Find an antiderivative F(x) of the function f(x) = - 2x²5x + 2 such that F(0) = - 15. F(x) = Now, find a different antiderivative G(x) of the function f(x) = 2x² - 5x + 2 such that G(0) = -9. G(x) =

Q: 4. Volumes of Solids of Revolutions. Find the volume of the solid generated by revolving the…

A:

Q: The Area bounded by the parabola ay=x^2, the x-axis, and the line x=b is revolved about the x-axis,…

A: Given, Parabola- y=f(x)=x²/a Line- x=b Revolved about x-axis

Q: (a) Assume that f(x) is a function defined by f(x) = x²-3x+1 2x - 1 for 2 ≤ x ≤ 3. Prove that f(x)…

A: Given.

Q: II. (3 + x, if x ≤ 1 (3-x, if x > 1 Sketch the graph of the given function. 6. Let f(x) Investigate…

A: we have to check continuity at x=1 for the given function

Q: Use the binomial theorem to expand the binomial. (5x+2)4

A: Please refer to the image below

Q: A geometric series has S3=37/8 S6 = 3367/512 Find the first term and common ratio

A: Given, S3=37/8  S6 = 3367/512

Q: ib Show that the function defined by F(x, y) xy √² + y² O is not differentiable at point (0,0) if…

A: As per the company's guidelines, we are supposed to solve first question for you, kindly repost…

Q: What is the component form of the position vector for a vector with an initial point of (-1,0) and a…

A: We have to find component form of position vector.

Q: z (hx) = h + k

A: y'+y=(xy)2

Q: 7. f(x) == 8. f(x) = |x| |x|+1

A:

Q: 2. Evaluate r sin rdr using integration by parts.

A:

Q: Find the unit tangent vector T(t) at the point with the given value of the parameter t. r(t) = 4√ti…

A: To find the unit tangentvector Tt at the point with the given value of the parameter t.rt=4t i+3t2…

Q: 2) Find AB and BA if : A = [1 2 3], 405 B = 0 -6 -7 8 9 10 -11 6] 7 -8.

A: For matrix multiplication , the number of columns in the first matrix must be equal to the number of…

Q: √3.01³ +2.992

A: We need to evaluate :

Q: 2 x 2 sin Evaluate the spherical coordinate integral p² sin dp do de. 00 0 The value is (Type an…

A:

Q: find the equation of the tangent line to the graph of f(x)=x^2(x^1/2 +1) at x=4

A:

Q: For what positive values of p the following Alternating Series converges 3n [(-1)"³" pn n=1 p=3 Ο Ο…

A: We have to find the value of p

Q: Set up the definite integral required to find the area of the region between the graph of y = 14-2²…

A:

Q: 2 OM a) Find the area of the region b) Find the length of the curve c) Find the surface area generat…

A: A detailed solution is given below.

Q: Find the centre and radius of the circle x² + y2² - 4x+6y-23 = 0. O centre (2,-3), radius 6 O centre…

A:

Q: Set up the definite integral required to find the area of the region between the graph of y 19-2 y =…

A: We have to find out area

Q: On the coordinate plane below, sketch the position vector (0, 3). PENCIL THIN BLACK

A: solution:-sketch the position vector 0, 3

Q: lin x→ Sin 2021x Sin 20222

A: We have to find the limit

Q: find differential equation of the following equation 3) dy +xsin(2y) = x cos² (y)

A: Given

Q: Determine the equation of the ellipse with center (-2,-4), a focus at (-2,5), and a co-vertex at…

A: Given:        center =-2,-4        focus =-2,5        co-vertex 10,-4 Equation of Ellipse is…

Q: H.W: Sketch the following functions 1. x² + y² = z + 1 2. x² + y² + 2y + 1+ 2+ z = 0 3. z² = x² -…

A: In these question , we can sketch the given function . Note : As per our Guidelines , we can solve…

Q: Which one of the following is a potential function of the following vector field? O f(x,y) = xy+2x O…

A: Find potential function

Q: 3. Evaluate sin5 xdx

A:

Q: 4.) Find an equation for the plane tangent to the surface 9x² +4y² +9z² = 34 at the point (1,2,-1).

A:

Q: Find the particular solution using the initial condition. y' sin(2y) - cos x = 0, cos x = 0, y() = 0…

A:

Q: Given the function f(x) graphed above, find f^-1 (5)

A: NOTE: Refresh your page if you can't see any equations. . as we can see from the graph, the point…

Q: 6. Find the area bounded by the curve y = log x, the x-axis, and the line x = 2.

A:

Q: For the given double integral, sketch the region of integration and write an equivalent double…

A: Given problem:-

Q: 2 cosh x +losion2x = 5

A: I am attaching image so that you understand each and every step.

Q: Evaluate the following integrals: 1. f(cos x + csc² x)dx 2. f(tan x + sec² x) dx 3. (1+sec² x) dx…

A:

Q: valuate the integ

A:

Q: Let A(z) = f(t)dt, with f(x) shown in the graph below. N -2- At what x values does A(x) have a local…

A: Ax=∫0xftdt, with f(x) shown in the graph.

Q: Let the vector v have an initial point at (5, −3) and a terminal point at (1, —8). Determine the…

A: Determine the components of vector V

Q: The function f(x) = 3x ln(1 + x) is represented as a power series f(x) = Σ cnon n=0 Find the…

A:

Q: Let C be the circle with radius 3 centered at the origin, oriented counterclockwise. Define a vector…

A:

Q: Define a vector field on the plane as follows: F(x, y) = (x + y², e³ + 6xy). Let C be the square…

A:

Q: y = x² and x² = y

A:

Q: 2. Evaluate x sin ædr using integration by parts.

A: Given: I=∫xsinxdx   We know the basic integration formula. ∫sinxdx=-cosx+C∫cosxdx=sinx+C

Q: 4) A headboard for a bed is built in the shape of a semielliptical arch. The headboard will be 8…

A: Given; a=4, b=3

Q: Q3: Find the solution of the Laplace transforms of the following functions: -3s²-12s-87 1) L-1…

A: Given problem:- Find  L-1[(-3s2 -12s-8)/(s+2)3]

Q: find Sexcos'x dx by using integral by Parts.

A:

Q: The following integral will be evaluated using integration by parts with the indicated choices of u…

A:

Q: Find the transition points. y = 3x² - 42x6 (Use symbolic notation and fractions where needed. Give…

A:

Q: Convert the following parametric curve into Cartesian form: x=2 sint, y = 3 sin t O 3x² + 2y² = 1 O²…

A:

Q: √√3+ rdr then 0 (2)=√√3+230 I X

A: