5. [3] Determine the value of k when x³ + kx² + 2x -3 is divided by (x-1) and the remainder is 2.

Q: Using the four-step procedure in finding the derivative of O O -6 (√2x+2Ax+1)(√2+1)…

A: Topic = Derivative

Q: (x⁹ + x4)dx (x5 - 5)10

A:

Q: Differentiate. Don't simplify. 17. f(x) = sin 3x 18. g(x) = (sin 3x)³ 19. h(x) = (sin 3x)³ + 5x…

A:

Q: 3. A certain bacterial culture grows at a rate proportional to the number of bacteria present. If…

A:

Q: (-7)=|

A: Topic:- derivatives

Q: 5. Rewrite the expression as an algebraic expression in x. X cos( 1¹ (3)). H≤3 |x|≤3 (a) cos sin

A:

Q: A free-falling object falls from rest and has a weight of 89 N. The force due to air resistance (in…

A: Option A is correct the detailed explanation is given below

Q: 57-62. Transcendental functions Determine the end behavior of the following transcendental functions…

A: As per the guidelines we are supposed to answer only one question at a time. If you want answers of…

Q: c) lim 818 sin(x+3)

A:

Q: Find the following limits. Show all work a) lim x-0 b) lim X-8 c) lim X18 √2x+1-√√x+1 X 2x³-3x+1…

A:

Q: Find the derivative of the following functions. Whenever possible, express answer in factored form.…

A:

Q: The graph below is the function f(x) -5-4-3-2 Find lim z 2 19 NA Find f(2) Z -2 -3 4 f(x) Find lim…

A: Here we have to use the graph to find the limit of the function.

Q: Based on the given table of data, compute each of the following derivatives (fog)'(2) (gof)(4) = X 2…

A:

Q: 2. Determine dy/dx of the following equation. y = a. C. eeez dy dx = dy dx eeez = e. None of the…

A:

Q: Given 10t² 14t 80 t³ 8t² Evaluate *10t² - 14t - 80 ³ - 8t² c) antidifferentiation Add Work - Submit…

A: Given 10t2-14t-80t3-8t2=  3t+10t2+7t-8Evaluate: ∫10t2-14t-80t3-8t2dt

Q: Let f(x) = { 6-x_ x4. a. Find lim f(x) and lim f(x). Select the correct choice below and fill in any…

A: Topic:  Limit and Continuity   The answer is given below:

Q: G(r)=3r^3/2 + r^5/2 /r  *differentiate the function How do I approach problems like this? Like…

A:

Q: Question 3 Let P(t) be a deer population (in thousands) of an ecological region t years after 2000.…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Solve the problem. Find an equation for the least squares line representing weight, in pounds, as a…

A: Solution: We can directly use here Excel for regression, Step1) Enter data in Excel.

Q: II. Find the equation of the normal line to the curves at the point of tangency, if given. 1. y…

A: Recall: The slope of tangent line to the curve y is, mT=y'x0,y0 The equation of the normal line is,…

Q: Find the (a) velocity, (b) acceleration, and (c) speed of a particle with the given position…

A:

Q: A tank with a capacity of 300 L is full of a mixture of water and chlorine with a con- centration of…

A: We need to find amount of chlorine.

Q: 9. Eric wants to make a cylindrical water tank from sheet-metal. It must have a top and bottom. The…

A: Volume of the cylinder , V =πr2h ; where , 'h' is the height and 'r' is the radius of the circle.…

Q: (1) Let A 1 2 1 10 1 1 1 2 Express A¹ and A as products of elementary matrices.

A:

Q: Find the general solution of y'=ysinx

A: Given, y'=y sin x

Q: Find an integrating factor for the D.E. (2xy³ – 2x ³y ³ − 4xy² + 2x) dx + ( 3x²y² + 4y) dy = 0

A:

Q: (d) Two boats leave a port at the same time. One boat travels in a direction of N 70°E at 12 mph and…

A:

Q: Given the demand equation x + -- 20 = 0, where p represents the price in dollars and x the number of…

A: given demand equationx+p8-20=0

Q: Solve the following system of equations using Gaussian elimination method. If there are no…

A: The given system of linear equations, 5x-6y-6z=2-6x-8y+7z=9-20x+24y+24z=8 We have to find the…

Q: II. Determine the point(s) of intersection, m, and m₂, and the angle(s) of intersection of the given…

A: Given:     The curves 2y=2x2-6x+7                       y=x2-3x+72 ...1    Curve 2y=x+4…

Q: Solve the ODE d²c dt² dc +4 = -2C dt at C(0)= dc dt = 1

A:

Q: Find the limit. X+1 lim 2 x-1x + 5x +4 X+1 lim 2 x-1x + 5x +4 (Type an integer or a simplified…

A: We have to find the limit  limx→-1 x+1x2+5x+4.

Q: Let f(t) = et+3-7√5 + 3t-14. Find the first derivative: ƒ'(t) = Find the second derivative: f"(t) =…

A:

Q: Find the derivative of the following functions. Whenever possible, express answer in factored form.…

A:

Q: ƒ (x) = 3x² + 3, x = 7|

A:

Q: Use the Law of Cosines to determine the indicated side x. (Assume a-b-40. Round your answer to one…

A: Given query is to find the value of x.

Q: If 2 is a differentiable function of x and y satisfying the equation sın (x²z + y²) + 2x³=y2²+2,…

A:

Q: Consider the following complex numbers (b) (cle. Complete the following table Complex number 21 22…

A:

Q: A particle is moving in a straight line with velocity given by v=2e-1 for 014 where v is in ms and…

A: A particle is moving in a straight line with velocity given by        v=2e-t2-1    for  0≤t≤4where,…

Q: Find the derivative of the following functions. Whenever possible, express answer in factored form.…

A: We have to find derivative of given function.

Q: Find the equation of the line tangent to the graph of f(x) = (In x)5 at x= 11.

A: Topic = Functions

Q: Consider the following functions. f(x) =x+7² g(x) x + 7 5x - 7

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub- parts for…

Q: 13. Find the point (x, y) on the curve y = x² + 1 that minimizes the distance to the fixed poi (4,…

A: Given curve:- y=x2+1 We know distance between points x1,y1,x2,y2d=x2-x12+y2-y12

Q: etermining the Maximum and Minimum Values of Quadratic Functions rocket is launched in the air. Its…

A: Given query is to find the maximum height attained by the rock.

Q: Find the formula for the graph of the function f(x) given in the graph above. f(x) = 5sin(pix)+2 AN…

A:

Q: Find the standard form of the equation of a PARABOLA opening to the right such that the endpoints of…

A:

Q: A tank initially holds 200 gal of brine solution containing 3 lb of salt. At t=0, another brine…

A: Let's solve given problem. Solve for time t = ?.

Q: #1 Cπ/2 ST 0 (8 + 4 cos x) dx

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

Q: Suppose that a function f(x) is defined for all real values of x except at x = c. Can anything be…

A:

Q: total cost (in dollars) of producing xx golf clubs per day is given by the formula…

A: Given query is to find marginal cost function and marginal cost at level of 55.