Sketch the region and find the area of the region bounded by y = 3x + 1, the lines x = 1 and x = 4, and the x-axis.

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of F(2) = | sin(t*)dt F'(x)…

A: Given query is to find the derivative.

Q: Find the total area of the shaded regions. ... Ay 64 y B+x y 64-xf -10 8-6 -4 | -2 2 46 8 10

A: -8≤x≤9Intersection points:8-x=64-x2x2-x-56=0(x-8)(x+7)=0x=-7, x=8Area bounded=∫-8-7[(8-x)-(64-x2)]dx…

Q: a. Graph the function f(0) = 6 sin(0). 6- 4 -/2 3/2 -2 -4 -6 -8+ Clear All Draw: W b. Graph the…

A: We want to plot the graph.

Q: Find the derivative of the function. f(x) = In(sinh(x)) f '(x) =

A: f(x) = ln(sinh(x)) here we use chain rule f'(x) = cosh(x)/sinh(x) f'(x) = cot(h(x))

Q: Determine all real zeros of f. Ax) = x³ + 4x² – 9x – 36

A:

Q: Find the indefinite integral. (Use C for the constant of integration.) cosh(8x) dx

A: We have to find the indefinite integral ∫cosh8x dx.

Q: The rate of growth G, in thousands of dollars per year, in sales of a certain product is a function…

A: We need to solve growth model.

Q: Use the arc length formula 2 dx 2 L = dy dt dt dt to find the arc length of the curve. x = cos 12t,…

A:

Q: Find the curl of the vector fleld F(z, y) = 9ye" i+2ejat the point (-2, 0). Enter an exact answer.…

A: F(x, y)=9y2 ex3 i +2x2 ey jcurl F→=∇×F→curl F→=ijk∂∂x∂∂y∂∂z9y2 ex32x2 ey0         =∂∂x(2x2…

Q: Which of the following numbers is a rational number? V25-1 V5 O the above the above the above None…

A: We need to choose correct option.

Q: Find the area enclosed by the curves y=2r2, y=2x ,x=- and x = 1 4 A 59/76 B 45/51 49/96 D 65/89

A:

Q: Jse cylindrical shells to find the volume of the solid generated when he region enclosed by the…

A:

Q: 8. The base of a solid is a region in the first quadrant bounded by the r-axis, the y-axis, and the…

A: The given is a half cone which has radius =4 Height =8

Q: 'he graph of a periodic function f is shown below. f(4) 4 \1.57 3.14 4.71 6.28 a. What is the period…

A:

Q: The cost C (in millions of dollars) of removing p% of the industrial and municipal pollutants…

A:

Q: S(2) = - – 4x – 2 a) Determine the intervals on which f is concave up and concave down. f is concave…

A: Note:- This is multiple sub parts question and according to our company guideline we can do maximum…

Q: Find the area bounded by the curve y = 4x - x2 and the lines x = 0 and y = 4.

A: topic - area bounded by curves

Q: Find the volume of the solid that results when the region enclosed by y = Vx, y = 0, and x = 121 is…

A:

Q: Convert the polar coordinates (2, 60) to Cartesian coordinates. (1, √3) (√2, √2) (√3, 1)

A:

Q: (In x)² dx. use integration I

A: topic - integration by parts

Q: For the integral, tanx secx dx, if we let u = tan x, what is the re-written form of the integral:…

A:

Q: Use the power reduction formulas to rewrite the expression, sin2(6x)

A: Given query is to rewrite the expression.

Q: 3x2+ 7x+28 A f (x) |*+ A x³+x²+7x Using Partial Fractions in evaluating dx, the decomposed fraction…

A:

Q: Given the differential equation -7x y" + y' = 6x2 Use Reduction of Order and the letter "R" to…

A:

Q: Calculate the vector line integral F. dr. where Fis the vector field (z+ Sy, 2z - y) and Cis the…

A: To find the value of the given line integral.

Q: Convert the polar coordinates (T, 7) to Cartesian coordinates. O ( T, TL) O(- T, 0) O (0, - T1)

A:

Q: The graphs show the position s, velocity v = ds/dt, and acceleration a = d²s/dt2 of a body moving…

A: The graphs show the position s, velocity v=dsdt, and acceleration a=d2sdt2 of a body moving along a…

Q: (4/3,4) to polar coordinates. Convert the Cartesian coordinates O (4, 30) (V42, 150) (8, 30)

A:

Q: [43 80 -60 Let A = Find an invertible matrix X and a diagonal matrix D such that [30 60 -42] D =…

A:

Q: Use the integral test to determine whether the series is convergent or diverg n2 n3 + 1 n = 2…

A:

Q: Find the indefinite integral. (Use C for the constant of integration.) 1 XV x4 dx - 16

A:

Q: y3 x³ – 4x – 1 = 0 3 Consider the implicit curve dy/dx and use this to explain why dy/dx is always…

A: SOLUTION GIVEN BELOW

Q: Find the indefinite integral. (Use C for the constant of integration.) 1 dx 4x2 – 1 XV

A: We have to determine integral

Q: Use quadratic formula to find all the real zeroes of the 2nd degree polynomials 6x²-x-1

A: The given polynomial,      6x2-x-1

Q: Solve the given differential equation. Ans: + cos x = c 1. y' +y2 sin x = 0 %3D y

A: The objective of the question is solving the differential equations.

Q: 12 x*y dx dy 12 I*y dx dy i

A: topic - double integration

Q: 2.

A:

Q: 1 2 dx

A: ∫9x12dx=9∫x12dxusing formula ∫xn dx = xn+1n+1here, n =12

Q: At least one of the answers above is NOT correct. Suppose f(x) is continuous on [3, 7] and -2 <…

A: Solved below

Q: ng the shore and 60 meters from the sh mps into the water and swims from the second and swim at a…

A:

Q: The polar coordinates expressed as Cartesian coordinates are |(1, O) (-1, 0) (0, 0) O (0, 1)

A:

Q: 1- 2x2 - cos 2.x 3. Use the Taylor series to evaluate lim DO NOT USE L’HOSPITAL'S RULE. x4 Evaluatee…

A:

Q: Question Using Rolle's theorem for the following function, find all valuesc in the given interval…

A: Given query is to find the value of c for the given interval.

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of f(x) = dt 2 f'(x) =…

A: Using fundamental theorem of calculus,

Q: 1. A force of 1000 pounds is acting on an object at an ang of 500 pounds is acting at an angle of…

A:

Q: Suppose that '(t) and F(0) . Find 7(t) F(t) = <

A:

Q: 18 Find the inverse function of F (x) = 2 arccosx F-1(x) = _____ cos2x cos1/2x 2cosx

A:

Q: ニ1 近。 Question 2 D. O E OA 3. (A) 3. 3. (). 32 3. (C) 16. (B) zg (7) The area of the region enclosed…

A:

Q: Find the length of an are with parameterization r(t) = (-7 sin (t), -7 cos (t), -4). on the interval…

A: In this question, We will use the formula of the length of an arc of the parametrized curve.

Q: If g(x) = 5 – x³, find g'(0) and use it to find an equation of the tangent line to the curve y = 5 –…

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