9. (a) Express 2 x4 – x² as partial fractions. (b) Hence, compute the exact value of the following definite integral. 2 x4 -d.x x²

Q: Write the vector shown above in component form. Vector = Note: In the graph, each box is 1 unit by 1…

A:

Q: I'm still confused on the position vector. The question is Let r(t) be the position vector…

A:

Q: 13. A certain type of glass is such that a slab 1" thick absorbs one-quarter of the light —which…

A: We need to find thickness.

Q: The region D is bounded by the curves y = 5, and y = 5x². Which of the following can be used to…

A:

Q: In Exercises 1-2, let u = (3, 2, −1), v = (0, 2, −3), and w = (2,6, 7). Compute the indicated…

A: Note:- according to the company policy we can attempt only three subparts of a question so please…

Q: Find the one-sided limit (if it exists). (If an answer does not exist, enter DNE.) lim_(x². + +x+5)…

A: We have to find the one side limit

Q: Find the following limits (if they don't exist write DNE, ∞o or -∞o as appropriate): Answer: lim h→0…

A:

Q: Find the equation of a plane passes through (1, 2, 3), (3,2,1) and (-1, -2, 2) ○ 4x - 3y + 4z = 10…

A: This question is based on finding equation of plane that passes through 3 points.

Q: Let a-2-3j.kb-41-) and c-1-31-2k. If d is such that da-9. db-7 and dc-6, then d is equal to 01-31-2…

A:

Q: Find the derivative of f (y) = 9 tan (y) V 2 12 y³√√

A: To find the derivative of the below expression. fy=9tany−y2−12y3y

Q: Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary Integer…

A:

Q: Evaluate the double integralfor, f(r, e) dA. Sketch the region R. O π/6 8 O sin(0) cos(8) dr de -5…

A:

Q: Find the general solution of the differential equation y"-y-6y 16e²t. NOTE: Use c₁ and ca for the…

A: Given  y"-y'-6y=16e2t

Q: Use a double integral to find the volume of the indicated solid. X 6 N 2 40 30 20 10 z = 36- y² y =…

A:

Q: 21 (a) ²x¹ d(x³). Note a(x) = x³. 3 (b) (²x² d(ex). Note a(x) = ex 2

A: Given :∫1213x4dx3∫24x2dex

Q: use logarithmic differentiation to find the 1st derivative f(x)= x²(2x+3) (x²+1)*

A: given function  f(x)=x22x+3(x2+1)4

Q: 9 (4) Giver Sifon dx = 37 g(x) dx = 16 So Find S (2 f5r1 + 3 ger)) f(x) dx and

A:

Q: The masses m, are located at the points P. Find the center of mass of the system. = 2, m3 4, m2 6.…

A:

Q: Find the divergence of the vector field F. F(x, y) = 4x²i + 5y²j

A:

Q: y 42², x², y y = 0, x = 4

A:

Q: Choose the value of the area of the region enclosed by the curves y = 6x³, and y = 6x. O 3 O mla 316…

A:

Q: 12. Let x be a positive real number and f(x) = log₁0x. Then f(10-x-2) is equal to: I1 f(x) B.…

A:

Q: Q4 (a) Calculate the surface integral: [] (² + (y² + 2yz) dS where o is the first octant of the…

A: To evaluate the surface integral Given plane 2x+y+2z=6

Q: 1. Find the area of the region enclosed by the following curves: x₁ = y²2, and x₂ = y. Follow the…

A:

Q: Evaluate the function at the given values of the independent variables. Simplify the results. f(x,…

A: Topic = Functions

Q: Find the general solution of the differential equation. y(4) + 14y" +49y = 0. NOTE: Use C₁, C2, C3,…

A: Given :y4+14y''+49y=0

Q: Find the derivative of f (y) 30% In(y) Enclose arguments of functions, numerators, and denominators…

A: To find the derivative of the given function.

Q: Evaluate the integral using the following values. 6 6 6 [°x³ dx = 260, ["x dx = 10, [° dx = 2 + 6 (³…

A:

Q: Suppose 150 trout are seeded into a lake. Absent constraint, their population will grow by 35% a…

A:

Q: Find the one-sided limit (if it exists). (If the limit does not exist, enter DNE.) lim +3) 6 +

A:

Q: Find the limit: ху lim (x,y)→(1,1) x² + y²

A: Apply the limits

Q: Use Green's Theorem to evaluate the line integral Icov for the given path. (y-x) dx + (2x - y) dy C:…

A:

Q: What is the velocity of a ball dropped from a height of 150 m when it hits the ground? Take the…

A: The Solution is given below

Q: Find y" of y=- y" = y" = O y" = y" = X-1 2 (x-1)² 2 (x - 1)³ 1 (x - 1)³ -2 (x - 1)³

A: Topic = Derivative

Q: Let f(x) be defined by f(x) = 3x² + 5x + 2. Find the slope of the tangent line to the curve y = f(x)…

A:

Q: Differentiate y = sec a tan . y' -

A:

Q: Tutorial Exercise Consider the differential equation x²6xy +10y=0; x², x5, (0,00). Verify that the…

A:

Q: Finding the Volume of a Solid. use the shell method to write and evaluate the definite integral that…

A:

Q: FIND THE DERIVATIVE OF THE FOLLOWING FUNCTIONS. g(x)=xnx

A:

Q: Evaluate the limit. 1-x² lim *+1 sin(27x) a) lim b) x+2x² C) lim - - 2x *→(π/2)- (2-) tan r Show all…

A:

Q: Identify the type of solution for each problem and solve for the general solution. Choose the most…

A: To identify the type of solution for the given problem and to solve for the general…

Q: Evaluate the integral by interpreting it in terms of areas. In other words, draw a picture of the…

A:

Q: 5. The sum of thrice a number and two equals 6 less than four times the number. Find the number.

A:

Q: Use spherical coordinates to evaluate the mass of a solid given by the integral below: 2 To LT SVET…

A:

Q: Let f g and h be the functions defined below i. 11. f(x) = 5¹ = 10x₁ (²² = 4) g(x) = log5 h(x) = 6 x…

A:

Q: Determine whether the vector field is conservative. F(x, y) = 6y6(yi + 7xj) conservative not…

A:

Q: Evaluate the function at the given values of the independent variable. Simplify the results. f(x) =…

A: The given function, fx=6x-1

Q: 2 + y²

A:

Q: Use implicit ?х ਹੈ: ду = = x + y2 + z? = 6xyz 6- 6x differentiation to find əz/ax and Oz/dy. 6- 2y

A:

Q: 8 -6 4 수 +

A: