Integrate the following:  use the U-substitution. ∫ (x2+5x)dx/4√x+9

Q: Integrate the differential equation in which A is being made at a rate k1and destroyed…

A:

Q: The definite integral of f(t – 1)dt = f dv is v – v. =t2 – t - t %3D %3D O True O False

A:

Q: The series > cos" (2) is divergent. n=1 This statement is true by the test for divergence. This…

A:

Q: Find the Laplace transform of f(t) = u(t – 4) · e' F(s) %3D 8-2

A:

Q: Find the derivative of the following using General Rule. 7) y = vt3 8) f(x) = 6 + 5 1 9) y =-+ 2 x3…

A: We have to find derivative of Given function.

Q: (ese e cot e-s cot e de CSC

A:

Q: Find the vector component of v = 2i – j+ 3k along b = i+ 2j + 2k and the vector component of v…

A: We have to find the vector component along another vector

Q: Given z = sin(1 - 2). x = 2 – ts and y = 2t – s - then calculate when t = -1 and s = -1. dt

A:

Q: (ii) Using the result of the derivative above and the fact that integration is the antiderivative…

A:

Q: dx xVx -1 6.

A:

Q: To save for graduate school, a student invests $1780 semiannually in an ordinary annuity with 7%…

A:

Q: 8) Find a power series representation and determine the interval of convergence for 2 f(x) = 3 – x

A:

Q: F. Boolean Matrices Го 1 A = 1 0 3-- [1 0 1] C=0 1 1 0 1 0 [1 1 1] D= 0 0 1 |1 0 0 Let B = [1 0 0 1]…

A:

Q: Your explanation should answer WHY you are doing the work and HOW you are doing the work briefly…

A: If f'x is:→ then fx is-ve→decreasing0→horizontal +ve→increasing=a & ≠0 →slant with slope…

Q: S sin(ln x)dx A 1 x sin(lnx) – cos(Inx) + C x sin(lnx) – cos(lnx) + C| B D x sin(Inx) + cos(Inx) + C…

A:

Q: 7) f(t)=e"(Acos(ßt)+B sin(ßt)) -at

A:

Q: v +3v° dv 35.

A:

Q: 2²y ds, C:x = cos t, y = sin t, z = t, 0 < t < a/2

A:

Q: dy + y = y² sin x dx

A:

Q: (a) Find an equation of the tangent plane to the surface at the given point. x + y + z = 10, (3, 3,…

A:

Q: 11.)y- 2y y y= 3 when x = 0

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 18 3. dz 36.

A: Topic = Integration

Q: dy 1+y+1

A:

Q: 30. | (Зи — 2)(и + 1) du

A:

Q: A culture initially has 700 number of bacteria. At 1=5 hour the number of bacteria is measured to be…

A: The differential equation that describes the given model can be solved by using the variable…

Q: 7 dx 5. S 2 2 3 xVx-4

A: We will solve the integration.

Q: (-1,3) -2,1) (0,1)

A: Topic = Functions

Q: 2 * - 3 dy 4. S 1 y +y 2

A:

Q: Determine whether each improper integral below converges or diverges. dx 3. S. x* + 2x – 3

A:

Q: Determine whether u and v are orthogonal, parallel, or neither. u = -5i + 24j – k v = 5i + j - k O…

A:

Q: Determine whether the lines L1 and L2 are parallel. L: x = 2 – 31, y = 4 +1, z = 7- t L2: x = 5 –…

A:

Q: good

A: We will solve the integration using integration by parts.

Q: y= {(z) -4 -3 -2 -1 3 7

A: We have to find the points

Q: (x + 1)³sinx dx x+1)° cosx+3 (x + 1)2 sin x-6 (x + 1)cosx-6 sinx+ C | (x + 1) cos x 3 (x + 1)2 sin x…

A: Solving the problem by finding the integral by oarts method.

Q: 8xy® 8x8 + 8ys if(x, y) ± (0,0) Let f(x, y) if (x, y) = (0,0) 3xy® За? + 3у12 if (x, y) + (0,0) and…

A:

Q: 21. ( (3r'- + 30) dt

A: We have to find the solution

Q: A body moves along a horizontal line in accordance to s t + 9t2 + 24t. Find the total distance…

A: Given query is to find the distance traveled by the body

Q: | cos(Vx) dx A 2 Vx sin (Vx) - 2 cos ( Vx) + C C 2 Vx sin x (Vx) - 2 cos (Vx) + C B 2 Vx sin (Vx) +…

A: To evaluate: I=∫cos xdx Substitute x=u⇒12xdx=du⇒dx=2udu So, I=∫cos u 2u du=2∫u cos u du

Q: (p? –1) cos[cosh (In r)]dr

A:

Q: 1. Evaluate the indefinite integral, ſx² sinh x3 dx.

A: To evaluate the indefinite integral, ∫x2 sinh x3 dx.

Q: A curve C is defined by the parametric equations x(t) y(t) = 8t³ – 2t² + 4. Write the equation of…

A:

Q: 2 + x? -dx •4 29.

A: We have to find the integral

Q: What is the solution of the differential equation y' + 6y + 25y = 64e-3 ? %3D

A:

Q: Is the line through (4, 1, – 1) and (2, 5, 3) perpendicular to the line through (-3, 2, 0) and (5,…

A:

Q: 5) x²dx + y(x – 1)dy = 0 %3D

A:

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive.…

A: We will create a Lagrange's function to solve the problem.

Q: Hello! Please help me answer these with full solutions. Thank you!   1. Show that the absolute value…

A: Topic = Functions

Q: Evaluate the following equations using Reduction Formulas

A:

Q: Find an equation of the tangent plane to the surface at the given poin h(x, y) = In Vx2 + y?, (6, 8,…

A:

Q: Determine whether each improper integral below converges or diverges. dx 3. S 0 x* + 2x – 3

A: