Suppose that lim an = 5 and lim bn = 9. n-0 n→∞ Determine the limits. lim (an + bn) = n→∞o lim a = n48 lim cos (лbn) = n→∞ lim (a - 2an bn) = n→∞

Q: 1. Determine the derivative with respect to 'x' of: a) f(x) = 4cos(x³) - sinx b) f(x)=x² cos² (5x)…

A:

Q: 2. Solve by separating variables and check y'= 4x³y with initial conditions_y(0) = 2…

A:

Q: Find all the second partial derivatives. f(x, y) = xy - 4x5y² fxx(x, y) = fxy(x, y) fyx(x, y) = =…

A:

Q: Can you please help me how to do this problem, can you show me how you do it step by step so I…

A:

Q: The region bounded by f(x) = -3x² + 18x + 81, x = ( volume of the solid of revolution. Find the…

A:

Q: Find the area of the region enclosed by y = 3.25x and x = 7.5-y². 2 2 1 2 w A 5 6 N Use horizontal…

A: The area bounded by the curves x= f(y) , x= g(y) between y= a and y = b is given by A = ∫abfy-gy dy

Q: for fage 5 f(x)=(74³-t²45) (15t+4) f(x)= (x²1)(x²2) 6²3)

A:

Q: Describe the translations performed on f(x) = log(x) to graph g(x) = log(x – 7) – 7. Select all…

A:

Q: Use the Shell Method to calculate the volume of rotation, V, about the x-axis for the region…

A:

Q: Consider the following. dz Find by using the chain rule. (Enter your answer in terms of t.) dt dz dt…

A:

Q: me Value Theorem, which of the following is true?   A) f(x) achieves a maximum f(c) and…

A: f(x)=x2

Q: If f is a differentiable function with derivative 1-x x²+1 intervals is f concave up? f'(x) = 3 then…

A:

Q: Find the area of the parallelogram whose vertices are given below A(-1,4) B(4,0) C(9,3) D(4,7) The…

A: We have, A(-1,4) , B(4, 0) , C(9,3) , D(4, 7)

Q: (2) Given f(x)= numbers √x+2c_if x>4 [ex² if x≤4 find the value of c so that f(x) is continuous for…

A:

Q: 7. Sketch the region and then use the disk/washer method to set up an integral to find the volume of…

A: To sketch the region and then by using the disk/washer method to set up an integral  to find the…

Q: Find the mass of the two-dimensional a density function of p(x)= x³-5x + 6. object. An oversized…

A:

Q: Construct a limit evaluation problem with an answer of 1. (do not use L'Hospital's rule)

A:

Q: Water is leaking from a 2 foot tall rectangular tank at 0.1 cubic foot per hour. Suppose that the…

A:

Q: Σ(-1)" √TI 2n + 3

A:

Q: y = 1/(x² + c) is a one-parameter family of solutions of the first-order DE y' + 2xy² = 0. Find a…

A: y=1x2+c is a one parameter family solution of differential equation:  y'+2xy2=0.Initial condition…

Q: When an initial amount of money, A, in dollars, is invested into an account that earns interest…

A: Ft=A·ert     Ft=19000·e0.094·t   A.  For t = 9 Ft=19000·e0.094·t=19000·  e0.094·  9=44275.83

Q: The equation of the line that goes through the point (3, 8) and is parallel to the line 2x + 5y = 3…

A:

Q: Find the differential of the function. z = x ln(y5 + 2) dz = )dx + ( Jay dy

A: Finding a function's derivative is a step in the mathematical process known as differentiation. The…

Q: This problem is represented by the following system: 3x +9y+22=98 8z + 5y +32= 105 4z +10y+z=100…

A:

Q: Simplify the following numbers and write them in standard form: a. (4√-16+2 (150) -2(-4+3 (205)

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

Q: Subject: calculus  what is the definition of derivative?

A: Calculus

Q: [b] Take a limit of the standard slope formula, as shown below, to find the instantaneous rate of…

A: The given function is gx=x2+2x. To find the derivative at x=2 and the equation of tangent line at…

Q: Use the Shell Method to find the volume of the solid obtained by rotating region above the graph of…

A:

Q: Find a parametrization of the line in which the planes x+y+z=4 and y + z = 8 intersect. Find the…

A:

Q: How did you get from step 2 to the solution? I dont understand your example. Am I taking the…

A: The answer is in step 2.

Q: Find all values of m so that the function y = emx is a solution of the given differential equation.…

A:

Q: Determine the slope and the equation of the tangent to the curve f(x) = sin(x) + sin(x) at X = π

A: The curve is fx=sin2x+sinx at x=π.To find : Determine the slope and the equation of the…

Q: Use the Shell Method to find the volume of the solid obtained by rotating region above the graph of…

A:

Q: Use the chain rule to find the indicated partial derivatives. z = x² + x²y₁ x = s + 2t - u, y = stu²…

A: z=x4+x2y, x=s+2t-u, y=stu2 given s=1, t=3, u=5

Q: A company manufactures a units of one item and y units of another. The total cost in dollars, C, of…

A: We have to find the minimum cost and additional cost or saving.

Q: Find a Cartesian equation relating and y corresponding to the parametric equations Write your answer…

A: x=3sin6t ,y=6cos6t

Q: II. Find a vector parametrization and parametric equations for the line with the given description.…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: f(x) = x² - 4 - 2 k-x X if x # 2 if x = 2

A: A function f(x) is continuous at x=2 if left hand limit and right hand limit and the function at x=2…

Q: (c) Given equation r²+(2-1)² = 4 in the cylindrical coordinates. (1) Express the equation in…

A:

Q: 3. Determine the absolute extreme values for the function Y=3sinx + 4cosx on the interval [0,27]

A: y = 3sin x + 4cos x ,on the interval [0, 2pi]

Q: Find the vector parametrization r(t) of the line L that passes through the points (4, 1, 2) and (9,…

A: The line L passes through points 4,1,2 and 9,3,7

Q: 2. Consider the function: a) Determine the derivative. y = 2sinx b) Calculate the exact value of x…

A:

Q: Use integration by parts to find the integral. (Use C for the constant of integration.) [x²1 x…

A: I=∫xnlnaxdxusing integration by parts, taking u=lnax  and…

Q: Use the table to the right to find the given derivative. d[ f(x) dx x+3 x=4 f(x) [X3] (Simplify your…

A: Given that ddxfxx+3x=4

Q: A hot air balloon rising vertically is tracked by an observer located 2 miles from the lift-off…

A: dθdt=0.1 rad/min In ∆ABC…

Q: (b) Find the co-ordinates of the turning points of the following function: y = 3x4 - 16x³ + 24x² -…

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: 10. Given = [10,4] and = [12, 13], find the projection of u on v. -

A:

Q: The total cost function for a product is C(x)=700ln(x+100)−100, where x is the number of items…

A:

Q: Construct an equation that has an absolute maximum of 5 when graphed. Please show steps.

A:

Q: 6. Given u = a. Su - b. ū c. v [2, -5]and V V = [-7,2] find

A: 6) Given u→=2,-5 and v→=-7,2