Find the linear approximation of the function f(x) = Vr + 15 at a = 1 and use it approximate the number V14.99 to six decimal places.

Q: Find the derivative dydx for the function x=1t+t, y=1t2 at the point t=12.

A: Here given

Q: 9) Where is the function ht) = (t+ 5) differentiable?

A: Given         h(t)= t+51/3

Q: Find the linearization of the function f(x,y) = ln(x3y6) at the point (x0,y0) = (4, 3). Leave all…

A: Given fx,y=lnx3y6     at (4, 3) The linear approximation in 2 variables is given by Lx, y=fa,…

Q: Use the intermediate Value Theorem to show that between x = 0 and x = 1, the function f(x) = 3 sinh…

A:

Q: Find the derivative of the function rsin(x) 1- t2 dt. 1+t4 g(x) /1

A: Explanation of the answer is as follows

Q: Find the maximum rate of change of the function f(x, y) : 4y4 at the point (1,3)

A: We will solve the problem

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: Given,

Q: What is the formula for the linearization of a function f at the point x = a? %3D

A: Given :To provide the formula for linearization of a function f at the point x=a

Q: Consider f(x, y) =(ax² + by²). Based on the second derivative test, what are the conditions…

A: Answer

Q: Use a linear approximation (or differentials) to estimate the given number. V 99.4

A:

Q: Find the maximum rate of change of f(x,y) =x²y+ /y at the point (1,1). In what direction does it…

A:

Q: Use the second-derivative test to show that the function f(x, y) = x²eY – y²e* has a saddle point at…

A: A point (a,b) of function f(x,y) is said to be the saddle point if it is a critical point…

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. Зx +…

A:

Q: Find the linearization of the function F(x)=tan-1(2x)= arctan(2x) at x=0. Then use linearization to…

A: We know the linearization of the function f(x) at x=a    L(x) = f(a) + f'(x)*(x-a)   In the…

Q: Find the linear approximation of the function at the given point. f(x, y) = 4 sinx - 6 cos y at (0,-

A: Given,           The function fx,y=4sinx-6cosy  at  0,π2.

Q: Q3. Find the coordinates of the point(s) of the function y=3x – 5x +2, where the tangent has a…

A:

Q: Find the maximum rate of change of f (x, y) = xy ^ 2 + root (y) at the point (2,1). in which…

A: The maximum rate of change of f(x, y) happens along the direction grad(f) at the given point (2, 1).…

Q: Find the direction at which the function f(x, y, z) = x In(e' – xz) increases fastest at (-2, 0, 0)…

A:

Q: Find the linearization of the function f(x, y) = /36 – læ² – 2y² at the point (3, -1). L(x, y) = Use…

A:

Q: Find the maximum rate of change of f (x, y) = xln /x2 + y2 at (1,2) and direction in which it…

A: To find the maximum rate of change of fx,y=xlnx2+y2 at 1,2 and direction in which it occurs.  First,…

Q: Find the point where the CAUCHY- RIEMANN equation is satisied for the function f(2) =xy+Xyi

A:

Q: Find the linearization of the function z = x/j at the point (3, 64). L(x,y)

A: According to the Bartleby guideline only one question can be solved at one time, post the remaining…

Q: Find the linearization of the function a) z = cos(sin y – x); at (-2,0) and use it to approximate…

A: Suppose f(x,y) be a differentiable function at (a,b). Then linearization of f(x,y) at (a,b) is given…

Q: Find the derivative of the function. f(z) = V - VE f '(x) =

A:

Q: Find the linearization of the function f(x) = sin(x) at a = π and use it to approximate the number…

A:

Q: Use differentiation to find the gradient of the curve y : = ax sin(bx) at x = 3.

A: The solution is given as

Q: Estimate the indicated derivative by any method. x = 4t + t2; estimate ds/dt | t= -2

A: Given, x=4t+t2 We have to find dxdt at t=-2 We will use following formula to differentiate the…

Q: 2. Use second order derivative to derive the acceleration, a for an object that falls where its…

A:

Q: Estimate the slope f'(3.5) for f (x) = sin(3x) using: a. Forward difference approximation with h =…

A: f(x)= sin3x x y y1 y2 y3 y4 3.3 -0.1557             -0.193       3.5 -0.3507   0.0139…

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

A: Given: f(x)=1-x

Q: Find the linear approximation of f(x) = sin x, for x close to 0

A: The given function is: f(x)=sin x To find the linear approximation of it close to 0.

Q: The finite difference approximation of the first derivative in the simple implicit method used to…

A: given  ∂2u∂x2=∂u∂t to find the finite difference approximation of the first derivative in the…

Q: Find the gradient of the curve y = a²xe-b*x at x = 1.

A:

Q: %3D 10. Find the derivative of the function )= V 5T4 using the limiting process.

A: Given,

Q: Find the derivative of the function. F(x) = et dt F'(x) = %3D

A: We know that by Leibniz rule of differentiation under integral sign, we have

Q: Find the linear approximation of the function y = x' at point xo 1 О а. у %3D Зх — 2 -

A:

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: We have to solve

Q: Obtain the MSE of f(x) = ex.

A: MSE = Maclaurin Series Expansion f(x)=ex formula f(x)=∑k=0∞f(k)(0)k!xk

Q: Determine the length of the curve TC f(x) = In[sec(x)],0 < x < 4

A: The given curve is- f(x)=lnsec(x)Interval 0≤x≤π4We need to determine the length of the given…

Q: Use the definition of partial derivative of a function f(x, y) = 3x² – xy? to illustrate fi and f2 '

A:

Q: The average rate of change of the function f(z) = 13z +4 on the interval [1, 4] is

A:

Q: Find the derivative of the function. F(x) etd dt F'(x) =

A:

Q: Show that the function f(x, y) = 3x - 4y² is differentiable at point (−1, 2)

A: answer is in next step. please give a like !!!

Q: Find the linearization of f (x) = xe¯* at a = 0. (Hint: Remember thne product rule.)

A: Given : fx = xe-x2

Q: The total derivative of the function f(x, y) =3x'y- xy is

A: Find the total derivative

Q: Find the unit direction vector of greatest decrease of f at xo = [0 - 1 1]' and evaluate the…

A:

Q: Find the direction at which the function f (x, у, 2) %3 хIn(е' — хг) increases fastest at (-3,0,0)

A:

Q: . Find the linearization of √ x at a = 49. Then use your linearization to approximate √ 56.

A: I am going to solve the given problem by using some simple calculus  get the required result.

Q: What is the maximum value of the directional derivative of f(x, t) = f (x, t) = x² + t²/8 – 10 at…

A: Note: The directional derivative of a function is the rate at which the function changes at a…