Find the linear approximation of the function below at the indicated point. f(x, y) = In(x – 3y) at (10, 3) f(x, y) × Use the approximation to find f(9.92, 3.08). (Round your answer to three decimal place f(9.92, 3.08) Illustrate by graphing fand the tangent plane.

Q: find an equation for the line in the xy-plane that is tangent to the curve at the point…

A: To find an equation for the line in the xy-plane that is tangent to the curve at the point t = 2…

Q: find an equation for the line in the xy-plane thatis tangent to the curve at the point corresponding…

A:

Q: Find the linear approximation of the function below at the indicated point. f(x, y) = V17 - x² – 4y²…

A: Given function f(x,y)=17-x2-4y2 and point (2,1) Calculating partial derivatives…

Q: Find the equation of the tangent plane to z = ey + x + x2 + 11 at the point (5, 0, 42).

A:

Q: Let f(x, y) = e* ln y. a)Write down the linearization L(x, y) of f(x, y) at (x0, Yo) = (0, 1).…

A: Here is the solution of the given problem. Linear Approximation:

Q: 5) For f(x) = Vx² + 2: (a) Find the tangent line to y = f(x) through (5, 3). (b) Find the…

A: The given function is f(x)=x2+23 We have to find,  a) Tangent line to y = f(x) through (5,3)  b) The…

Q: Consider the curve in the xy-plane repre- sented by = e' and y = The slope of the line tangent to…

A:

Q: Find an equation for the tangent plane to the function f (x, y) = Jy – x at (1,2,1). %3D

A:

Q: Find the curve length of the given functions in the given interval

A: Find dx/dt and dy/dt using product rule.Then find (dx/dt)^2 and (dy/dt)^2.

Q: Find the linearization of the function f(x, y) 155 – 2x2 – 5y² at the point (5, 4). L(x, y) = Use…

A: Given:      f(x,y) = √ (155 - 2x2 - 5y2 )     Point : ( 5 , 4 )  Now     Linear approximation f (…

Q: f(z+h) f(x) For f(z) = V71 + 37, find f '(z) using the definition f '(z) h this, find the tangent…

A:

Q: Find an equation of the tangent plane to the graph of F(r, s) at t F(r. s). - (3r4 1 + 1), (-1, 1.…

A: Introduction: Let z=f(x,y) denote the equation of a surface S in R3, and P=(a,b,c) denotes a point…

Q: Find the linear approximation L(x) of the function f(x) = V1- x at a = 0. Use L(x) to approximate…

A:

Q: VF at c=4 Build the tangent line approximation (linear approximation) to j (z) = a)L(z) = 8 + -4) b)…

A: We are given function and a point as

Q: Let f'(z) = tangent line to the graph of the function h(z) = g(13x+3) at e and g(x) = f(/#). Let L…

A: Given, f'x = ex2  gx = fx L is the slope of the tangent line to the graph of function hx = g13x+3 at…

Q: 21 Find the value of c such that the line y = -x + is tangent to the curve y = c/x.

A: Given line ⇒y = 76x+212    .....(1)curve y = cx   ....(2)Differentiating w.r.t 'x'       (2)y' = c2x…

Q: The Tschirnhausen cubic is the curve given by the equation x^2=y^3+3y^2 At which point(s)…

A:

Q: 3. For the function h(x, y) = x2 + y2 - xy+x find h and h, and then find the tangent plane to h(x,y)…

A: To solve the following problem, We use the standard formula of differentiation and  after that we…

Q: Find the equation of the tangent plane to z = e + x + x³ + 9 at the point (2, 0, 20). z =

A: According to question We have to calculate the equation of the tangent plane .

Q: Using the plane tangent to the graph of the function f(x, y) = ln(y - 2x), determine the approximate…

A:

Q: Q4] Find the equation of the tangent plane and normal line to the surface z + 8 = x e' cos z at…

A:

Q: ) Find the linearization L(x, y) of the function f(x, y) = ez+y at (0,0). Use it to estimate f(0.01,…

A:

Q: Find the linear apporoximation of the function flW = V4-X at a= o %3D Ose L to approximate the…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: dt F(x) = | 6+ 8t Find the interval on which the curve is concave downward.

A:

Q: Find the linear approximation L(x) of the function g(x) = V1+ x at a = 0. L(x) = Use it to…

A:

Q: The tangent line to a point on the curve r(t) = (3t2 + 2t+ 3)i + (t² + 2t + 4)j+ (2t2 +t+ 2)k…

A: Differentiate:

Q: The tangent line to a point on the curve r(t) = (3t² + 2t + 3)i + (t² + 2t + 4)j+(2t² +t+ 2)k…

A: Differentiate:

Q: 11. Find the slope of the tangent line t = 2. Show all your worka x = v2t, y =t %3D t

A:

Q: Find all points on the curve where the tangent line has the given slope. (If an answer does not…

A:

Q: Using your answer to the previous question, find an equation of the tangent line of f (x) = Va – I…

A:

Q: For the function z = f(x, y) = x² − xy² + y³, find the equations of the tangent lines in both the…

A:

Q: Find the equation of the tangent plane to z = e" + x + x² + 6 at the point (5, 0, 37).

A:

Q: Find the linear approximation of the function below at the indicated point. f(x, y) = In(x – 4y) at…

A: For the detailed solution of the problem follow the next steps.

Q: 1. Consider the function f(r, y) = 70 – 4.x2 – y2. (a) Find the tangent plane to f(x, y) at (-3,…

A:

Q: The gradient of the tangent to the curve y = 2e"- 3e" at the point where x=0 is %3D A 5. B 7. C -L D…

A:

Q: Let f: R2 → R. At some point, a , we have that f(a) = 5 and that Vf(a) : What is the equation of the…

A: answer is in next step

Q: Find 1) equation of tangent plane and 2) the linear approximation of the function below at the…

A:

Q: For f(x, y) =xe−y, (a) find a tangent plane to f at (1,0) (b) use the tangent plane to approximate…

A:

Q: (c) Find the equation of the tangent plane to the graph of f(x, y) at (1,1,3).

A: Suppose surface S defined by a differentiable function  z=fx,y and point Px0,y0,z0 lie on the…

Q: Find all points (x,y) on the curve C:x(t) = t² + 6t + 12, y(t) = 5t – 8 where the tangent line to…

A: We need to find the point (x,y) on the curve C,whose tangent line to the curve is vertical

Q: The tangent to the curve x? – xy + 2y? – 4x + 2y +2 = 0 that is parallel to the line x– 4y = 2. The…

A:

Q: Find an equatlon of the tangent to the curve at the glven polnt. x - 9 sin(t), y t+t, (0, 0) Graph…

A:

Q: Find the equation of the tangent plane to f(x,y)=√2xy+ 1 at the point            (2, 2),and use it…

A:

Q: Find an equation for the tangent plane to the graph of f(x, y) V3+ r2 – 3y2 at the point P(2, 1,…

A:

Q: 3. Find the value of c such that the line y = x + 3 is tangent to the curve y = cvx. C =

A:

Q: Find the point where the tangent line to the curve c(t) = (8t2 – 6, 3t2 – 12t) is horizontal. (х, у)…

A:

Q: Tangent to the curve z? = 2xy + x2 , z = 3 ,at the point ( 1, 4,3)

A:

Q: Find the linear approximation of the function below at the indicated point. f(x, y) = V 29 - x2 -…

A:

Q: Find the equation of the tangent line T to the graph of f at the given point. Use this linear…

A:

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.