1. Let f and g be continuously differentiable functions. PROVE: div(fvg -g v f) fag gAf %3D Hint - Use Thm 4: If ü is a vector field an f is a scalar field , then div( f ü) = f div ü + f ū

Q: paper 2 4. INDICES AND SURDS 2012 J Q2 (b) Solve the equation 363y-5 63y 62y-1 216 y+6

A: Solution:-

Q: Activity Solve the initial-value problem 1. y" - 3y' – 10y = 0 , y(0) = 0 , y'(0) = 7. 2. y" + 14y' ...

A: Note: We are entitled to solve only one question at a time. As the specific number is not mentioned,...

Q: 8. Let A = Z* U {0}, define relation R on A × Z* by (k, l)R(m,n) → kn = lm. (a). Prove that Ris an e...

A:

Q: Determine where the graph of each function is concave upward and where it concave downward.  f(x) ...

A:

Q: Using bisection method, find the point of intersection of the curves y=x°

A: Given, y= x3-2x+1, and y=x2 in the interval 1, 2 

Q: Consider the Galois field GF(24), with standard addition, and multiplication defined modulo the (pri...

A:

Q: 37. Which of the following accurately shows the constraint on the daily capacity for the third produ...

A:

Q: For the line through P(2, – 1) and Q( – 1, 5 ), determine each of the following :  a) Vector equati...

A:

Q: For the Euler operator, LEyI=x?y" +3xy' -34 the homogenous Schution ioi Y,=C,x*+C,X. Aosure thió à t...

A:

Q: Solve the ODE : X+5xy+9y=0,x> 211

A:

Q: [4 2 21 2. Let A = |2 2 0 [2 0 2] a) find the generalize inverse symmetry of A b) find the generaliz...

A: Given:A =422220202

Q: Draw a line on the graph that will intersect the given line at the point (3,2) ei Jor

A:

Q: Which of the following sets are closed under scalar multiplication? (1) The set of all vectors in R ...

A:

Q: Using Newton's Divided Difference, the interpolating polynomial of the points (xo.Yo) = (- 2,1), (x1...

A: We use Newton's Divided Difference interpolation formula. x      x0      x1      x2      x3y      y0...

Q: (a) If lim a, = 0 then >(-1)" an is convergent. n=1 (b) If 2(-1)" an is convergent and an is converg...

A:

Q: 5" + sin? (n) En=1 3" – sin(n)

A:

Q: Let f(z, y) = la + ly + 2 be a two-variable function,and the graph of z = læ + ly + 2 is sketched be...

A: To find level curve put value or z= - 3 in the equation z=x+y+2

Q: 4. A golf ball is shot into the air and modeled by the function h(t) = - 4.7t + 13t + 0.3 where h is...

A:

Q: cos x xp - cos? x d)

A: Here we have to find anti derivative of d) 

Q: This problem deals with the RC cirouit shown to the right containing a resistor ohms), a capacitor (...

A:

Q: 6. Find the complement of the following sets if universal set is the set of natural numbers. (a) {x ...

A:

Q: Use Y=sin) and reductiori of order to find the generale soletion to the homogeneous differenticl equ...

A:

Q: (c). A forest with 5 vertices and 4 edges. (d). A binary tree to represent expression + d) · (e + (f...

A: In graph theory, a tree is an undirected, connected and acyclic graph. In other words, a connected g...

Q: Q4. Using Laplace Transforms determine the solution y(t),to the initial value problem following dy -...

A:

Q: 1. Given P(x) = 3x° + 6x² - 6x - 30. Using the rational root theorem, identify the list of all possi...

A: Rational root theorem

Q: 7" is 3n+1x5 Jnz1 The sequence a. geometric O b. diverges O C. Bounded O d. arithmetic

A: Geometric series

Q: Prove by contradiction: If x is a nonzero rational number and y is an irrational

A:

Q: Find the pattern of addition/subtraction from one x-value to the next and from one y-value to the ne...

A:

Q: Which of the following statements are always true? (i) If A is a 3 × 3 diagonalizable matrix then A ...

A: Linear algebra.

Q: Given f(z) = (y + 1) i(x – 3 x). Find the set of all points zo = xo + i Yo where f is differentiable...

A: Solution:-

Q: by constructing täble of lues. t-0 3t t -1 -0.5 -0.01 -0.001 f(t) 1 0.5 0.01 0.001 f(t)

A:

Q: 2. A right cylinder of radius r is inscribed in a hollow sphere of fixed radius a. The tv circular e...

A:

Q: Below is the graph of a conic section. Identify, among the options, a possible equation for this con...

A:

Q: A right cylinder of radius r is inscribed in a hollow sphere of fixed radius a. The

A: Given, a right cylinder of radius 'r', is inscribed in a hollow sphere of fixed radius 'a'. The twoc...

Q: +00 4 Determine if the series converges or diverges. If it converges, find its sum. n² + 4n + 3 n=1

A:

Q: What is the percentile rank of a student with a weight of 53kg? (input the rank, use whole numbers o...

A: Given data set of weight of 20 senior high school students of SMU are We can write it in ascending ...

Q: Answer the following. All fractions are in lowest form. 5x² - 3x + 18 dx x(9 – x-) dr 12. r³ (Vr² – ...

A: As per our  guidelines we are supposed to answer only first question. kindly repost other parts in t...

Q: If m` E = 0, then E is measurable.

A:

Q: Solve the matrix equation AX = B for X. 1 6 A = B = - 15 X=

A:

Q: :: Find the y-coordinate of the point on the plane x+ 6y + 7z = 3 that is closest to the point (-14,...

A:

Q: only use comparison test, dont use integral test in answering.

A:

Q: For the given function, find all values of c over the interval (,50) stipulated by Rolle's Theorem s...

A: This is the problem of application of differentiation, Rolles theorem.

Q: C. Optimization 1. Use the first derivative test to determine the relative extrema of the following ...

A:

Q: In one of the earlier pre-class activities, we said that the alternating harmonic series converges t...

A:  

Q: Sketch the level curve of the function y? f(z, y) : %3D 4 36 for c = 1.

A:

Q: 1 Let an n > 3. n ln n +00 Show that the sequence {an}"3 is decreasing.

A:

Q: Exercise 1. H Let 3 A = 19 -2 4 -8 11 1. Form the augmented matrir 2. Carry out row operations acros...

A:

Q: If S is a region in the xy-plane whose moment about the x-axis is given by the definite integral 1 (...

A: Given S is the region in xy plane whose moment about x-axis is Mx=12ρ∫01(x-x2)dxwhere ρ is density o...

Q: If f is bounded and integrable on [a, b] such that | f(x) | 0).

A:

Q: Find the triple integral of the function F(x, y, z) = z over the region in the figure. Assume that a...

A: Our first task to determine the equation of the plane lying above xy-plane and standing on x-axis.