tional derivative Daf. Describe precisely what the relationship is. b) In WA2 Q2(c) we saw that the existence of fa, fy and dsf is not sufficient to guarantee the differentiability of f. It might be tempting to think that differentiability will be guaranteed if all of the directional derivatives were to exist. This is not the case. In fact, this does not even guarantee continuity! Find an example of a function f : R² → R and a point (a, b) such that: (i) Daf(a, b) exists for every unit vector i E R², but (ii) f is not continuous at (a, b). Be sure to justify vour claims.

Q: lim {n→∞} ( sqrt(n2+n) - n)

A:

Q: Find the length of the following three-dimensional curve. r(t) = (cos t, t, sin t), for 0sts8 L3D (T...

A:

Q: ppose that T : R² → R² is a linear transformation and that 7([일) -B] T and ar (H) nd T

A:

Q: Define f(x)=x^3 for all x. Verify the ε-δ criterion for continuity at each point x_0.

A: X3 is continuous at every point in R.

Q: Given an acceleration vector, initial velocity (uo.Vo). and initial position (xo.Yo). find the veloc...

A: Given that: Acceleration, at=cost,5sint Initial position, x0,y0=3,0 Initial velocity, u0,v0=0,1 To...

Q: Exercise 16 Find the complete solution of the following differential equation 1. y"-y'-6y = 10e* y =...

A:

Q: c. Solve the initial value problem for y(t). y(t) = 1/4(cos(8t)-cos(10t)) help (formulas) d. Plot th...

A: Given: Differential equation y''+100y=9cos(10t), with initial conditions y(0)=0 and y'(0)=0.

Q: Find the Maclaurin Series of the following functions. sin(x) 2 5 x'e*

A:

Q: Use a calculator to approximate the length of the following curve. Simplify the arc length integral ...

A:

Q: If we choose po very close to the fixed point p = 3 of f(x) : 6 - the sequence (p,) of iterations of...

A: we check the iteration are converges or not we use |f'(x0)|<1.

Q: Solve the system of congruences 2x + 6y = 3 (mod 15) 3x + 7y = 6 (mod 15)

A:

Q: Consider the recursive relation 1 X1+1 9. (a) Find all equilibrium points. Answer: x = and x (b) The...

A: Please check step 2 for the solution.

Q: Q.59 Consider the function f(x) = x2 – x - 2. The maximum value of f(x) in the closed interval [-4, ...

A: Introduction :

Q: etermine whether S is a basis for R3. S = {(2, 4, 3), (0, 4, 3), (0, 0, 3)} O S is a basis for R3. O...

A: We can solve this by the help of linear combination 

Q: A sequence {a,} is defined recursively by aj = 1, az = 4, a3 = 9 and an = an–1 – an–2+ an-3 + 2(2n –...

A:

Q: 1. A business man deposits ₱50,000 in a bank account which pays 4.5% interest annually, compounded c...

A: We will find out the required values.

Q: Determine the length of the curve r(1) = t*i+ t°j – 5k, 4 <1 < 1. %3D Give your answer correct to tw...

A: Given curve is  r(t)=t4i+t6j-5k,    1≤t≤4

Q: Ca²x.+by, cx+d

A:

Q: 5 x²e*

A: 5. Given that, the function is fx=x2ex. Note that, the Maclurin series representation for ex≈1+x+x22...

Q: Prove that x ∈ E' iff there exists a sequence (xn) in E\{x} such that xn -> x.

A:

Q: Let R be the set of all continuous functions. It is known that (R,+,×) is a ring where + and × are b...

A:

Q: Consider the function f(z,y) 16r-9y +8ry over the unit siquare 0SaS1, 0SUS1. %D NOTE: Enter the ezac...

A: The function given is as follows: fx,y=16x2-9y2+8xy Over the square, 0≤x≤1,  0≤y≤1. (a) At edge x=0,...

Q: Solution of the differential equation dx + y? 1× (x-y) | x2 Tox-y) dy = 0 is

A: Introduction :

Q: 1 - 2 0 1 2 -4 2 4 6 Let A 3 - 6 1 4 1 1 - 2 -2 1 -3 1) Find the rank of A. 2) Find the nullity of A...

A: As per our guideline we are supposed to answer first three subparts.kindly repost other question. Th...

Q: Find the amount accumulated FV in the given annuity account. (Assume end-of-period deposits and comp...

A:

Q: Find the Taylor Series of the following functions at the given value of a. 10 X – x³ at a = -2 12 e-...

A:

Q: Footlocker and Footaction are each having a sell on all of the latest name brand shoes. At Footlocke...

A: Footlocker : The price of 2 pairs is $69.98 Therefore the price of 1 pair is 69.982=34.99 Therefore ...

Q: 33. The five finalists in the Miss Universe contest are Miss Argentina, Miss Belgium, Miss U.S.A., M...

A:

Q: Determine the length of the curve r(t) = 4sin(3t)i + 3tj + 4cos(3t)k, 0 <t < -. 2 Give your answer c...

A: Arclegth of the position vector

Q: If Alice is tall, Bob is taller than her, and Carol is taller than both of them, then Carol is tall.

A: Given that Bob is taller than Alice, So Bob&gt;Alice    (1) Carol is taller that Alice and Bob. It m...

Q: Let (a,) be the sequence defined by a¡ = 5 and a, = 2a,-1 – 3 when n > 2. What is a4?

A: Here an be the given sequence which is defined by a1=5 and an=2an-1-3 when n≥2 . We have to find a4 ...

Q: Evaluate the iterated double integral: esec y+1 dy dx. VE sin y sec

A: To evaluate the iterated double integral :               ∫14∫sec-1xπ3  esecy+1sin ydydx

Q: A connected graph has 40 even vertices and no odd vertices. Determine whether the graph has an Euler...

A: A connected graph has 40 even vertices and no odd vertices. according to the Euler theorem of the gr...

Q: The number of ducks and pigs in a field totals 35. The total number of legs among them is 98. Assumi...

A:

Q: Find the first three nonzero terms in the Taylor Series of f about x = a if (i) f(r) = cos(2x), a : ...

A: Since you have posted a multiple question according to guildlines I will solve first question for yo...

Q: y mathematical induction): f, f2, f3,... is a sequence that satisfies the recurrence relation f, = f...

A:

Q: What is the area of a regular pentagon (in square meters) with side 5 m? ROUND OFF ANSWER TO TWO DEC...

A: In this question, concept of area of a regular pentagon is applied. Regular Pentagon The region encl...

Q: Given the matrix -17 A = -2 -1 -1 find all values of c for which the matrix A is singular. Enter the...

A: Here the given matrix is                                   A=c2-1c-2-1-15c We have to find the value...

Q: You want to buy a $14,000 car. The company is offering a 2% interest rate for 48 months (4 years). W...

A: We will find out the required value.

Q: min z = -4x1 + 12 th s.t. 3x, + X2 S s.t. -x, + 2x2 s

A:

Q: i. For a convergent real sequence sn and a real number a, show that if sn ≥ a for all but finitely m...

A:

Q: Calculate the flux of the following vector field V = (2æz, (x+2), y (z² – 3)) through a square surfa...

A: The general form of a vector-valued function in three dimensions is given by F=(F1,F2,F3), where F1,...

Q: State whether each of the following statements is true or false. Then give an explanation, proof o c...

A: considering a=a-1 and b=b-1 as a=a-1 and b=b-1 the inverse of ba is given by ba-1=a-1b-1            ...

Q: Use definite integrals to solve for the consumer surplus, producer surplus and total surplus, given ...

A: We will find out the required values.

Q: 1. z1(x) = 3x2 +xe®, z2(x) = xe² – x² are solutions of a second order, linear nonhomogeneous equatio...

A: (1). Given,                  z1(x)=3x2+xex,  z2(x)=xex-x2      are solutions of a second order, line...

Q: An average seated adult breathes in and out every four seconds. At any given time, the lungs contain...

A: Given, an average seated adult breathes in and out every four seconds. At any given time, the lungs ...

Q: Question 2. Find lim sin (1 – 3e-/")e-/2. (Justify your solution.)

A:

Q: 4. What is the integrating factor of the first-order linear differential equation below? (y – 1) sin...

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

Q: 3. Use Wilson's Theorem to prove 6(k - 4)! = 1 (mod k:), if k is prime.

A: Wilson's Theorem: Let k be a prime number, then by Wilson's theorem, (k-1)!=-1(modk)

Q: The function f: x 1-> a + b cos x, is defined for 0sxs 2n. Given that f(0) = 10 and that %3D n)= 1, ...

A: