Evaluate the double integral: y SLAZ+1 y²/3 x + 1 (Hint: Change the order of integration to dy dr.) da dy.

Q: Q6. Let W = f(r,0), r = 0 = tan"'(y/x), find aw Ох > and ди ду in terms of r and 0.

A:

Q: 2. Solve each of the following integrals using integration by part: a) [3x² In 2x dx b) 5x sin 3x dx

A:

Q: Let R be the region that is inside the polar curve r = 3 and outside the polar curve r = 2 + sin(0),…

A:

Q: Let R be the region enclosed by the polar curve r (0) = 1 + 2 cos² (0) where ㅠ 0≤0 ≤ iss 3

A: This is a problem related to area bounded by the region. Based on the formula of polar curve we will…

Q: II. Find the inverse of each matrix. 5 -11 1. -7 -9

A: This is a problem related to matrix. Based on the general formula and concept we will find out the…

Q: xy³ = Let f(x,y)=2x²+y² 1 (x, y) = (0,0) Is f continuous at (0,0) ? Is f continuous at every point ?

A: If limit tends to 0 and function tends to 1 then f is continuous.

Q: 2. The Substitution Method states that A. If F'(x) = f(x), then [ f(u(x))u' (x) dx = F(u(x)) + C B.…

A:

Q: ./ which expression best to describe 31% ? (a) Just under a half (b) A tiny fraction (c) Nearly a…

A: Given data÷

Q: 1. Find the Inverse Laplace Transforms of the following. 3) 3s³+3s s6 3

A:

Q: +00 0 x (x²+4)3/2 dx

A:

Q: show that V(x, y) = x 'f (2x+y) is the genera Solution of : du 2X x av ах 1 ду

A: First, we find ∂v/∂x and ∂v/∂y  and substitute them in the given equation, if it satisfies the…

Q: Evaluate the following √ (2²2 + + 6x − 1)²(x + 3)dx (x²+6x-1)-5 + C 2 (x²+6x-1)-5 3 +C (x²+6x - 1)5…

A: We have to solve given integration.

Q: Find the particular solution of the DE y11 + 24y = 0 subject to the initial conditions y(0) = 2 and…

A:

Q: Derivative of arctan(ln(n))

A:

Q: 8. The value of ve A. sin-1 (e) + C C. sin-1 (e-x) + C dx B. -sin-1 (e-2x) + C D. sin-1 (e-2x) + C

A: Topic = Integration Correct option = A

Q: Evaluate the following * 5 Sa 4x - 1 In(4x - 1) 4 O II -dx + C 5ln(4x - 1) 4 + C 5ln(4x − 1) + C 4…

A:

Q: Given f(x)=x²-1 on [-2,2]. a. Find the critical numbers of f on the given interval. b. Determine the…

A: A critical number of a function of a single real variable, f(x), is a value x0 in the domain of f…

Q: I. 1.) Simplify. Write "undefined" for expressions that are undefined. 2 [164] -6 -5

A: Topic = Matrix

Q: (3) If R is an integral domain has non zero characteristic, then Char(R)=..... (i) 5 (ii) 4 (iii)9

A: This is a problem related to function and number system of the function. Based on the general…

Q: 6 By Separation of variables, Solve the following 5 PDES :- ²4. ²4 0 o 2 dt² dx² u(e,t) = u(5,t) =6…

A: Given

Q: Find the area of the region enclosed by the curves y = x³ and y = 4x. 24 8 16

A:

Q: Set up but do not evaluate an integral that represents the volume of the solid of revolution…

A:

Q: Evaluate: 2[z³(x+y)³] dz dy dx

A:

Q: Evaluate the following * [: 2x(4x² – 3)³dx (4x²-3)6 +C 24 O (4x² - 3)-6 24 +C (4x²-3)6 24 O " (4x² -…

A:

Q: 2. I. Evaluate each determinant. -4 3 -3 2

A:

Q: q-Sin ²1x1 1²/x/_alx

A:

Q: a A person's intelligence quotient (IQ) is measured by the function I(m, a) = 100m where a is the…

A: see below the answer and explanation

Q: Find the area of the region bounded by the curves 1 y=; y = = 4 and the x-axis using vertical strip.…

A: Let's find area of the region bounded by curves and given line y=4.

Q: Find an equation of the tangent line to the graph sin(x) + y² = 4 at (π, 2).

A: This question can be solved using the concept of tangent and normal.

Q: 10) y7 exbx

A:

Q: Solve the initial value problems dy 19. (x + 1)- dx -2(x² + x)y=x+1' x>-1, y(0) = 5 dy 17. 0 + y =…

A: Given (x+1)dydx-2(x2+x)y=ex2x+1       y(0)=5, x>-1To find Solution of Differential Equation:

Q: 13. Use integration by parts to evaluate [x rlnrdr.

A:

Q: Find the area of the region enclosed by the curves y =

A: answer is in next  step

Q: Q4: A) For each of the following ,find fx fy fxx fy fyx and fxy 1.f(x, y) = ln(2x + 3y). 2.f(x, y) =…

A: According to the company rule we can answer only first question and rest can be reposted

Q: Let a, b ∈ R. a) Find the determinant of  a 2  b -2 1 2 4 -2 -1   b) Suppose u, v, and w are…

A: Concept: Determinant of the matrix: The determinant of the matrix is the expansion of the matrix…

Q: Find an equation of the tangent line to the curve at the given point. y = 2x3 – x2 + 4, (2,16) y =

A:

Q: hi what is the simplified final answer of this?

A: Given problem:-

Q: (d) Give the local maximum and minimum values of f (x). Enter your answers in increasing order of…

A: Local maxima and minima and concavity

Q: Let F(x,y)=ln(x² + y2), then answer the following (1) Find the function's domain (2) Find the…

A:

Q: 4 Find the area of the region bounded by x = 2y²+1 and the y-axis using the horizontal strip.

A: Given: x=42y2+1

Q: Evaluate the integral. a 6 dx ਚ 2 + a> 0

A:

Q: dy Solve the differential equation. X dx = y + x³ + 3x² -2 x

A:

Q: Choose 1 answer: A 13 klo ㅠ 4t2 + 16 sec4 (t) dt

A: Please refer to the image below

Q: (2) Z/(5) =....... (i) (5) (ii) 5Z (iii) {[0],[1],[2],[3],[4]}

A: We have to find the operation

Q: Which integral represents the area of R? Choose 1 answer: 3π A 16³ (²1 + 2 cos² (0) + 2 cos¹ (0)) de…

A:

Q: find the Fourier series of half rang periodic function. f(x) = x|x| -π < x < π <x<π

A: We know the following. Fourier series of function fx on interval -L≤ x≤ L is defined as:…

Q: Evaluate: ³4₁ [2³(x + y)³] dz dy dx

A: To evaluate the given integral.∫-43∫-12∫01z3x+y3 dz dy dx

Q: Evaluate: (4x²yz - ) dz dy dx

A: Let,    I  =∫23∫-14∫10 (4x2yz - z44) dz dy dx           I = ∫23∫-14[∫10 (4x2yz - z44) dz] dy dxI=…

Q: Evaluate the following * S sin(4x) dx O cos(4x)/4+C -4cos(4x) + C O-cos(4x)/4 + C O-4cos(4x) + C

A: We can find the answer as below.

Q: Differentiate the function. g'(x) = g(x) = 2x² - 8x + 13 gx 8 2 X Read It Need Help? Master It

A: