Find the area of the surface. The part of the plane 3x+2y+z=6 that lies inside the cylinder x² + y² = 4.

Q: Solve the following initial value problem for the unknown function y(x) a) y' = 2xy², y(1) == b) 2…

A: Topic:- application of integration

Q: Evaluate the definite integral by the limit definition. [²₁x² + (x² + 5) dx Submit Answer

A:

Q: QUESTION 10 Use cylindrical coordinates to evaluate the integral below. √x² + y²dv, where E is the…

A:

Q: 3. A particle moves along the x-axis with velocity v(t) = t2-1, with t measured in seconds and v(t)…

A: Given velocity v(t)=t2-1 To get the total distance traveled, we have to integrate the velocity…

Q: 7rer dr =

A:

Q: This

A:

Q: Find the limit, if it exists. lim X-- 12-1 xº-1

A:

Q: Find the area under the curve y 7 x over the interval [1, 5]

A: Given curve y=7x

Q: dy Solve the separable differential equation = dx - 7y, and find the particular solution satisfying…

A:

Q: 3 If ƒ (x) = 2 + x, evaluate Σƒ (k+1). k=1

A: We can answer the question as below.

Q: ∞ 1.00 8e- dx = (If the integral diverges to ∞ or -∞, type oo or -oo; if the integral diverges in…

A:

Q: y=x4Inx

A: Topic = Derivative

Q: 4) Differentiate each of the following: a) y = - cos²x c) f(0) = sin(20 — π) b) y = sin(20) - 2…

A: Differentiate the following  a) y=-cos2x b) y=sin2θ-2cos2θ c) fθ=-π2sin2θ-π

Q: For the function f(x) shown below, determine lim f(x). f(x) = x² - 10 -3 - 2x for for +-←æ x -4

A:

Q: 6) Line y=x between x = 0 and x = 1 is rotating around the x - axis. (It forms a cone). Calculate a)…

A:

Q: A stone is thrown straight up from the edge of a roof, 925 feet above the ground, at a speed of 16…

A: solution of part A So the stone is 829 feet high 3 second later.

Q: Given r(t) = 9t² i + 18tj and t = 1, find the tangential and normal components of acceleration. ат…

A:

Q: у 3 2 1 -1- -2 -3 1 2 3 4 5 6 X

A: Here is the solution:

Q: Find two positive numbers that satisfy the given requirements. The second number is the reciprocal…

A:

Q: y = ln(4x³ + 7x)

A:

Q: - -5 -4 -3 -2 1 - 1 y 5 3- N 1- 1 -2H -3- 1 2 3 4 5 X

A:

Q: = 4) Use the recursion formula Stan" xdx to calculate Stan³xdx tan" X n-1 n-1 -ftan”-2 xdx

A:

Q: = Approximate the area under the curve y = x² from x with 6 subdivisions. 3 to 6 using a Right…

A: We have to approximate the area under the curve using Right Endpoint Approximation.

Q: A cylindrical can without a top is made to contain 10,000 cubic cm of liquid. Find the dimensions…

A:

Q: tan' (2)

A:

Q: Please correct me if i'm wrong. The points where f(x) appears to concave downward appears to be…

A: Given , the point where f(x) appears to be concave downward appears to be (-2 , 2.9 )

Q: Find the velocity, acceleration, and speed of a particle with position function r(t) = (5 cos t,…

A: Given, r(t)=5 cos t, -3t, 5sin t

Q: 15 Lo - - dx 15 X (x + 1) ²/ O 0 O or| 800 88 O 1 O 176 5

A: The answer is 0.

Q: 150 5 -4 -2 100 50 -50 -100 -150 200! 2 4 6 8 Xx

A: We know that, The highest point the graph ever reaches is the absolute maximum. The lowest point the…

Q: Is the following piecewise function continuous? if x < 0 0<if x < 3 if 3 < x f(x) = -3x² x - 3, . -x…

A:

Q: Consider the function f(x) x² + 7x + 12 2-5 a. Find the first derivative. f'(x) = b. List any…

A: Solution is here

Q: Find f(x) such that • ff(x) dx = 1/√ √ x² + 4 + C

A:

Q: = $r(t)dt 5. Use the graph of f(t) = 2t - 5 on the interval [-2, 10] to write the function F(x),…

A:

Q: X 2 Find x² +1 -dx

A:

Q: -3. For the function f(x) = -5x - 3, find the slope of the tangent line at x =

A: We can find the slope in the following steps.

Q: 53. y' - y = ex/y

A:

Q: 3.2 Bus A leaves Worcester at 08:00 and travels north along the N1 at 50 km/h. Bus B leaves…

A: Given that The Bus A leaves at 8:00 with speed of 50 km/hand bus B leaves at 10:00 with 70 km/hSo,…

Q: Calculate each of the following given that: a. b. a-b a x (2b - 3c) |b x 3c| C. d. projac a = 2i -…

A:

Q: Find the exact area of the region bounded by 2y = 4√√x, y = 4, and 2y + 2x = 6

A: Here we have to find the area of the region.

Q: Differentiate the following. Do Not Simplify. y=(sin x)(lnx) b) y = (e² + √√cos x) c) y = = a)…

A: To differentiate the following.a y=sin xln xb y=ex+cos x37c y=1-tan x3x3

Q: Find the indefinite integral and check your result by differentiation. (Use C for the constant of…

A: To give the solution with proper explanation for the given problem. To find the indefinite integral…

Q: A particle is moving along the curve having the vector equation R(t) = ti+t²j+ tk. Find the vectors…

A: The given position vector is  Rt=t i + t2 j + t k.   The velocity vector is given by Vt=R't=i+2t j…

Q: Evaluate the integral (2x + 4) (2² + 4x + 2) dz by making the substitution = x² + 4x + 2. Submit…

A:

Q: Consider the function f(x) = x 52+4 x + 1 a. Find the first derivative. f'(x) = b. List any critical…

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost other parts as…

Q: The function f is shown below. What is the value of answer in simplest form. -10 -9 -8 -7 -6 -5 -4…

A:

Q: Use a system of linear equations with two variables and two equations to solve. A number is 8 more…

A:

Q: dy Find in each of the following: (be sure to use proper notation and simplify) dx (a) (b) y = sin¹…

A:

Q: 1. Use the Mean Value theorem to show that for any two real numbers a and b, we have | sin b - sin a…

A:

Q: U V U a) f(x) = sin x The trigonometric function pictured here is b) f(x) = csc x O c) f(x) = sec x…

A: we need to find which trigonometry function has the following graph

Q: Find the solution to the differential equation that passes through the origin. z(t) = dz dt = 6te42

A: dzdt=6te4z⇒e-4zdz=6tdtIntegrating both sides we get,⇒zt=-ln-12t2-c14