curve passes through (0, 14) Select one: O A.y =x+ 5x +14 B.y = x +…

A:

Q: x² dx /1 + 2x 3

A:

Q: Describe the domain of : POINT 2) f(x, y) = Ln(2 + x + y) %3D

A:

Q: Test the function defined by f(x, y) = exp 2x-y x+2y -cos 2x-y x + 2y for its homogeneity. If it is

A: Given: The function is fx,y=exp2x-yx+2y-cos2x-yx+2y. To check: The given function is homogenous or…

Q: Let f(x) = x^2 + 15  ^5√ x and g(x) = 3 − 2x. Find the following: d/dx(x^2g(x))

A:

Q: Function f(x) is positive when 1<x<2, and it is negative when 2<x<3. If the area of the region…

A: the area from 1 to 2 is 5. so we can write the area from 2 to 3 is 7. so we can write

Q: Using four triangles to estimate the area under f(x) is approximately

A:

Q: (2) Compute the integral and then verify that you got the correct answer by differentiation. (a)…

A:

Q: Determine the area, in square units, bounded above by f(x)=−x^2−10x−16 and g(x)=2x+16 and bounded…

A: Given that fx=-x2-10x-16gx=2x + 16 The objective is to find the area of the region which is bounded…

Q: Find f. f "(x) = 1//1- x?, () - = 2 f(x) =

A:

Q: Prealgebra f（z)=z^21-5z^7+9z^4 find Im（f(-1+√3i）) i need calculation process.

A:

Q: 3 (x²+2)

A:

Q: help me understand this.    F(x)= 3x-x^3 what is/are the x-intercept(s)?  what is the y-int? what is…

A: Given, y = F(x) = 3x - x3 For x-intercepts, y=0 ∴ 3x - x3 = 0 =&gt;x(3-x2) = 0 =&gt;x = 0, √3, -√3 ∴…

Q: Find ao of the function f(x) = ÷(n - x)² |3D IT ^ 2/12 O 5 T^ 2/6 π^ 2/6 O T^ 2/6 5 π^ 2/12

A: Fourier coefficient ao of the function in the Fourier series

Q: (а) 4.x dx -2 (b) / (2.² Зх + 6) dx

A:

Q: 5. (12 points) Use the geometry or symmetry of integrals to evaluate the following definite…

A: Step 1:(a) The following formula of integration is known:∫a2−x2​dx=2x​a2−x2​+2a2​sin−1(ax​)+cwhere c…

Q: a) A function is given by f(x) = 5x³ -6x² +x -e*. Find the slope of the tangent line to this curve…

A:

Q: Find the area under the graph of f(x) = x² + 10 between x = 0 and x = Area = 6.

A: Givenf(x) = x² + 10x = 0 &amp; x = 6