6. Evaluate the indefinite integral (use C for the constant of integration). a. b. C. f(3x - (3x-6)2¹ dx I Sin 37t dt (In x)46 dx X [

Q: Consider the function f(x)=x/x^2+12x+32. Determine the intervals on which f is increasing and…

A: We have to determine the intervals at which the function  is increasing or decreasing.

Q: Suppose that we're making and selling some widget and the revenue (in dollars) when making a widgets…

A: The objective of this question is to find the average revenue, marginal average revenue functions,…

Q: Using rectangles whose height is given by the value of the function at the midpoint of the…

A: The given function in the interval .The aim is to find the area under the curve using the midpoint…

Q: 2. S x³ +1 x³ - x² da dx

A:

Q: Use the formula f'(x) = lim Z-X f(x)=x²-x+4 f'(x) = f(z)-f(x) Z-X to find the derivative of the…

A: we need to find f'(x)

Q: 9x Find the Maclaurin series of e 10

A:

Q: 16. You are designing a rectangular steel vat with a square base, an open top, and a volume of 32…

A:

Q: Please answer parts C and D

A: We have to find the limit of the given function.We will use the L Hospital rule to find the limit.

Q: Estimate the average value of the function between x = 0 and x = 7. 3 لیا 2 1 N - 1 2 3 The average…

A:

Q: Find the mass of a lamina bounded by y=5√x,x=9,and y=0 with the density function σ(x,y)=x+1

A:

Q: A company incurs debt at a rate of D'(t) = 102(t+10) √ ₁²+ + 20t dollars per year, where t is the…

A:

Q: A square-based pyramid has a height that is increasing at a rate of 7 inches per minute while the…

A:

Q: 9. The angular displacement of a spinning shaft is given as = 0.7t² - 5t+3, where is in radians and…

A: Given that the angular displacement of spinning shaft is where  is in radians and t is in seconds

Q: Find two positive numbers whose product is 100 such that the sum of the first and four times the…

A: Find two positive numbers whose product is 100 such that the sum of the first and four times the…

Q: 2x³+x²+x+1 x→∞0 4x³-x²-8 √x²+x+1 lim x→∞ √4x²+3 k. lim 1.

A: K) limx-infinity (2x3+x2+x+1)/(4x3-x2-8)I) limx-infinity +x+1)/sqrt(4x2+3)

Q: Find the demand function for the marginal revenue function. Recall that if no items are sold, the…

A: R'(x)= 0.03x2-0.08x+189

Q: Find ∫∫R  −3x+5y/(x+6y) dA where R is the parallelogram enclosed by the lines −3x+5y=0, −3x+5y=3,…

A:

Q: 8. Use the method of substitution to evaluate each of the following general antiderivatives 6x² (a)…

A:

Q: Find the Maclaurin series of e 00 1 0

A: The given function

Q: Simplify the following rational expression. State the domain restrictions: a) x3-8 2x3-8a

A: To simplify the following rational expression and to state the domainrestrictions.

Q: √ 5x(x² +4)√√x² + 4 dx. 2

A: To evaluate the following integral.

Q: In a large city, the road system is set up like a Cartesian plane, where streets are indicated by…

A: Given that in a large city, the road system is set up like a Cartesian plane, where streets are…

Q: 7. Linear Algebra - Linear Equations 2 Which of the following statements is true about the solution…

A:

Q: 5 1 - 9x Compute the first few coefficients of this power series: Represent the function -Co C1 C₂…

A: The given function is 5/(1-9x).

Q: Solve the initial value problem If the solution is y = co + C₁x + ₂x² + C3x³ + C4x² + C5x5 +C6x6 +…

A:

Q: 16. Split the number 15 into two parts so that the product of one part and the other is maximized.

A:

Q: Find the domain of f(x). f(x)=√x² + 7x + 10

A:

Q: Suppose g is a function which has continuous derivatives, and that g(0) and g"" (0) = 18. What is…

A: Suppose  is a function with continuous derivatives, and that .To find the Taylor polynomial of…

Q: Tonic 2: Functions The function f(x) = log10 (x-2) + 1 is given. a) Describe the transformations…

A: According to bartleby guidelines we are supposed to do only first three subparts . If you want more…

Q: 13. For the following limits, verify that direct substitution yields an indeterminate form. Then use…

A:

Q: 6. Σ. 1 n=1 1 ηγη2 +1 n

A: since you have posted multiple question in this question which are not interlinked so i have solved…

Q: = 16 a Problem #3: Find the surface area of the part of the paraboloid z = 64 - x² - y² that is…

A: z=64-x2-y2x2+y2=16The surface area is given by

Q: Suppose that we're making and selling some widget and the cost (in dollars) when making a widgets is…

A:

Q: 19. Use Newton's Method to estimate the one real root of f(x)=x²+2x-2. Start with x = 1, and perform…

A:

Q: i. x+1 lim X→∞ X-1

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Use implicit differentiation to find the equation of the tangent line to the function defined…

A: The given equation is; 6x2+2x4y5=8Point (-1,1)

Q: Let F(x) = sin(6t²) dt. S Find the MacLaurin polynomial of degree 7 for F(x). S Use this polynomial…

A:

Q: 4. Solve Cauchy problem: y" - 5y' + 4y = 0, y(0) = 1, y'(0) = 2

A: To solve the following Cauchy problem.

Q: 5. Calculate the following limits: x-5 a. lim x-5x2–25 b. c. d. lim x--5 x²+3x-10 x+5 t² +t-2 lim…

A: 5)a) limx-5 (x-5)/(x2 -25)b) limx-(-5) (x2 +3x-10)/(x+5)c) limt-1 (t2 +t-2)/(t2 -1)d) limx-(-2)

Q: Find the exact length of the curve described by the parametric equations. x = 8 + 3t², y = 7+2t³,…

A:

Q: Minimizing Heating and Cooling Costs A building in the shape of a rectangular box is to have a…

A: We have to find the dimensions of the building that will result in a minimal annual heating and…

Q: Determine the critical numbers, if any, of the function f. f(x) = 3x² + 3x³ - 54x² - 81x + 21 Give…

A:

Q: Suppose that lim f(x) = 10 and lim g(x) = -4. Find the following limits. X-3 X-3 a. lim [f(x)g(x)]…

A: According to the guide line we do only the first three parts of multiple part questions.

Q: Find the indicated term of the binomial expansion. (√2₁² +1³); second term 3 u

A:

Q: Find an equation of the curve whose tangent line has a slope of f'(x)=x given that the point 1,-…

A:

Q: Considering the interval [−2, 4], does the Mean Value Theorem for integrals hold for f (x) whose…

A:

Q: The equation z = 5r cos (0) is given in cylindrical coordinates. Convert the equation to Cartesian…

A:

Q: What substitution(s) would make the following integral simpler? I.e., simple enough to integrate by…

A: Given

Q: a) x2+5x-14 x²+8x+7 + x²-4x+4 3x²-6x

A:

Q: Find the exact value of each of the following under the given conditions. 6√85 85 5 sin a = 13 (a)…

A: