15. Determine if the given functions are linearly dependent or independent. (Prove your answers) {e ,3x} b. (-9x +1,3x - c. (1-2 sin' x,cos 2x} с.

Q: Which of the following values is the directional derivative of f (x, y) = ln (x² + y² + z²) at the…

A: To Find: The Directional derivative of fx, y, z=lnx2+y2+z2 at the point 1, 3, 2 in the direction of…

Q: Eliminate the arbitrary constants (a, b) in the function to obtain the differentialequation. I e =…

A:

Q: The equation sin(πxy/3)+x=3y implicitly defines y as a single function of x at (and near) the point…

A: Differentiating both sides with respect to x

Q: 4–6 Find the directional derivative of f at the given point in the direction indicated by the angle…

A:

Q: 2. Determine the directional derivative for u = log,y x2lnz if it is defined by the direction at dx…

A: The given function is, u=logyx2lnz Given that, dxdz=1,dydx=2. From the above, x=z+c,y=2x+d Then, the…

Q: 18. If u = [13,7,-2] is orthogonal to v--5,k,7], d A mine the value(s) of k %3D %3D 19. Find the…

A:

Q: 18. Find the directional derivative of * f(x, y) = -2e* cos y at (0, 7) in the direction of v = (-6,…

A:

Q: Find a linear differential operator that annihilates the given function. 2.3 + e* cos 2x

A: Let, the given function:fx=3+excos 2x

Q: 1) Find the directional derivative of f at the given point P in the direction of the point. Q- f(r,…

A:

Q: 1. determine the derivative with respect to time t of the following: a) 4x + 8y = 12 b) xy = 15 c)…

A:

Q: 3. Find the differential of the function P(K, L, M) = KMe-L²-M² %3D

A:

Q: 8 Find the linearization L(x, y) of the function at the given point f(x, y)=1+xIn(xy-5), (2,3)

A: Given: f(x,y)=1+xln(xy−5)(2,3)L(x,y)=?

Q: In Exercises 19–24, find the directions in which the functions increase and decrease most rapidly at…

A: Given function is Firstly, we will find gradient f at point (4,1,1)

Q: 30 Which one of the following is the gradient of the tangent line at the point (5, 1) on the graph…

A:

Q: b. Using differential equations, find the orthogonal trajectories of the following family of curves:…

A:

Q: Find the maximal directional derivative of function f(x,y) = xln(x+y)+x²y at the point (-1,2).…

A: To find -

Q: 5. Find the gradient of cos(xy) – 3y* + 3 at the point (1,4)

A:

Q: Consider the function [cos: cos 30 Sin 30 x² x₁x₂-1 f(x)=x₂+- Determine the directional derivatives…

A: As per the question we are given the bivariate function f(x) = x2 + x1²/(x1x2 - 1) Now we have to…

Q: 9-20 Compute the differential dz or dw of the function. 17. w = x'y?z

A: Given

Q: 1. Consider the curve F(x, y) = 0. Show that if F has continuous second derivatives, then a formula…

A: We will use chain rule of partial derivative  If F is a function of  two independent variables x and…

Q: Q1: a) Find the directional derivative of S = In(2x +3y) at point (-1,1) in the direction of 4i – 3j…

A: (a) Given S=ln(2x+3y) Differentiate S partially with respect to x and y Sx=22x+3y…

Q: Find a linear differential operator that annihilate the given function d) Sin5x + 10 cos5x e)…

A: (d) Given that y=sin5x+10cos5x We have to find a linear differential operator that annihilate the…

Q: 3. Given the function f(x, y, z) = In(x² + y² – 42²), find the directional derivative f, in the…

A:

Q: Q/1: Find the derivative of the non-uniform B-Spline curve with (k=3, n=5) Basis Functions N2.

A:

Q: 10x Find the directional derivative of f(x,y) = at P(5,0) in the x + y direction of Q(4, –3). NOTE:…

A: Here is the solution:

Q: H.W: 1. find the derivative of the function f(x, y, z)= xy + yz + zx ,at the point P(1,-1,2) in the…

A:

Q: 5. Express the curve by an equation in x and y. x(t) = 2- sin(t) y(t) = cos(t) a. (x-2)² + y² =1 b.…

A:

Q: 1. Find the first derivative of y with respect to x (y') of the given functi 1. x³y-xy² +x² +y? = 0…

A: To find the first derivative of y using the given equation.

Q: For function y implicitly defined by the equation 3 cos(y) = x + 2y + 4, find its linear…

A:

Q: 10. Use differentiation to find the gradient of the curve y = ax sin(bx) at x = 3. 7. -17 b= 19

A: Please refer to the image below

Q: Let a function y(x) be given implicitly by the formula: y° - 3xy2 +y cos(x) – x = 10. %3D Find the…

A:

Q: În 10 In 10 (2x- 7) 2 IH 10 Find the indicated tangent line. 17) Find the tangent line to the graph…

A:

Q: (b) Note that by the chain rule and implicit differentiation, dI aSI – bI aSI + -aSI 6 1 – 1+ dI bI…

A: Given thatI is a function of tand S is a function of tBy chain rule and implicit differentiation…

Q: Given a function (r, y, 2) = 3x2 + In (3y2+ 1) + e cos 2. i. Find the directional derivative of o at…

A: Here we will find out the required value.

Q: 13. Find the derivative of the function T(z) = dz +b cz +d numbers such that ad – bc + 0. When is…

A: Hello. Since your question has multiple parts, we will solve first question that means question (13)…

Q: * Find the directional derivative of. f (x, y) = -2e* cos y : (0, 4) in the directic of v = (-6,8)…

A:

Q: Let x and y be differential function of t and suppose they are related by the equatin xy-1=y^2. Find…

A: Differentiating with respect to t, we get

Q: 3. Find the derivative of y with respect to x in the following functions : 18x'y (3x' – 2)' u? a) y=…

A:

Q: Q1: a) Find the directional derivative of S = In(2r +3y) at point (-1,1) in the direction of 4i -3i…

A:

Q: If C, and C, are constant vectors and A is a constant scalar, show that H - e* (C1 sin Ày +C2 cos…

A:

Q: 1. Find the directional derivative of the function f (x, y, z) = In (3x + 6y + 9z) at the point…

A: To find: the directional derivative of the function f(x,y,z)=ln (3x+6y+9z) at P1(1,2,3) in the…

Q: Let a function y(x) be given implicitly by the formula: y3 − 3xy2 + y cos(x) − x4 = 10. Find the…

A:

Q: Consider the step size h = 0.1 and h = 0.001, how does the step size affect the accuracy in %3D…

A: Given that, A=82, B=16.4f(x)=Aex+Bx2sinxFor the given values of A and B,f(x)=82ex+16.4x2sinxWe need…

Q: 1-t2 The differential of u=In, is 1+t?

A: Given u=ln1-t21+t2

Q: 1. Consider the curve F(x, y) = 0. Show that if F has continuous second derivatives, then a formula…

A: Consider the curve F(x, y)=0. The objective is to show that if F has continuous second derivatives,…

Q: 5. Find y' at the point (0, e) where xy² + In(x² + y) = 1.

A: Find y' = dy/dx At point (0, e)

Q: Let f(x, y) = -4x + 3y. Find the directional derivative in the direction of v = from the point P =…

A:

Q: 4. What is the direction in which the function f(x, y) = yx² -- decreases most rapidly at the point…

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

Q: 7) Let x = t – sin(t) , y = 1– cos(t). Determine the equation of the line tangent at t = n.

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.