Find the linear approximation of the function f(x) = V1 – x at a = 0. L(x) = Use L(x) to approximate the numbers V0.9 and Vo.99. (Round your answe V0.9 2 V0.99 2 Illustrate by graphing fand the tangent line.

Q: Assumee thát ic COst C(x) = 25,600 + 100x + 0.01x² dollars to manufacture x 32GB iPods in a day. t…

A: given cost functio cx=25600+100x=0.1x2

Q: Q2 Use the chain rule to find the derivative of dw w = x2 + y2 with respect to t ). with x = cost -…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: is differentiable at r 2. 2. (a) Using the definition of derivative, compute for the slope of the…

A:

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: 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 linear approximation of the function f(x) = /1 – x at a = 0 and use it to approximate the…

A: Given,

Q: +Inz Determine the equation of the tangent line to the graph of f(r) = V3 + 5t5 dt at x = 1.

A:

Q: Consider the function f(x, y) = y³ – 2y – x². Find the direc- tion of greatest increase at the point…

A:

Q: Find the derivative of the function using the definition of derivative. dy = lim dx Ar-0 Ar Ay 1.…

A:

Q: Compute backward difference approximations for the first derivative of the function, y =[ e'nxP, at…

A: We have to compute backward difference approximations for the first derivative of the function,…

Q: Defermine the derivative of the following functions using the long method (using limits). 1. y =t –…

A:

Q: Consider the curve in the xy-plane represented by the two equations below. The slope of the line…

A: Solve

Q: a) Find2 of the function y = dy 2 %3D dx cotx cotx b) What is the derivative at x = onk 4.

A: 1/CotX = tanX.

Q: Find the derivative of the funciton F(x) = ,5t dt. F'(x) =

A:

Q: 2. Find the derivative of the function f(x, y) = 2x² – y² at the point M = (1,1) in the direction…

A:

Q: Find the relative extrema using both the first and second derivative tests. f(r) = 2x³ – 9x² + 12x.…

A: Consider: fx=2x3-9x2+12x. Critical point is the point where the derivative of the function is either…

Q: Eliminate the parameter f) from the following X(+)= -sint yl)= cost

A:

Q: Supose z is implicitly defined by the equation qy+ 3x + xyZ + 32=9 in an enmrament of the point…

A:

Q: (a) Find the derivative of fix. y. 2) = x-xy-z at P1, 1,0) in the direction of v = 2i- 3j + 6k. (b)…

A: The directional derivative of a function f(x,y,z) at the point (x,y,z) in the direction of vector v…

Q: By using the definition of the derivative, use a clear diagram to argue that d S(t)dt = f(x). %3D dx…

A: We have to prove that ddx∫axftdt=fx This will be prove by Newton's Leibnitz rule in this rule we…

Q: Compute forward difference approximations for the first derivative of the function, y =[ eln(x)2, at…

A:

Q: Use the second derivative test to find the local extrema of the function f(x, y) = x+ 2xy – 6x –…

A: Step 1: Find the partial derivativesfx and fy and put both equal to zero and we getcritical points…

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: Find the derivative. F(t) = In(sinh(2t)) %3D F'(t) %3D

A: Find the derivative of the function

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

A: The solution is given as

Q: Use the definition of the derivative to show that the derivative of y = f(x)3 2/ is 1 f'(z) = VI %3D

A: GIVEN f(x) = 2√ x CALCULATE f'(x) = 1/ √ x

Q: Find the derivative of a linear function y=ax+b using the definition of derivative.

A: The derivative of a function f' of function f is defined as f'x=limh→0fx+h-fhh

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

A: Topic- Vectro

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

A:

Q: Find the (a) approximate error and (b) relative approximate error of the following: The derivative…

A:

Q: Find the derivative of the function y = 7.7+ 6 -6*. dy dt %3D e Textbook and Media Save for Later

A:

Q: What is the difference between the linearization, L(x), of f at a, and the linear approximation (or…

A: Given question:- What is the difference between the linearization, L(x), of f at a, and the linear…

Q: Find the linear approximation of the function f(x) = V4 - x at a = 0. L(x) = Use L(x) to approximate…

A:

Q: I. Determine the equation of the tangent line to the graph of f(x) V3+ 5t5 dt at I= 1.

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Differentiate the function and the function of the tangent line at the given value of the…

A: Given, s=t^3-5t^2 t= 3

Q: 3) Find the slope of the curve defined by f (x) = x° sin x at x = T. 4) Differentiate g(x) = e* .

A: The slope of a curve y=f(x)  at a given point x=a is the value of dydx  at the given point x=a. So…

Q: Find the derivative of the function f(x,y) = tan at the point (3, - 3) in the direction in which the…

A:

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

A: Given,

Q: +Inz 1. Determine the equation of the tangent line to the graph of f(r) = | V3 + 5t5 dt at x = 1.…

A:

Q: Let fx) - V4X-3 vux-3 %3D O Find the arer age rate o ofe change in respect to x aver the intoy vel…

A:

Q: y is a function of  x and the slope of the function is zero at x=10 then to determine that y reaches…

A:

Q: find the derivative of the function at P0 in thedirection of v. ƒ(x, y) = 2x2 + y2, P0(-1, 1), v =…

A: Given: fx,y=2x2+y2  We know that, The direction of v is the unit vector obtained by dividing v by…

Q: Q1) Find the tangent y = vx² – x + 7 at x = 2.

A: The detailed solution is as follows below:

Q: Evaluate the derivative of Z F5.png sin (b V) x² f(x) = acosh %3D cx3 if a = 12.91, b = 3, and c = 6…

A:

Q: Find the gradient of the tangent to the curve xy“ + y+ ( log_(x – 2))² = 14 at the point (3, 2).

A:

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

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Q: Calculate the derivative of the function g(x)=x∫√x(t2−t)dt at x=1.

A: using the fundamental theorem of calculus we find g'(x)

Q: Confirm the approximations by using the linear approximation at x = 0

A: