ow that the differential form in the integral below is exact. Then evaluate the integral. 5,1) 20x dx + 2y dy + 6z dz 0,0)

Q: : Evaluate the following integrate: 1- S x²dx √9-x² 2-√(2 + 5x) e dx

A:

Q: 12) Consider the following exponential function f, Given that f(x) = -616, what is the value of x?…

A: exponential function

Q: Find the general solution of the differential equation: y' - 5y = te-2t Use lower case c for the…

A:

Q: Use the rules of differentiation to find the derivative of the function. y = sin(0) -11 2.2.025.

A:

Q: Q1:Discussion a continuity of the function f(x, y) at the point (0,0), where ey sinx f(x, y) = X (x,…

A: We want to check the continuity of the function at (0,0)

Q: Find the tangential and normal components of the acceleration vector. r(t) = 4(3tt³)i + 12t²j aT an…

A:

Q: 4. Lim ¹G- X-0 1 Arctanx.

A:

Q: Rewrite the polar equation r = = 6 sin(0) as a Cartesian equation.

A:

Q: Using Cramer's Rule to solve (if possible) the system of linear equations 1 A -10 1 B 11 N SSSUSU…

A:

Q: test if (AB) =B¹A¹ A = 4 0 L3 1 2, B = 5. 4 -3 14 02

A: We  can check the matrix as below

Q: Problem 2: Use the definition of the Laplace transform to find the transform of the piecewise…

A: Basic identities of integration are used

Q: dy dx 11 1 + x-F y.x +5

A:

Q: 4. 2x³y = y (g2 + 3z2)

A:

Q: Simplify to an expression involving a single trigonometric function. Please show work so i can…

A: SOLUTION-

Q: The graph C' of the equation y = gives the course taken by an oil tanker after leaving port, which…

A:

Q: Question 17 :S- Given : 4x - 3 A = √ (21²+8) √u²+2 ® / / / 1 (2011 B (2u²+11)u √u²+2 © ²/2 √ ( 2 u ²…

A:

Q: A region is bounded by the y=x2 and y=6x-x², Which of the following integrals would approximate the…

A: Option (a)

Q: The region in the first quadrant bounded by the graph of y=8-x3/2, the x-axis, and the y-axis is…

A: Given problem:- The region in the first quadrant bounded by the graph of y = 8 - x3/2 , the x-axis,…

Q: Find the area bounded by y=e*, y=lnx, x=e, the x-axis and the y-axis. (A) 12.1435 B) 13.1435 12.7834…

A: The region bounded by y=ex, y=ln x, x=e, the x-axis and the y-axis.

Q: 5. y = 5 tan x³ + sec (3x)

A: Topic = Derivative

Q: 2. The Minimum point of y= 8x+4 (x-2)²

A: To find the minimum point of y=8x+4x-22.

Q: By using Interval Halving nethod, If the lies in the nterval [1,2], e=0.02the oot of the f(x)=x^2-3,…

A: Follow the procedure given below.

Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method,…

A:

Q: (b) Find the area of the region that lies inside the first curve and outside the second curve. r = 1…

A:

Q: Can u do 6 and 7 . I will rate you thank you

A: step 2 complete solution

Q: To integrate x³ exdx'' X we apply integration by parts and in the form u dv, u is set as:

A: To integrate x3ex dx. We apply integration by parts amd in form of udv. u is set as

Q: 3: Fill in the blanks in the following: 1 3. 4. If = (-12, 4, 8) the position vector of u…

A: Topic:-  vector algebra

Q: -3 4 For the matrices A = 2 1 -11 2 Determine whether the matrix 6 7 A The matrix is not a linear…

A:

Q: Q1: A. Find the general solution of the following Initial Value Problem (IVP): y+9y-10y = -40t²-72t…

A:

Q: Find the general solution to differential equations 2 #) (-2xy) dx + (Siny-x²) dy +³

A:

Q: Problem 2: Use the definition of the Laplace transform to find the transform of the piecewise…

A:

Q: Evaluate fxsin zdz. 00 01

A:

Q: Question 4 A conical water tank has its top at ground level (consider this to be the x-axis) and its…

A: The given problem is solved below in detail.

Q: 6) INVERSELY LOGARITHMIC The following information is given about a logarithmic function of the form…

A: The objective is to find the rule of the inverse of the function.

Q: Let f(x) = 2x³-9x² - 24x+2. a. Find all points on the graph of f(x) at which the tangent line is…

A: Topic = Derivative

Q: Fill in the blanks in the following: 1. Ifa (3,-2, 6) and b=(4,-1,-6) the axb:

A:

Q: egion in the first quadrant is bounded by the curve y=1+ sin²x, the coordinate axes and the line x==…

A: Topic:- application of integration

Q: A. Given that f(x)=2x-3 and g(x) = 6x-1. calculate the value of f(5). derive an expression for…

A:

Q: dw Q11- express by using the chain rule: dt w = ln(x² + y² + z²) x = cost, y = sint, z = 4√t

A: We have to express dwdtby using the chain rule:

Q: Let f(x) = 2x³ - 3x² - 120x+7. a. Find all points on the graph of f(x) at which the tangent line is…

A:

Q: A tank in the shape of a right circular cone is full of water. If the height of the tank is 10 feet…

A: answer is in next step .please give a like !!!

Q: 2. Given the following logarithmic expression: log, 1+ 2log 5 + log₂ 2 +log, c-log, 100 Which of the…

A: Given: logc1+2logc5+logc2+logcc-12logc100

Q: Solution: Here f(t) = 24,0 < + <l 0,1 < t <2 Here period of f is 2L = 2 L = 1 ". The Complex Fourier…

A: Given problem:-

Q: Solve for So So Szyzdzdydz. 0522 108

A: To solve for ∫03∫02∫15 xyz dz dy dx.

Q: A group of 10 individuals is used for a biological case study. The group contains 3 people with…

A: Concept of combination is used

Q: Find the third Maclaurin polynomial to f(x) = e sinx

A: The Maclaurin series; fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+.... Where the center is at x=a=0…

Q: Find a potential function f for the field F = 4y + 5z ( i + 4x j + 5x k). A general expression for…

A: Solve as general

Q: Find the area bounded by the following functions/lines/curves: f(x) = 3x3 - x2 - 10x; g(x) = -x2 +…

A: Given: f(x) = 3x3 - x2 - 10x; g(x) = -x2 + 2x Let's first find the intersection point  3x3-x2-10x =…

Q: 11. y = tan e³x + etan3x

A: We can find y' as below.

Q: Question 16 The area bounded by y=1-x²₁x+y=1 and the x-axis is submerged vertically in the water…

A: We need to choose correct option.