Two numbers greater than zero add up to 6. Find the numbers so that the product of the first number and the square of the second number is maximum.

Q: Does the sequence {an} converge or diverge? Find the limit if the sequence is convergent. 2 - 5n4 an...

A: Solve the following

Q: (d) There exists a relation U on A so that U is symmetric and antisymmetric, but U is not transitive...

A:

Q: メ+4 dx x²+4

A: Given:       ∫x+4x2+4dx      =∫xx2+4+4x2+4dx Apply linearity:      =∫xx2+4dx+4∫1x2+4dx

Q: Q4: Find an equation for the line tangent to the curve 2y cos x = 4x sin y , at the point where x = ...

A:

Q: Find the vector component of v = (4, – 1,7) along b = (3, 6, –6) and the vector component of v ortho...

A: We can solve the given problem as follows:

Q: Construct a truth table to show that (p^q) → p is a tautology.

A:

Q: Find the tangent line approximation T to the graph of f at the given point. Then complete the table....

A:

Q: Find the vectoy with the given magnitude and the same direction as u Magnitude Direction ||v|| = 4 u...

A:

Q: z, Z2 Prove

A: If z =x+ iy then  z = x- iy. i2 =-1.

Q: (

A:

Q: cos x dx

A:

Q: Consider the function f (x) = re. Answer each question, showing your work. A. Using derivative analy...

A: Explained below 

Q: Determine the set of points satisfying the condition described by |z – 3| + |z + 3| = 10 Then expres...

A:

Q: 1. |x² In x dx; u = In x, dv = x² dx 2. 0 cos 0 de; u= 0, dv = cos 0 d0 %3D

A:

Q: 1. f sin³ 4xcos³4xdz

A: To evaluate the given integral.

Q: 2. S sin° () dx

A: Integration

Q: I+x 5. Show that y = has three points of inflection and they all lie on one straigl 1+ x2 line.

A:

Q: Find the vector projy 2i - 2j - 4k, u = 5i - 12 k

A:

Q: eny x+9 dx dy e+y en8 Iny dy %3D en8 e [ e-e] dy eny en8 [ye- e° ] dy | ل ام مو ] en8 | ye- e° - e ]...

A: Let I=∫1ln(8)∫0ln(y)ex+ydxdyI=∫1ln(8)∫0ln(y)exeydxdyI=∫1ln(8)ey∫0ln(y)exdxdyI=∫1ln(8)eyex0ln(y)dyI=∫...

Q: Consider the following planes. -6x + y + z = 6 12x – 2y + 6z = 36 (a) Find the angle between the two...

A:

Q: If a cars position on a straight road is given by p(t)=t^3-6t^2+8t find the inflection point for the...

A: Given query is to find inflection points.

Q: me: urse/Year/Section: Date: Find the derivatives of the following: 1.) x* + 2y = 6x 2.) f(x) = (tan...

A: We are asked to find the derivatives of the following.

Q: e*Vex-1dx ex+3

A:

Q: In the diagram below, the cube's side length and the sphere's diameter is equal. If the sphere's rad...

A: Given: Sphere radius is one and four tenths feet  And also the cube's side length and sphere's diame...

Q: Set up an integral for the area of the shaded region. Evaluate the integral to find the area of the ...

A:

Q: Suppose that for a company manufacturing calculators, the cost, revenue, and profit equations are gi...

A: To find the rate of increase or decrease in cost, revenue and profit.

Q: (3x – 1)" 5" /n +1' Find the radius and interval of convergence of the power series n=1

A:

Q: n. 2n + 1 Σ n tan -1 n n=1

A:

Q: Find the solution of the following differential equation by Laplace transform with itial conditions ...

A: To solve the differential equation dxdt+2x=2 by the use of Laplace form. Given information: The init...

Q: ch of the following sequences. Always justify your ans 1+ncos(2m) sin n+ c - In с) а, d) а, 2n 3 n°

A:

Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answ...

A:

Q: 2n +1 Σ n n tan-1 n n=1

A:

Q: A plant encloser is in the shape of half of a cylinder. Find the surface area of plastic covering. L...

A: Surface area

Q: Sx² – 1, (2x + 1, 3 < x < 10 x< 0 Evaluate lim f(x) if f(x) = x→3

A: Since left and right limit at x =3 not equal then we say that limit does not exist at x=3

Q: 4. § xe¯ dx 6. |t sin 2t dt Jx² cos mx dx 8.

A:

Q: An automotive engineer studied the effect of car weight in tons on fuel efficiency, which is measure...

A:

Q: 1 1 3. lim ed - 1

A: Given query is to find the limit of the expression.

Q: 2х — а, х < -3 Find the values of a and b so that lim f(x) and limf(x) both exist given: f(x) = {ax ...

A: The objective of the question is determine the value of a and b for which limits exist.

Q: Find the lim(-). 4 x→2x-2 x2-4 3/4 None of these O 1/4 O undefined

A: We have find lim above question 

Q: 3. Find the following integrals. Most of them (but not all) require partial fraction xdx 2х + 3 b) s...

A:

Q: Determine whether the planes are parallel, orthogonal, or neither. 9x – 8y + z = 6 x + 2y + 7z = 1 O...

A:

Q: S cot5xdx ха

A:

Q: The functionf is a continuous function with the following characteristics: f(x) <0 on the interval -...

A:

Q: .... a) What percentage buy the game without seeing a TV ad (x = 0)? 19% (Type an integer or a decim...

A:

Q: ++8, Express the answer in rectangular form. (2+3i B. Evaluate the expression () - (). 1+2i

A:

Q: Let h(x) = /(t)dt, where f is the function whoseaph is shown. 1 4 6. -1 -2 A. Evaluate h(5) E. Evalu...

A: Given query is to find the Indicated values from the graph.

Q: d²q (c) dt2 dq = t2 + 2t F(0) = 4 F'(0) = -2 %3D %3D dt

A:

Q: Find the critical points c for the function f and apply the Second Derivative Test (if possible) to ...

A:

Q: Find a and b such that v = au + bw, where u = (1, 2) and w = (1, -1). v= (6, 9) a = b =

A:

Q: A chemical substance has a decay rate of 9.5% per day. The rate of change of an amount N of the chem...

A: