4. Find all the points at which the direction of fastest increment of the function f(x, y) = x² + y² – 2x - 2y is parallel to i – 2j.

Q: Evaluate the integral / V4x4 - 12r? +7 xdx A - {(2x?-3) /4x4– 12x?+7 - 2 In |2x?– 3 + V4x4 - 12x2+7|...

A:

Q: Find the Maclaurin polynomials of orders n = 0, 1, 2,3, and 4 and th find the nth Maclaurin polynomi...

A:

Q: Inz Let U = ry ,x= Vst, y = s? - 1². Use the chain rule to find when s = 1, as 4. -. t = 2.

A:

Q: Write the first five terms of the sequence, give the exact answer: +00 n+ 19 n=1 Determine whether t...

A:

Q: Solu) du. rg(u) = Using u-substitution, the integral u+1 reduces to a new integral , evaluate the ne...

A: Explanation of the answer is as follows

Q: Differentiate the function by using the definition of derivatives. f(x + h) – f(x) f'(x) = lim h0 f(...

A: Given: f(x)=x3

Q: The differential equation x*(x – 2)²y" + 3(x – 2)y' + y = 0, as the singular points at x = 0 and x =...

A:

Q: O g(x) = (3t+ 2) dl t %3D

A:

Q: rot F - dS, where F = (y+1)i – (x² + y² + z)k and S It is given by Use Stokes' Theorem to calculate ...

A: This is a problem of vector calculus. Based on the stokes formula for vector calculus we will evalua...

Q: The graph shown is f (x) = sin x. If g (x) = / f (t)dt, find g' (7). %3D AY 6.28 -3.14 3.14 6/28 -2 ...

A:

Q: y' + y = 5 sin(2x)

A:

Q: 3. a) Find the percentage error in computing u = Vx at x = 2.45, when x is 4 p) | If Ax = 0.005, Ay ...

A:

Q: Using the (e- 6) definition, show that f(x) = 3x – 1 is continuous at point x = 1.

A:

Q: 1. Let (r + 2)², if I 0. (a) Give the r coordinate(s) of the possible point(s) of discontinuity of ...

A:

Q: (c) The function f(x) is defined in the interval [-1,6] by 3-x, -1<x<2 f(x) ={ x -a, 2<x<b |(x-9)²-4...

A:

Q: Differentiate f(æ) = 27. 1.

A:

Q: 3. Define the function sin(2x – 2) x 3 3' - Determine if f is continuous at x = 1 and x = 3. If dis...

A:

Q: Find the nth Taylor polynomial for the function, centered at c. f(x) n = 4, c = 4 P(x) =

A: solution:-f(x)=1x2,     n=4,       c=4f'(x)=-2x3f''(x)=6x4f'''(x)=-24x5f4x=120x6

Q: Is the series divergent or convergent? Show solution and explanation. +oo In n E(-1)": n2 n=2

A:

Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at...

A:

Q: What is the horizontal shift? y= 2 tan X-180 +3 O 180 degrees O360 degrees O 45 degrees 540 degrees

A:

Q: Find the centroid along the y-axis of the plane area bounded by the equation y^2=4x, x=1 and the x-a...

A: Given curve is y2=4x ,x=1

Q: (d) The function k(x)is defined as follow: 3 x+ 17 -- 4 k(x) = { 2, x =1 5|x-1| x² -1 x>1 Discuss th...

A:

Q: To evaluate the possibility of using pyramid-shaped vessel, the rate of change of the dimensions wer...

A: This question can be solved by using rate of change of physical quantities.

Q: Question 5 5 Given: dx. Using u-substitution and transformation of integrand, what is u and du? 3/x ...

A:

Q: f(x) =(x^2/3 − 1)^2 Take note that the 2/3 is the exponent if x (a.) the critical numbers of f (b....

A:

Q: -to determine if the sequence {ne"} is strictly increasing or strictly decreasing. An an+1 Use the r...

A: 1st we have to find an  then we have to find an+1 . Then by ratio we may find it's increases or decr...

Q: 2. (a) Prove the following inequality n(n- 1) ,2, 120 (1+ 1)" 2 1+ nz + 2 for any n 2 1. (b) Show th...

A:

Q: a. Show by means of slope that the four points (0,0), (-2,1), (3,4), and (5,3) are vertices of a par...

A: This is a problem related to geometry. For parallelogram opposite sides are parallel to each other. ...

Q: An agriculturist wanted to plant seven different organic crops in a small field. To properly study t...

A:

Q: Solve the following ODE. y" + 2y" – y- 2y = 9 - 123 NOTE: Write arbitrary constants as c1, Cg, and c...

A:

Q: Question 12 For the following function , find the equation of f-(x) and hence show that f({=}) = f (...

A:

Q: x4 + 2y = x2 – x +1 y(1) = 1/2 dr

A:

Q: I. Determine the derivative of the ff. exponential functions 1. y = 8 e -4x 2. y = 15 e 7x + 3 3. y ...

A: As per our company guidelines we can answer only three subparts question at a time, but if you need ...

Q: is the sequence divergent convergent? {vñ - v n +1}

A: Topic:- sequence and series

Q: Please see the image to see the given. thank you (a.) the critical numbers of f (b.) all relative e...

A: To find: (a.) the critical numbers of f(b.) all relative extrema of f(c.) the intervals on which f i...

Q: Using u-substitution, the integral f(x)dx Srwax u+1 reduces to a new integralg(u) du. If g(u) = , ev...

A:

Q: dy 2. V16 + y²

A:

Q: Determine whether the series converges, and if so find exactly its sum. Otherwise type none in the b...

A:

Q: tan (In |4x2|) -dx is b in cos (In |(2x)*|)|+c. The integral of What is b?

A:

Q: (т — 3)" - Determine the interval of convergence of 2n +1

A:

Q: State whether the following series is Convergent or Divergent. (-1)" Vn +1 n=1

A: Absolutely convergent :If the the mod of the alternating series ∑n=1∞(-1)nan i.e., ∑n=1∞|(-1)nan | =...

Q: n2 - 6 with n5 + 6 Write an inequlity comparing for n > 1. n3 (Express numbers in exact form. Use sy...

A:

Q: Which of the following is the general solution of the DE: у" - 36у %3D0? Select one: o y=C,+Ce 36x -...

A:

Q: Assume that g(x) is a function given by 2.x? + 3x +2 g(x) = x² + 2 Prove that g(x) is bounded for al...

A:

Q: Question 10 cot (2x) Evaluate the integral Vcot (2x)- 15 cse (2x) A) --Arcsec 4 4 cot (2x) B) Arcsec...

A:

Q: 8-2х (f) lim- нх* — х—12

A:

Q: dx The integral can be re-written as (A) (2-2 V1-m ) lim m- 00 B none of the choices lim (-2+2 /1-m ...

A:

Q: 3) A businessman ventures to put up a digital printing shop which caters to printing of t-shirts for...

A: Let the number of t-shirts that will obtain maximum gross return is = 50+x. In this case x t-shirts ...

Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)...

A: