Which of the following equations is(are) true? 1 2x du I. -dx x² + 1 S 5.² o √u √2 1 2x II. -dx 10 √x² √x² +1 0 S Oll only O Both I and II None of them I only = 2du

Q: KIN KIN 0 2 d2 sinr do dr dọ

A: A detailed solution is given below.

Q: Q3- Sketch the region of integration and evaluate the integral: In8 lny [TD [t ex+y dxdy

A: Given problem:-

Q: (a) Find where x² + 3xy + y² = 3 at (√3,0). da

A: topic- implicit differentiation

Q: 2. A water treatment plant processes gray water at a rate given by r(t) = 16e0.2t million gallons…

A: Disclaimer: “Since you have asked multiple questions, we will solve the first question for you. If…

Q: Complete the parametric equations for the line where the planes - 7x + y + 3z = 3 and 4x7y + z = 23…

A:

Q: A function g is given. Identify the parent function. Then use the steps for graphing multiple…

A: 10.The given function gx=15x-2.3-7.4

Q: interval of convergence. b. sin² x

A:

Q: A particle moves along a straight line such that its displacement at any time (t) is given by…

A: Note: There is a typo in the question.  Incorrect:  S = t^3 - 6t^3 + 3t +4   Correct:  S = t^3 -…

Q: Evaluate 2 x√√x² + 4 dx.

A:

Q: If y = (sin x)e, what is dy ? dx

A:

Q: ππ 2 CAP• 0 0 0 ¢ sinr do dr dộ

A:

Q: A) Explain with short examples the algebraic vector properties. 1. A+B=B+A 2. A+ (B+C) = (A + B) + C…

A: To explain with the examples with the algebraic vector properties given.

Q: -2x let f (x) = 3x · e¯¯

A:

Q: 4 5 5 Let A = -1 -1 0 4 6 Use determinants to decide whether the matrix is invertible. Enter the…

A:

Q: 4. Find the Taylor series for f(x) = ln(1 + x) centered at a = 3. Give the first 5 terms of the…

A: This is a problem related to taylor series expansion. Based on the general formula and concept we…

Q: Consider the region bounded by y = ex+1, ¹, y = 1, and y-axis.

A: Follow the procedure given below.

Q: en ủ × ʊ = (2, 3, 4), find (ũ − 4v) × (ũ + 3v).

A: Topic:- vector algebra

Q: 4. Given f'(1) = 4, g'(1) =— 2, ƒ(1) = 1, g(1) = 1, find h'(1) if h(x) = xg(x)+7 f(x)

A: Using definition if derivative of f/g

Q: Find the volume of the given solid. Under the surface z = 1 + x²y2 and above the region enclosed by…

A: To find the volume of the given solid.

Q: Determine the surface area generated when a portion of the curve in the 1st quadrant of y² = 9(x² -…

A:

Q: A rectangular field is to be enclosed with a fence. The available fencing material is 150 meters…

A:

Q: The inverse Laplace transform of H(s) = + (t) ==²e²+e-²t 8 1 " (3s+2)(S-2) b) f(t) ==e+e-2t -3 d)f…

A:

Q: lim 818 sin n+1 n + sin n+2 n + sin n n+3 n +... + sin (2) = cos(1) - cos(2).

A:

Q: Evaluate 1¹ 1 - cos 2x sin 2x dx In | csc 2x + cot 2x | -ln | sin 2x | +C In 1|csc 2x-cot 2x |--In |…

A: The given integral is: I=∫1-cos2xsin2x   As we know the common integrals; 1). ∫cscxdx=lncscx-cotx+C…

Q: 2. Raya Is making a closed rectangular jewelry box with a square base. She is using two different…

A:

Q: A container with square base, vertical sides, and open top, is to be made from 3,000 ft² material.…

A:

Q: Express the repeating decimal as a fraction. 0.789626262626... 0.789626262626... =

A:

Q: Solve the following x³-x²-√√2x limx→2²-11x+18

A: Above question is solved.

Q: Identify the number of significant figures (sig figs) in each of the values. I sig fig 2 sig figs 3…

A: We can find the significant figures.

Q: How do i figure out whether this function is continuous or not (proving it) without given at which…

A:

Q: f(x csc² 6x - x cos 6x)dx

A: We need to evaluate integral.

Q: Calculate Differentiate. 1 = 2 z² + 1 f(z)

A:

Q: 4x² + 4y2 +422-8x + 16y=1 presents a sphere, and find its center and radius.

A:

Q: The power series n=1 0-1≤ x < 5 01≤x≤5 0-1 < x < 5 0-1≤x≤5 (x - 2)" 3n converges if

A:

Q: Evaluate lim x tan a x - x cos x

A:

Q: x² Evaluate using Partial Fraction Decomposition: f(x+1)²(x-1) dx

A: To evaluate the given integral by using Partial Fraction Decomposition. ∫x2x+12x-1 dx

Q: A rectangular field is to be enclosed with a fence. The available fencing material is 150 meters…

A: This is  a problem related to maxima and minima of the function. Based on the general formula and…

Q: A small metal bar, whose initial temperature was 30° C, is dropped into a large container of boiling…

A:

Q: 3. Find the volume of the solid that lies under the paraboloid 5z = x² + y², above the xy-plane, and…

A: To find the volume of the solid that is bounded by given curves.

Q: ng the problem) an interval in which the solution of the given initial value proble (t-4)y' + (Int)y…

A: We have to find the interval of t

Q: Calculate lim X10 3x²-x-2 5x² + 4x + 1

A:

Q: The particular solution In (x) = 3x + 4y, y(0) = 0 is A. e³x + 3e-4y = 4 B. 4e3x3e-4y = 3 C. 4e3x +…

A: Topic = Differential equation

Q: Given the following vector field and oriented curve C, evaluate SF.T ds. C F= (-3y,3x) on the…

A:

Q: 0 KIN TC TC 2 KIN 0 0 02 sin o dr do de

A:

Q: Solve the following equation by using LONG DIVISION 6x³5x²49x + 60 = 0

A:

Q: f(x csc² 4x - x cos 4x)dx

A: The answer is given below:

Q: If dx = e-²y and y = 0 when x = 5, then the value of x when y = 3 is dx e6 +9 A. e5 C. 2 B. e6 + 1…

A:

Q: (2x -۱۱۶ (3x44795

A:

Q: Find the constants a and b such that the function is differentiable everywhere. x²-9 x+3 if x < -3…

A:

Q: A stone is released with zero velocity from the top of a tower, reaches the ground in 4 sec. The…

A: