What u-substitution should be made in order to evaluate the following integral? dx (6x² + 4)* u =

Q: Determine the directional derivative of f at the specified point and direction. f(x) = x³ + y³ – 3x2…

A:

Q: þr+2|dx -3

A:

Q: x + 4 1. Evaluate dx. Vr2 + 8.x

A:

Q: O5 D Set yp but do not evalvate em integral that represent3 the volume of the solid of…

A:

Q: Question 8 Evaluate the given double integral by changing it to an iterated integral. JJ xy dA; S is…

A: Note: Graph the triangular region and find the limits

Q: y" + 2y' + 5y = 4e¬t cos 2t, y(0) = 1, y'(0) = 0 %3|

A:

Q: the 6) Find the a by curves y=x° and y=X ea of the region enclosed A) D)

A:

Q: Differentiate. 10. y = e

A:

Q: 5. The denominator of a fraction is four less than the numerator. If the denominator is doubled and…

A:

Q: Question 1 Give an integer a E Z which makes the following equality true for y = a". 7 log.ry (y) 8…

A:

Q: A forest has a population of cougars and a population of rabbits. Let æ represent the number of…

A: A detailed solution is given below.

Q: Find the required limit or indicate that it does not exist. lim o+ (in (t6), 12 in t O 6i O Does not…

A: We have to find out

Q: 5. lim X-0 e2x-1

A:

Q: I need help with question 7

A: Volume

Q: Problem 3.4 Parameterize the following surface. Then, integrate the given function over the…

A:

Q: Solve the differential equation for general solution y' = 2x - xy; y = 5 when x = 0 %3D O y =…

A:

Q: The eccentricities and foci of a hyperbola centered at the origin of the xy-plane are shown below.…

A: The eccentricity of the hyperbola centered at the origin of the xy-plane, e = 2 The coordinates of…

Q: coso de by trigonometric substitution.

A: answer is in next step

Q: Optimize Z= In(4x2 - 24x + 2y2 - 20y) optimize the function. Find Zx, Zy, Zxx, Zyy, Zxy. Comment…

A:

Q: Find the particular solution determined by the given condition. F(x) = 3x2 - 2x; f(O) = 9 %3D %3D O…

A: Given query is to find the solution of the differential equation.

Q: Verity Gauss' theorem for the vector feld f (x,y, z)= (y,x,2) on the surface of the sechere with…

A:

Q: 4. lim (sinx)tanx X0+

A:

Q: -2 12) Find the sum of the Series 2".30" A C) D) 2 E) 9

A: Let    I= ∑n=1∞2n3-n-2Rewriting 2n3-n-2=2n3-n3-2                                  =2n3n×132…

Q: ) Syppose f and g are functions with continuous lerivatives, and that they satisty the following. S…

A: Let's find.

Q: H.W: Evaluate the integral 3 0 1 | (x?y – 2xy)dydx | |(x + y + 1)dxdy 1. 2. 0 -2 -1 -1 3 1 4 1 (2х —…

A:

Q: Solve the initial value problem. 4 y(x) = 4 sec(3.xr) tan(3x) ; y(7) = 3

A:

Q: Evaluate the triple integral. Xyz dV, where G is the solid in the first octant that is bounded by…

A: Integral

Q: A business is planning to purchase a piece of equipment that will produce a continuous stream of…

A:

Q: x²+x dx x2+1

A:

Q: Question 5 Find the volume of the solid that results when the region enclosed by the given curves is…

A: Given, y= sqrt(25-x²) y= 4

Q: dy = 2 – y dx Find the correct direction field for the differential equation ノー\\ ババーと

A:

Q: 19 Suppose that Ts (x) centered at 2 for f(x) is gien by. Is (X=3+5Cx-2)+8(x-2)²+2G-2)°+(x-2) (3)…

A: T5(x) centered at 2 for f(x) is given by,T5(x)=3+5(x-2)+8(x-2)2+2(x-2)3+(x-2)5

Q: Evaluate the definite integral. ¤(x² + 7)°dx (b) / z x/1 – x²dx (a)

A:

Q: +2 dx: Consider the indefinite integral a) This can be transformed into a basic integral by letting…

A: The given integral,        ∫e7x+2dx

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly.…

A: Here , we have given an integral and we have to integrate over a rectangle whose vertices are given…

Q: Q3) Apply the logarithmic differentiation to find the derivatives of: x+1 y=(sinx-x)**

A:

Q: Question 5 3 Consider the function f(x) = Let F(x) be the antiderivative of f(x) with F(1) = 0. Then…

A:

Q: Inx F (x) = So It dt %3D

A:

Q: A) S sin edo b)S sec edo )Side Ssec?eddo E)S cos ede

A: We have to find the integral

Q: Evaluate the indefinite integral. -dx 1 – x8

A: We use the standard integration result ∫11-x2dx=sin-1x+C

Q: Solve the problem. Solve the differential equation model of a population growth: dP 0.5P. dt O P(t)…

A:

Q: The acceleration function (in m/s2) and the initial velocity v(0) (in m/s) are given for a particle…

A:

Q: dr J z(x+1)² 14.

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Let e, = ( ) be a unit radial vector, where r = Vx? + y + z?. = (1 (a) Calculate the integral of F =…

A:

Q: 9. 5+ 8 7- 6- 3 5 4 2 g(x) 2 h(x) 1 1 1 2 3 x-values 4 5 1 2 3 x-values 4 If f(x) = g(h(x)), then…

A: Explanation of the answer is as follows

Q: Qs show that : sinh CA+B) = SinhA. coshB + Cosh A. simhB

A: This question is related to Hyperbolic functions, we will solve it using given information.

Q: 33) In Problems 33) through 35), given MB ' (x) = HD(x), HD' (x) = PR (x) , PR' (x) = RB(x) with the…

A:

Q: Express the integral as an equivalent integral in which the z-integration is performed first, the…

A: Here,  0≤x≤4-yy≤z≤8-y0≤y≤4 To change the order of integration to dx dz dy to dz dy dx

Q: 4 sin 3xcar" 3xdx

A:

Q: Solve the initial value problem. 1 u'(x) = – 2; u(0) = 1 x2+1

A: Explanation of the answer is as follows