Explain why the function is differentiable at the given point. f(x, y) = x³y?, (-2, 2) The partial derivatives are f,(x, y) = and f,(x, y) = , so f,(-2, 2) = and f,(-2, 2) = . Both f, and f, are continuous functions, so f is differentiable at (-2, 2). Find the linearization L(x, y) of the function at (-2, 2). L(x, y) =

Q: Differentiate the following 1. g(x) = x³ cosx 2. g(x) = 4 sec x + tan x 6. h(x) = 5x sin-x 7. h(x) =...

A: 1) g(x)=x3cosxDifferentiateg'(x)=3x2cosx-x3sinx2) g(x)=4secx+tanxDifferentiateg'(x)=4secx.tanx+sec2x...

Q: Let ro = -a; xi = 0; and x2 = a. Compute the interpolation polynomial for f(x) = -r* using Lagrange ...

A:

Q: It is known that x>5000. Find the least positive integral solution of the system of congruence equat...

A:

Q: 4. (4x2 - y?)dx - xydy = 0

A: Let's find. 

Q: Use the Root Test to determine the convergence or divergence of the given series or state that the R...

A:

Q: Determine the particular solution. dy _' x = 1, y = 0 dx x O ev/x - In(x) = -1 O ey/x + In(x) = 1 O ...

A: To determine the particular solution of the following initial value problem.dydx-yx=eyx; x=1, y=0

Q: Consider the equation below. f(x) = 5 cos2(x) – 10 sin(x), OsxS 2n (c) Find the inflection points. (...

A: f(x)=5cos2(x)-10sin(x)Differentiate f'(x)=10cos(x).(-sin(x))-10cos(x)f'(x)=-10cos(x)(1+sin(x))Differ...

Q: の dy Sーメ+ リーX +5

A: This is a problem related to differential equation. Based on the general formula we will solve the q...

Q: Find dy/dx in terms of t if x = t – t, y = 2 – 5t dy/dx = %3D

A:

Q: F. Find the derivative of each quotient 4x+9 b. h(x) = 3r2-1 3x a. h(x): c. h(x) = - %3D 1-10 2x³-4x...

A:

Q: Determine the value of C in on the antiderivative of F(x) = sin (x)cos°(x) for x = 0.055 and y = 0.9...

A: Find your answer below 

Q: х4—х2+1 - [3] S [3] s e*ve*-1dx еx+3

A:

Q: If ye – 6y = 5, find dy/dx. dy %3D dx

A: yex-6y=5y(ex-6)=5y=5ex-6Differentiate w.r.t x

Q: Determine the vertical asymptote(s) of the graph of the function. x+9 4) f(x) = 7x + 9x - 10

A: We have to find out vertical asymptote

Q: Find the average rate of change of the function over the given interval. (Round your answer to three...

A:

Q: Prove the identity. (Recall sinh(a + b) = sinh(a) cosh(b) + cosh(a) sinh(b).) sinh(2x) = 2 sinh(x) c...

A:

Q: 2 Given a circle with radius, r, and a sector with area, A, formed by angle of 0 radians. Find a for...

A: Here we have to find the area of the sector.

Q: Section 5.2 p. 466/468 # 76 In the following exercises, compute the general term a, of the series wi...

A: Solve the following

Q: - f(x) = - f(x) = x-2 g(x) = 5 In x - 2* g(x) = 4x' log, x %3D f(x) = 10* · e*

A: Solution of question is written in below steps.

Q: x²-2x -3 (15) Rational function r(x) = has a vertical asymptote at x = 4. The asymptotic behavior X-...

A: Solve the following

Q: Copy the vectors in the figure and use them to draw the following vectors. (а) а + b (b) а — b (c) a...

A: Note that, according to Bartleby guidelines, we can answer only the first 3 sub-parts in the case of...

Q: For what values of a and b wou la the function f be continuous at every 'humber x'? real ax + 26 if ...

A:

Q: Find the maximum and the minimum points of each function on the given interval. 13. f(x) = 4x3- 3x2-...

A: As per the company guidelines we can solve first question. I hope that the given solution will help ...

Q: Let h(x, y) = , x = 41|12, y = 517t2. Use the Chain Rule to calculate the partial derivative. (Use s...

A:

Q: Consider the following alternating series. (-1)*-1 3k +2 k=1 a) An alternating series can be written...

A:

Q: 2 Represent the function as a power series f(x) : (1 – 7æ)2 n=0 e radius of convergence R

A:

Q: Q4/Find the value of b which I+ ė + ĕ -6. %3D Qn! For what value of r does the infinit Series Sn Con...

A: Recall: Infinite Geometric Series : Given that an Infinite Geometric series               a+ ar+ar2+...

Q: r 64 In(y) 49 VY

A: We need to solve definite integral.

Q: A crowd gathers around a movie star, forming a circle. The area taken up by the crowd increases at a...

A:

Q: A particle moves according to a law of motion s = f(t) = t3 - 15t2 + 72t, t2 0, where t is measured ...

A: Solution

Q: xdx + sin? (2) [ydx – xdy]

A:

Q: OFF The electric potential at a point (r, y) is given by V(z, y) = e-2* cos 3y. Determine the direct...

A:

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

A: We have to find the critical point

Q: D eter mine Paricular volution ( 2xy)dy = (y²-x²)dy j x=I,y= -2

A: In this question we have to determine the particular solution.  

Q: Approximate sin(179∘) by using a linear approximation of f(x)=sin(x) at x=π. Give your answer round...

A: In order to solve the problems of this kind we need to use linear approximation formula and then aft...

Q: 6. lim In(2+x)-In(1+x) 5. lim In(1+x*)-In(1+x)]

A: Topic = Limits

Q: dy Find dx S cos (P) at y = COS dy dx II

A:

Q: Find all values of x for which the series converges. (Enter your answer using interval notation n X ...

A: Since multiple questions are asked, I am answering the first question only.

Q: dz a) $. Y z – 10

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart...

Q: 1. lim In (x –9) 2. lim log, (8x-x*) x3* x-2" 3. lim In (cos x) 4. lim In (sin x)

A:

Q: 6 FW = (cos()" The coefficient of Sin(X) in the antiderivative of is Blank 1 (use fraction form not ...

A:

Q: 25 The function f(x) is represented in the following table. Give the best estimate for f(x)dx 10 X 1...

A:

Q: A cylindrical tank with radius 3 m is being filled with water at a rate of 4 m3/min. How fast is the...

A: We can find the required answer as below.

Q: A geometry teacher wants to draw a rectangle inscribed in the ellipse x? + 4y² = 16. What is the are...

A:

Q: Find the slope of the tangent to the curve y² In(x) + x<y = 5 at (1, 5).

A:

Q: For the curve x (t) = t², y (t) =t³ – 3t Given the curve crosses itself at (3, 0), a) Find the point...

A:

Q: 12w-5w2 +(20w-24) sec² (12w-5w )đw

A:

Q: If y? In(x) = 5, find dy/dx. dy dx

A: This question is based on differentiation with respect to x.

Q: q1

A: We have to find out Eigen values

Q: Determine the value of the arbitrary constant of the antriderivative of F(x) =x<In(x) given the init...

A: