-Fill in the first 3 levels of Richardson extrapolation to estimate the derivative of sin(x) at æ = 1.2 with ho = 0.8: j = 0j = 1j=2 i = 0 i = 1 i = 2 Estimate the absolute error based on the difference between the two most accurate estimates above: Find the actual absolute error of the most accurate estimate above compared to the analytic derivative:

Q: Find the partial derivative of the function with respect to each variable. 28 h(p,p.0) = p cos p sin…

A: The partial derivatives of the given Function is given as

Q: Use the properties of the derivative to find the following. r(t) = ti + 5tj + t?k, u(t) = 5ti + t?j…

A:

Q: dy For the function dt 5 cos t, the third order derivative dt is O 5 cost O 5 sint O -5 sint O -5…

A: Given  dydt=5 cos t          ............ (1) We have to calculate the third-order derivative of y…

Q: The derivative of z at z e is equal tol. Select one: O a. False b. True

A:

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

A:

Q: Let f(x) = 3x − ex + 5. (a) Find the equation of the tangent line to f(x) at x = 0.  (b) Find all…

A:

Q: Find the actual error when the first derivative of f(x)% 3D e* at x = 1 is approximated by the…

A: fx=e-2x substitute x+h for x fx+h=e-2x+h fx+h=e-2x-2h . fx=e-2x substitute x-h for x fx-h=e-2x-h…

Q: a. Evaluate the following derivative d tổ tan(t) dt. sin(x) dx

A: We will use the Newton Leibniz formula to evaluate the differentiation

Q: Given f(x) = 6xe® csc(x), answer the following: a) f'(x) = b) The equation of the tangent line to…

A: A function f(x)=6xexcsc(x), we have to find the derivative of the given function i.e. f'(x) also…

Q: Let Q(t) = t2. Find a formula for the slope of the secant line over the interval [1, t] and use it…

A: the slope of the secant line over the interval [1, t]   For slope of the tangent line, replace t…

Q: ind the derivative with respect to x for the follo a. y = 43x b. f(x) = 22x3cos x c. y = tan(23*) d.…

A: Since you have posted multiple questions with multiple subparts, we will solve the first three…

Q: Use linear approximation, i.e. the tangent line, to approximate 2.7^6 as follows: Let f(x)=x^6. The…

A:

Q: Use linear approximation to approximate v25.1 as follows. Let f(x) = Vx. The equation of the tangent…

A: equation of tangent line is :  y - y1 = m ( x - x1 )  here m is a slope and ( x1 , y1 ) is a point…

Q: The Ist derivative of f (x) =tane 3x cot 3x is A) none of the given choices B f'(x) = 3(e"cse2, 3M +…

A:

Q: Given f(0) = sec(@)tan(@), answer the following: %3D f'(8) = Select one of the options below are…

A: The objective of the question define the derivative of the given function.

Q: Use linear approximation to approximate v81.4 as follows. Let f(x) = Vx. The equation of the tangent…

A:

Q: Calculate the derivative indicated in the figure below

A: rs=s, 2s, s2

Q: Let f(x) = x + vx . The equation for the tangent line at the point (1, 2) is y = m(x – 1) +2, where…

A: Given: fx=x+x

Q: Use implicit differentiation to find without first solving for y. dæ (x + y)° = x°y³ %3D dy a) dæ…

A: Given equation(x+y)5=x5y3differentiae with respect to x

Q: Find the given higher-order derivative. f (4)(t) = t cos t, f (5)(t)

A:

Q: If the derivative of y = etanx is y' = m etan x, what is m? A. sec x tan x B. 1+ tan?x C. 1- tan?x…

A:

Q: Obtain the derivative dh when the radius is 5 m. First, substitute 5 for rin the volume of cylinder.…

A:

Q: The directional derivative of f(x, yat the point (a, b)in the positive y direction is fr(a, b) O…

A: Use the correct formula for the directional derivative.

Q: Find the actual error when the first derivative of f(x) = sin(2x) at x = T/8 is approximated by the…

A:

Q: Apply the 1t derivative property to : 1) f(t) = e-2tsin5t 2) f(t) = = cost sint 3) f(t) = e²tsin2t…

A: Solution

Q: Find the derivative of the function f(x, y) 5x2-3y at (8,4) in the direction of A = 3 i-4j O 412 492…

A: First of all we will find gradient, then we will find the directional derivative

Q: Given that f(x) = 5x° + x³ + 2, find the derivative of f- by using dy che formula d.x 1 Check dx…

A: To find: The derivative of inverse of f(x)=5x5+x3+2 by the formula dydx=1dxdy. Calculation: Find the…

Q: a. Find the equation of the tangent line to f(x) = (93 + x)-1/2 at æ = 7 y = b. Use your answer to…

A: We have to solve the problem

Q: Use linear approximation to approximate v25.1 as follows. Let f(x) Vx. The equation of the tangent…

A: The given functin f(x)=x at x=25

Q: Use linear approximation, i.e. the tangent line, to approximate 3.6° as follows: Let f(x) = x°. The…

A:

Q: Find the actual error when the first derivative of f (x) = sin(2x) at x = 1/8 is approximated by %3D…

A:

Q: Use implicit differentiation to find the specified derivative at the given point. Find at the point…

A: To the specified derivative differentiate the given function with respect to y .(take z as a…

Q: The slope of the tangent to the curve f (x) = 2" at x = 1 is approximately (to three decimal…

A:

Q: Use implicit differentiation to find the specified derivative at the given point. dy 7. Find at the…

A: Given that,   6x-7y+5x2y2=0 at the point -1,1

Q: 3. Use the first derivative to find the location of all local extre ma for the following functions.…

A: Explanation of the answer is as follows

Q: Estimate the true percent relative error for the first derivative of the function, y = e*cos(x?), at…

A:

Q: Determine the derivative of the function f = log, | tan 5m + sec 5m| with respect to m. O cot (5m)…

A:

Q: Use linear approximation, i.e. the tangent line, to approximate V27.3 as follows: Let f(x) = Vx. The…

A:

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

A:

Q: Given that f(x) = 9x + x³ + 6, find the derivative of f- by using dy the formula dx 1 Check your…

A:

Q: Use linear approximation, i.e. the tangent line, to approximate V8.1 as follows: Let f(x) = a. The…

A: To approximate ³√(8.1)

Q: Find the derivative. sint 1 du 1-u? dt cost OA. 1- sin? t 1 OB. OB. 1- sin?t 1 Oc. cost (1- sin 2 t)…

A:

Q: 16. Find the derivative of the following functions: rcoS I a) F(r) = | tan(s²)ds. b) g(x) = / V1 –…

A:

Q: Use linear approximation, i.e. the tangent line, to approximate V27.2 as follows: Let f(x) = Vx. The…

A:

Q: Find the first order derivative for the following: cot(e(3•Z)t) sin(z•t²) S = t5

A:

Q: In what direction is the derivative of f(x,y)= xy +y at P(4,9) equal Select the correct choice below…

A:

Q: Use linear approximation, i.e. the tangent line, to approximate V1.4 as follows: Let f(x) : Va. The…

A:

Q: Find the derivative F'(x) for each of the following functions. (a) F(x) = [ sin(1 + e') dt (b) F(x)…

A: I hope that this solution will help you .Thankyou. Best regards.

Q: 3 dK Use the definition of the derivative to find for the function K(z) %3D dz 6z + 1"

A:

Q: Let f(x) = Vx. The equation of the tangent line to f(x) at = 1 can be written in the form y = mx + b…

A: